Flexible Patterns for Soft 3D Printed Fabrications

S S symmetry

Article Flexible Patterns for Soft 3D Printed Fabrications

Kanygul Chynybekova 1 and Soo-Mi Choi 1,*

Department of Computer Science and Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Korea; [email protected] * Correspondence: [email protected]

Received: 23 October 2019; Accepted: 7 November 2019; Published: 12 November 2019

Abstract: Rapid improvements in 3D printing technology bring about new possibilities to print with different types of printing materials. New studies have investigated and presented various printing methodologies. However, the majority of these studies are targeted at experimenting with rigid 3D printed objects rather than soft 3D printed fabrications. The presented research considers soft 3D printing, particularly focusing on the development of flexible patterns based on non-homogenous hybrid honeycombs for the interior of 3D printed objects to improve their flexibility and additional stretchability including the lightweight interior. After decomposing the area of an object into regions, our method creates a specific design where patterns are positioned at each partitioned region of the object area by connecting opposite sides of the boundary. The number of regions is determined according to application requirements or by user demands. The current study provides the results of conducted experiments. The aim of this research is to create flexible, stretchable, and lightweight soft 3D printed objects by exploring their deformation responses under tension, compression and flexure tests. This method generates soft 3D printed fabrications with physical properties that meet user demands.

Keywords: soft printing; soft 3D printed fabrication; flexible; stretchable; lightweight; soft filament; flexible pattern; non-homogenous hybrid honeycomb structure

1. Introduction Technological innovations in the additive manufacturing field enable us to fabricate different designs with an increasing range of materials. Recently, different communities have expressed a lot of interest in soft 3D printing since the soft filament material type broadens the range of flexible 3D printed objects. Different manufacturers have introduced materials with a variety of flexibility levels, mechanical performance, and qualities to the market. However, these materials do pose some challenges. The soft filament handling process can be different from that of hard filament material. Furthermore, most 3D printers are specifically hard filament type. Despite the adaptation of a soft printing mode, the quality of soft 3D printed objects is usually lower compared to similar rigid 3D prints. Furthermore, most studies focus on rigid 3D fabrications [1–8]. In this research, we closely examine soft 3D printing materials and created a comparison experiment to showcase our developed patterns. The most important choice for successful soft 3D printed fabrications is the selection of a suitable soft filament. This choice depends on the quality requirements of the project since the quality impacts the level of flexibility of the produced 3D objects. The major advantage of soft-filament materials is the flexibility that makes them deform under a load and revert back to their original state when the load is removed. This property makes it possible to fabricate durable 3D objects with high deformation stability. The hardness scale of soft 3D printing materials is measured with Shore values. For thermoplastic polyurethane (TPU) [9], the hardness scale ranges between Shore A 60–90 and whose level of flexibility can be classified from ultra-flexible to semi-flexible. Different polymer blends are used to create TPU

Symmetry 2019, 11, 1398; doi:10.3390/sym11111398 www.mdpi.com/journal/symmetry Symmetry 2019, 11, 1398 2 of 15 and its level of softness depends on this chemical consistency. In addition to its softness and flexibility, TPU is also known for its functional properties of being durable and being able to withstand ambient temperatures up to 80 ◦C. TPU is therefore practical for both consumer and industrial use. Another soft filament on the market is thermoplastic elastomer (TPE) [10], which was introduced earlier than TPU. It is an elastic printing material that is highly stretchable. It can be stretched to more than twice its original length and return to its original state without permanent deformation. Its elastic properties enable the fabrication of flexible 3D objects. TPE’s typical Shore hardness of 85A is softer than that of TPU. The technical characteristics of TPU describe it as much stiffer than TPE. However, both are widely used for soft 3D printed objects that require flexibility and stretchability. Another soft printing material is soft polylactic acid (soft PLA) [11], which is a thermoplastic polymer that is considered to be more eco-friendly compared to other 3D printing materials. The softness of soft PLA is mostly indicated with Shore values. Higher Shore values are used to create less flexible 3D fabrications, while lower Shore values are recommended for printing soft and flexible 3D fabrications. It is important to find a balance between flexibility and printability when working with soft 3D printing materials. Selection of materials requires a careful examination of their technical characteristics as well as a consideration of the application’s demands for soft 3D printed fabrications. In this study, we present honeycomb patterns that are positioned according to decomposed regions in order to create a specific design, which is defined by our method. The number of regions depends on the required demands of the application. The current study included the development of two types of honeycomb patterns with slight differences in their topology. These patterns were also compared to the grid pattern that is currently the standard for infill in 3D printed fabrications. The experiments focused on TPU and TPE printed 3D fabrications. These were compared through a careful examination of their performance under compression, tension and flexure tests that focused particularly on their flexibility, additionally stretchability and bending as well as by looking at their weight to judge the efficiency of material usage. The results of the conducted experiments show that the physical properties of soft 3D printed fabrications are affected by pattern type along with the elasticity of the printing material. The contribution of our study is as follows:

1. We compared soft printing materials to check criteria that we specified in the experiment. 2. We developed a specific design for the interior of soft 3D printed fabrications along with flexible patterns based on the non-homogenous hybrid honeycomb structure. 3. We conducted experimental compression, tension and flexure tests to reveal the efficiency of each presented pattern.

This paper is organized as follows: Section2 is dedicated to reviewing works related to soft 3D printing materials and research related to infill patterns. Section3 lays out the methodology of our interior design along with pattern descriptions. Section4 describes the flexibility of the proposed honeycomb pattern. Section5 provides the description of the hardness scale of soft 3D printing materials. Section6 summarizes the conducted tests to reveal the experimental performance of the proposed patterns with different soft printing materials. Section7 gives the conclusion.

2. Related Work

2.1. Soft Materials Soft 3D printing materials have a variety of features that make them a great choice for a wide range of uses in different fields depending on the chemical consistency, which impacts their properties. As we mentioned earlier, current existing soft 3D printing materials are mostly referred to as TPE and TPU, which are made of different thermoplastic blends. The chemical consistency of these blends plays an important role in the materials’ level of flexibility. There are different types of blends with various chemical consistencies that can be grouped into the four major categories: soft, medium soft, medium hard, and hard materials. These range from Shore hardness 20A to 100A. In the past few years, flexible Symmetry 2019, 11, 1398 3 of 15

filaments been widely used for soft 3D printing. A great number of flexible filament products have been introduced to the market by different manufacturers. One of the most popular flexible filament series is NinjaFlex [12] from the manufacturer, NinjaTek. NinjaFlex has two major lines of TPU and TPE variants that come in a wide range of colors. According to the technical characteristics of NinjaFlex products, its tensile strength is 26MPa, its elongation at break is 660%, and its melting temperature reaches 216 degrees. It claims to be the strongest and most flexible filament on the market, and it is available in 1.75 mm and 3.00 mm diameters. There are also a variety of brands of flexible filament products by various manufacturers such as SAINSMART [13], Fillamentum [14], and MadeSolid [15] competing in the market. These are also offered in a wide selection of colors and they come in 1.75 mm and 2.85 mm diameters. To fabricate 3D objects with certain technical characteristics and elastic properties, it is necessary to select an appropriate brand of flexible filament products along with a feasible level of flexibility. In study [16], samples were manufactured from NinjaFlex TPU to investigate TPU’s material properties and the compressive behavior of 3D printed honeycombs with graded densities. Similarly, researchers carried out another experiment in study [17], where they closely examined the mechanical properties of thick honeycomb structures. Soft 3D printing materials are integrated in many fields, including robotics, and study [18] used robotic fingers printed from soft 3D printing material, where the soft grippers handled objects more gently than rigid robotic fingers due to the elastic properties of their soft material. Another study, [19], experimented with foam structuring for 3D fabrications with controllable elasticity. This method integrates Voronoi foam to generate microstructures with controlled isotropic elastic behavior. The study also provides detailed descriptions for deriving the parameters of structures to produce gradients of elasticity. Their method produces rigid and flexible 3D fabrications through powder sintering 3D printing technology. Study [20] introduced a method with controlled elasticity along different directions, which is an orthotropic k-nearest foam design method that enables the fabrication of 3D objects while considering an input stress field. There are a limited number of studies dedicated to soft 3D printing, particularly the designing of flexible infill patterns to improve the physical properties of soft 3D printed fabrications. This work provides an early attempt towards exploring soft 3D printed fabrications by presenting a specific interior design that is filled with newly developed flexible infill patterns. The study also explores how soft 3D printed fabrications are affected by both the elastic properties of their materials and their interior design, including the infill pattern type. The experiments utilized two types of 3D printing material, TPU and TPE, to examine their elastic properties as well as their effects on soft 3D printed fabrications and to reveal their compression, tensile and flexure strengths.

2.2. Infill Patterns In 3D printing, structures that are printed in the interior of 3D fabrications are known as infill patterns. These are generated according to designed geometric shapes. Various geometries of infill patterns are offered by slicing tools [21–23], along with infill settings for providing thickness, scale, and printing speed. Unlike the existing slicing tools used in our previous study, [24], this study creates more convenience for users by including an option to use a scaling parameter to specify the number of rows and columns in infill patterns. This makes for a more precise structuring of infill patterns. This study also reviews designs from related studies and classifies them into several categories such as lightweight, lattice patterns, and adaptive infill patterns. Lightweight patterns: One of the earlier efforts towards creating lightweight designs for the interior of 3D fabrications occurred in study [25]. Researchers used skin frame structures similar to frame structures in architecture. Their method shows an efficiency in the reduction of material usage. Study [26] proposed a method that significantly reduces the weight of 3D fabrications and improves their physical properties by strengthening structurally weak parts of the models. This approach employs a Voronoi diagram to create honeycomb-like infill patterns. Study [27] has been presented as a cost-effective method that reduces 3D printing materials. This study introduced an adaptive voids algorithm for hollowing 3D fabrications. Their approach generates given a volume Symmetry 2019, 11, 1398 4 of 15 boundary, a parameterised adaptive infill primal and dual cellular structure for additive manufacturing. Furthermore, in study [28], researchers experimented with a new type of infills named Gyroid structures. Gyroid structures are experimentally verified to be a lightweight design for the interior of 3D fabrications that also improve the physical properties of the fabrications. Lattice patterns: Study [29] presented a method that generates lattice structures for 3D fabrications. This study considered several types of lattice structures that can automatically be generated within the input model after the Boolean operations. Study [30] introduced a method for designing lattice structures with a pipeline. This pipeline includes options to modify structure dimensions, strut shape, size, and additional connections between struts. This has been done in order to meet the required user demands for 3D fabrications. In the study [31] developed a method for optimizing lattice structures by utilizing the traditional bidirectional evolutionary structural optimization algorithm. Study [32] proposed a voxel-based method which utilizes voxels to generate different types of lattice structures that can be observed in their resulted 3D fabrications. Adaptive infill patterns: It is an undeniable fact that denser infill patterns supply stronger support to a fabrication. However, they consume more printing time. Study [33] proposed a new method of optimization based on a quadtree algorithm. This approach optimizes infill patterns to ensure that 3D fabrications meet the required user demands with less material consumption compared to conventional patterns. This study has similarity to study [34]; both of these studies aim to strengthen the structural weak parts of objects and consume less printing material. Along with these methods, which proposed adaptive infill patterns, researchers in study [35] experimented with adaptive rhombic infill patterns. These patterns strengthen 3D fabrications by applying denser infill patterns to structural weak points. The printability of infill patterns is extremely important. The printing technology depends on the design of infill patterns and printing material as well as application requirements. For soft 3D printing, there are 3D printing technologies such as the Fused Deposition Method (FDM) [36] and Liquid Deposition Modelling (LDM) [37]. LDM is a relatively new 3D printing technology that was introduced in 2015. It is considered as one of the promising 3D printing technology that fabricates objects with ceramic, wood-based materials, cement, clay and liquid silicone. However, LDM 3D printers are more expensive compared to FDM 3D printers and it requires special handling. FDM 3D printers are popular among users due to its easy handling mode—besides, it can print with rigid and soft materials—in addition there are a variety of affordable FDM 3D printers. Thus, we target to develop flexible infill patterns that are printable with FDM 3D printers, which are the most common and cost-effective. The reviewed works mostly target rigid 3D fabrications rather than soft 3D printed objects. In our research we developed a specific interior design that positions flexible patterns column by column within each predetermined region in order to improve physical properties of 3D fabrications, such as flexibility and stretchability, while also considering the need to minimize material consumption to reduce cost.

3. Method In this section, we provide the detailed description of our method, precisely the construction of the proposed interior design that positions infill patterns in a specific way by using the pattern columns. The beginning part briefly describes the pattern construction and the remaining part provides the description of the proposed method. Before we go further, the discussions about homogenous and non-homogenous hybrid honeycomb structures are required, since the flexible pattern is derived from non-homogenous hybrid honeycomb structures. As it is known, homogenous honeycomb structures could be found in nature while non-homogenous hybrid honeycombs are artificially designed for different applications. We are considering non-homogenous hybrid honeycombs which are made of hexagons and rhombs. There are noticeable differences between homogenous and non-homogenous hybrid honeycomb structures Symmetry 2019, 11, 1398 5 of 15 in their design and mechanical performances because of their topological differences. The differences inSymmetry their design2019, 11, canx FOR be PEER visually REVIEW observed from Figure1. 5 of 15

(a) (b)

FigureFigure 1. 1.(a)( aHomogenous) Homogenous honeycomb honeycomb structure structure (b ()b our) our non-homogenous non-homogenous honeycomb honeycomb structure. structure.

The main advantageadvantage of non-homogenousnon-homogenous hybrid ho honeycombneycomb structures is that they are lighter thanthan thethe aboveabove shownshown homogenoushomogenous honeycombs,honeycombs, which cancan bebe noticednoticed fromfrom theirtheir geometry.geometry. TheThe non-homogenous hybridhybrid honeycombhoneycomb structure structure consumes consumes less less printing printing material material because because it it consists consists of of a combinationa combination of of hexagons hexagons and and rhombs rhombs while while the the homogenous homogenous structure structure comprises comprises only only hexagons, hexagons, the perimeterthe perimeter of the of homogenous the homogenous structures structures is larger is compared larger compared to the perimeter to the ofperimeter the non-homogenous of the non- hybridhomogenous honeycomb hybrid structure,honeycomb which structure, can be which seen can from be their seen designfrom their in Figure design1. in The Figure proposed 1. The methodproposed can method create verticallycan create and vertically horizontally and positioned horizontally patterns positioned using the patterns non-homogenous using the hybrid non- honeycombhomogenous structure. hybrid honeycomb structure. The method in thethe currentcurrent studystudy waswas developeddeveloped toto generategenerate soft 3D3D printedprinted fabricationsfabrications with highly deformable stability. This uses a combination of tailored 3D fabricationfabrication withwith suchsuch physicalphysical propertiesproperties as as flexibility flexibility and and supplementary supplementary stretcha stretchability,bility, while while providing providing a lightweight a lightweight interior. interior. This Thisgoal goalwas wasaccomplished accomplished by bydeveloping developing flexible flexible infill infill patterns patterns based based on on non-homogenous non-homogenous hybrid honeycomb structures.structures. The The developed developed patterns patterns are applied are applied to the interiorto the ofinterior soft 3D of printed soft fabrications.3D printed Thefabrications. flexiblehoneycomb The flexible patternhoneycomb is constructed pattern is accordingconstructed to according the designed to the scheme designed and scheme its topological and its parttopological is shown part in is Figure shown2. in Figure 2.

Figure 2. Topology of the honeycomb pattern.

k1 The pattern elements elements ∀𝐸𝑙𝑒𝑚𝑒𝑛𝑡𝑠Elements − , where, wherei =𝑖=𝑍Z are are generated generated according accordingwith with thethe followingfollowing ∀ i subdivision matrix: subdivision matrix:    6 0 0 2    60024 4 0 0      k 144000 6 2 0  Sm =  . (1) 8 0 2 6 0    k 1 0620 S =  0 0 4 4  . (1) m   8 02602 0 0 6 0044 k 1 The honeycomb patterns are derived from a symmetric grid mesh Grid − with the set of elements k 1 = Elementsi − , which consists from the set of points2006Vi where i Z, it can be written in the following k 1 k 1 k 1 form as Elements − = [V1, V2, ... , Vn] where n = Z, Elements − Grid − and V can be written as hThe honeycombi patternsi are derived from a symmetrici grid∈ mesh 𝐺𝑟𝑖𝑑∀ with the set of V = Ek 1, Ek 1, Ek 1, Ek 1 , V Gridk 1. 1− 𝐸𝑙𝑒𝑚𝑒𝑛𝑡𝑠2− 3− 4− − 𝑉 𝑖=𝑍, elements , which∈ consists from the set ofT points where it can be written in the V = V , (2) following form as 𝐸𝑙𝑒𝑚𝑒𝑛𝑡𝑠 = [𝑉,𝑉,….𝑉 ] where n = Z, 𝐸𝑙𝑒𝑚𝑒𝑛𝑡𝑠 ∈𝐺𝑟𝑖𝑑 and ∀ V can be written as 𝑉= [𝐸 ,𝐸 ,𝐸 ,𝐸 ], 𝑉∈𝐺𝑟𝑖𝑑 . 𝑉=𝑉, (2)

𝐸 =𝑆𝑉, (3)

Symmetry 2019, 11, 1398 6 of 15 Symmetry 2019, 11, x FOR PEER REVIEW 6 of 15

Symmetry 2019, 11, x FOR PEER REVIEW 6 of 15 k where S is the subdivision matrix and 𝐸 k is a newk set of points. m Ei = SmV, (3) k whereIn theSk above, is the we subdivision described thematrix pattern andk constructi𝐸 is a newon alongset of points.with the topological part. Further, we where Sm m is the subdivision matrix and E is a new set of points. focused on the presented method. With ouri approach, the interior of a 3D fabrication is decomposed InIn thethe above,above, wewe describeddescribed thethe patternpattern constructionconstruction alongalong withwith thethe topologicaltopological part.part. Further,Further, wewe into different regions, where the number of regions depends on the application requirements or the focusedfocused onon thethe presentedpresented method.method. WithWith ourour approach,approach, thethe interiorinterior ofof aa 3D3D fabricationfabrication isis decomposeddecomposed user’s demands. intointo didifferentﬀerent regions,regions, wherewhere thethe numbernumber ofof regionsregions dependsdepends onon thethe applicationapplication requirementsrequirements oror thethe user’suser’s demands.demands. 𝑀𝑒𝑡ℎ𝑜𝑑 =𝐼/𝑃, (4) Method = I/P, (4) where I is the interior area of the object and P𝑀𝑒𝑡ℎ𝑜𝑑 is the number =𝐼/𝑃, of partitioned regions. Within the region,(4) awherewhere certainI Iis isinterval the the interior interior created area area a of columnof the the object object of pattern and andP Pis elements.is the the number number of of partitioned partitioned regions. regions. Within Within the the region, region, a certaina certainThe interval proposed interval created created method a columna wascolumn built of of patternwith pattern accordance elements. elements. of the following block diagram that can be seen from TheTheFigure proposedproposed 3. The methodmethoddiagram waswas shows builtbuilt major withwith accordanceaccordancestages for ofprocessingof thethe followingfollowing input blockblock models diagramdiagram in order thatthat to cancan produce bebe seenseen objectsfromfrom FigureFigure with the3 .3. ThepresentedThe diagramdiagram interior showsshows design majormajor and stagesstages infill forfo patterns.r processingprocessing inputinput modelsmodels in in order order to to produce produce objectsobjects withwith thethe presentedpresented interiorinterior designdesign andand inﬁllinfill patterns.patterns.

Figure 3. The diagram for the proposed method. FigureFigure 3.3. TheThe diagramdiagram forfor thethe proposedproposed method.method. For each sub-region, the Euclidean distance for each region is calculated as follows: ForFor eacheach sub-region,sub-region, thethe EuclideanEuclidean distancedistance forfor eacheach regionregion is iscalculated calculated as asfollows: follows: 𝐸𝐷 =(𝑥 −𝑥) +(𝑦 −𝑦) +(𝑧 −𝑧) (5) 𝐸𝐷2 =(𝑥 −𝑥 )2 +(𝑦 −𝑦 )2 +(𝑧 −𝑧 )2 (5) The regions are symmetricED = or( xasymmetric+ xn) + depending(y + yn )on+ the(z application+ zn) requirements and they(5) n 1 − n 1 − n 1 − are equidistantThe regions from are symmetric each other or as:asymmetric ∀𝐸𝐷(ℎ ,ℎdepending) = 𝐸𝐷 on(ℎ the,ℎ application), where ℎ=[requirements ℎ,…. ℎ and] theyare points.The regions are symmetric or asymmetric depending on the application requirements and they are equidistant from each other as: ∀𝐸𝐷(ℎ,ℎ) = 𝐸𝐷(ℎ,ℎ), where ℎ=[ ℎ,…. ℎ] are are equidistantA column fromof pattern each other elements as: ED is( hcreatedn, hn+1 )for= EDeach(h1 , partitionedh2), where h region= [h1, ...and. hn+ 1the] are presented points. points. ∀ honeycombAA columncolumn pattern of of pattern canpattern be elements position elements is in created biaxial is created for directio each for partitionedns, each as shown partitioned region in Figure and region the4. There presented and are the four honeycomb presented regions wherepatternhoneycomb we can created bepattern position columns can inbe biaxial positionof flexible directions, in biaxialhoneycomb as directio shown patterns.ns, in as Figure shown Each4. column Therein Figure are intervals 4. four There regions are are specifiedfour where regions we in Tablecreatedwhere 1. we columns created of columns ﬂexible honeycomb of flexible patterns.honeycomb Each patterns. column Each intervals column are speciﬁedintervals inare Table specified1. in Table 1.

(a) (b)

FigureFigure 4. 4. CreationCreation of patterns for(a each)each partitionedpartitioned region,region, ( a(a)) the the size size of of the (theb ﬁsh) fish model model is is 14 14 cm cm 8× cm8c × m 2× cm,2 cm, (b ()b the) the size size of of the the bunny bunny model model is is 10 10 cm cm ×8 8c cm m ×2 2 cm. cm. ×Figure 4. Creation of patterns for each partitioned× region,× (a) the size of the fish model is 14 cm × 8c m × 2 cm, (b) the size of the bunny modelTable is 1. 10Column cm × 8c intervals. m × 2 cm. Table 1. Column intervals.

A ABCDB Table 1. Column intervals.C D 𝐴 A≤𝑥≤1 x 𝐴An 𝐵B1≤𝑥≤𝐵x Bn 𝐶C1 ≤𝑥≤𝐶x Cn D𝐷1 ≤𝑥≤𝐷x Dn ≤A ≤ ≤ B ≤ ≤ C≤ ≤ ≤D or or or or or oror 𝐴 ≤𝑥≤𝐴 𝐵 ≤𝑥≤𝐵 𝐶 ≤𝑥≤𝐶 𝐷 ≤𝑥≤𝐷 A1 y An B1 y Bn C1 y Cn D1 y Dn 𝐴 ≤𝑦≤≤ ≤𝐴 𝐵 ≤𝑦≤𝐵≤ ≤ 𝐶 ≤𝑦≤𝐶≤ ≤ 𝐷≤≤𝑦≤𝐷≤ Column 1 [ A nor1, An] Column2 or[ Bn 1, Bn] Column3 or[C n 1, Cn] Column4 [Dorn 1, Dn] 𝐶𝑜𝑙𝑢𝑚𝑛∈ − 𝐶𝑜𝑙𝑢𝑚𝑛∈ − 𝐶𝑜𝑙𝑢𝑚𝑛∈ − 𝐶𝑜𝑙𝑢𝑚𝑛∈ − 𝐴 ≤𝑦≤𝐴 𝐵 ≤𝑦≤𝐵 𝐶 ≤𝑦≤𝐶 𝐷 ≤𝑦≤𝐷 ∈[ 𝐴, 𝐴] ∈[ 𝐵,𝐵] ∈[ 𝐶,𝐶] ∈[ 𝐷,𝐷] 𝐶𝑜𝑙𝑢𝑚𝑛 𝐶𝑜𝑙𝑢𝑚𝑛 𝐶𝑜𝑙𝑢𝑚𝑛 𝐶𝑜𝑙𝑢𝑚𝑛 ∈[ 𝐴, 𝐴] ∈[ 𝐵,𝐵] ∈[ 𝐶,𝐶] ∈[ 𝐷,𝐷]

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In this study, wewe introducedintroduced twotwo typestypes ofof honeycombhoneycomb patterns:patterns: (1) a regular honeycomb pattern and (2) a honeycomb trapezoid with a slightly distinctive topology, as shownshown inin FigureFigure5 5.. ForFor thethe comparison test we have investigated a standard grid-typegrid-type pattern.pattern.

(a) (b)

Figure 5. (a) Honeycomb pattern and ( b) hexagonal trapezoid pattern. The The size of the bear models is 14 cm × 88 cm cm × 22 cm. cm. × × 4. Flexibility of the Honeycomb Pattern The mechanical properties of honeycomb patte patternsrns can be described by analyzing a single honeycomb pattern element. Furthermore, Furthermore, it it is nece necessaryssary to take into consideration its geometrical parameters, since the parameters will change when thethe element is subjected to compression loads, as was explored in a similarsimilar studystudy [[38].38]. The pattern element along with its geometric parameters are shown in Figure6 6..

Figure 6. Geometric parameters of the honeycomb pattern element.

We denoted thethe parametersparameters ofof thethe elementelement asas follows:follows: hℎis is the the height height of of the the side, side,l is𝑙 theis the length length of ofthe the side, side, where whereθ is 𝜃 the is the angle angle between between the the horizontal horizontal and and inclined inclined edges edges that that we considerwe consider as θ as= 𝜃=30◦ 30°because because we arewe consideringare considering a regular a regular hexagonal hexagonal element. element. The The hexagonal hexagonal element’s element’s overall overall width width is isdefined defined as asL =𝐿2l cos = 2𝑙θ and cos 𝜃 and the the overall overall height height is H is= 𝐻=ℎ+2𝑙sin𝜃h + 2l sin θ In the current study, it is important to noteIn that the H current is defined study, as the it is full important overall height to note of that the element,H is defined while as in the other full similar overall studies—as height of the in element,the study while [39], basedin other on similar the homogenous studies—as honeycomb in the study structure, [39], based used on half the of homogenous the overall height honeycomb of the structure,honeycomb used cell. half In our of the case, overall the element height is of fully the ahoneycombffected by compression, cell. In our tension-case, the and element flexure is loadsfully affectedsince the by presented compression, flexible tension- pattern and is derived flexure from load non-homogenouss since the presented honeycomb. flexible pattern Depending is derived on the fromstrength non-homogenous of the loads, the geometrichoneycomb. parameters Depending of the on honeycomb the strength pattern of willthe beloads, changed the andgeometric will be parametersdifferent than of its the original honeycomb parameters. pattern will be changed and will be different than its original parameters.To test the flexibility of the honeycomb pattern, we conducted a simple compression test, which can be observedTo test the in Figure flexibility7. Figure of the7 showshoneycomb how infillpattern patterns, we conducted are a ffected a simple when compression we apply a y-directional test, which cancompression be observed load in with Figure a pen, 7. Figure which 7 was shows used how for visualinfill patterns observation are affected of the pattern when flexibility.we apply a The y- directionalstrength of compression the applied loadload changes with a thepen, geometric which was parameters used for ofvisual the element—henceobservation of the it becomes pattern flexibility.L , 2l cos θ Theand strengthH , h + of2l thesin θappliedduring load the compression.changes the geometric There are parameters affected areas of ofthe the element—hence element along itthe becomesx and y axial𝐿≠2𝑙cos𝜃 direction and is defined𝐻≠ℎ+2𝑙sin𝜃 as follows: during the compression. There are affected areas of the element along the x and y axial direction is defined as follows: Ax = (2l cos θ)b Ay = (h + 2l sin θ)b, (6) 𝐴 = (2𝑙cos𝜃)𝑏 𝐴 = (ℎ + 2𝑙sin𝜃)𝑏, (6) where Ax and Ay are the affected areas of the element by compression load, b is the depth of the element;

Symmetry 2019, 11, 1398 8 of 15

whereSymmetryA 2019x and, 11A, xy FORare thePEER aff REVIEWected areas of the element by compression load, b is the depth of the element;8 of 15 To provide detailed insights for the honeycomb deformation mechanisms we provided a model for biaxialTo provide loads, detailed but we practicallyinsights for considered the honeycomb y-directional deformation load mechanisms in Figure7. The we elementprovided sides a model are forconsidered biaxial loads, as beams. but we As practically it is known, considered the bending y-directional moment is load the in reaction Figure induced 7. The element in a honeycomb sides are consideredelement, which as beams. tends toAs bend it is known, the walls the of bending the pattern moment element is the when reaction the load induced is applied. in a honeycomb We defined element,the moment whichM ontends the tox and bendy directionalthe walls of beam the patte as follows:rn element when the load is applied. We defined the moment M on the x and y directional beam as follows: Pxl sin θ Pyl cos θ = = M x 𝑀 = and M andy 𝑀 = ,, (7) (7) 2 2 where P𝑃xx andandP 𝑃yyare are the the axial axial loads; loads;M x𝑀and andM y𝑀are are the bendingthe bending moments moments on the onx theand xy anddirectional y directional beam; beam;The loads can be defined from the following equation: The loads can be defined from the following equation: Px = σ1(h + 2l sin θ)b and Py = σ2(2l cos θ)b, (8) 𝑃x= 𝜎1(ℎ+2𝑙sin𝜃)𝑏 and 𝑃 =𝜎(2𝑙 cos 𝜃)𝑏, (8) where σ𝜎11 and 𝜎σ2 areare x x and and y y directional directional forces; forces; Here, in the above-mentioned Equation (7), we considered the directional overall height H and the overall length L.L. As it is shownshown inin FigureFigure7 ,7, the the pattern pattern elements elements bend bend easily easily because because of theof the elastic elastic properties properties of the of thesoft soft 3D printing3D printing materials, materials, TPU TPU and and TPE, TPE, and and due due to the to geometrythe geometry of the of honeycombthe honeycomb patterns. patterns. When the load is removed, the pattern elements return to their original state without permanent deformation due to the flexibility flexibility of the patterns and the material’s elasticity. In Figure 77,, thethe bunnybunny modelsmodels withwith largerlarger andand mediummedium sizesize patternspatterns cancan bebe seen,seen, thethe modelsmodels were tested by a pen and metalic stick to visually examine their flexibility. flexibility. Furthermore, to provide a quantifiedquantified evidenceevidence ofof thethe flexibility, flexibility, the the bunny bunny model model was was tested tested by by the the UTM UTM machine machine INSTRON-5690 INSTRON - (USA,5690 (USA, INSTRON). INSTRON).The The result result showed showed that itsthat compression its compression strength strength is more is more than than 1000 1000 N. N.

(a) (b) (c)

Figure 7. CompressionCompression effects effects on on bunny bunny model, model, the the size size of of bunny bunny models models is is10 10cm cm × 8 cm8 cm× 2 cm.2 cm.(a) × × the(a) thebunny bunny model model with with larger larger infills infills tested tested with with a apen, pen, (b ()b the) the bunny bunny model model with with smaller smaller infills infills tested tested with a pen (c) the bunny model withwith smallersmaller infillsinfills testedtested withwith metallicmetallic stick.stick

In the current study, thethe builtbuilt modelmodel that determines the flexibilityflexibility of the honeycomb pattern is differentdifferent fromfrom thethe majority majority of of the the proposed proposed models. models. Our Our flexible flexible honeycomb honeycomb patterns patterns are derived are derived from fromthe non-homogenous the non-homogenous honeycombs, honeycombs, and for and this for reason this reason we considered we considered the full overallthe full heightoverall in height Young’s in Young’smoduli as moduli follows: as follows: Fx/Ax FxLx Fy/Ay FyLy Ex = ⁄= and Ey = ⁄ = , (9) 𝐸U=x/Lx =AxUx and 𝐸 =Uy/Ly= Ay,U y (9) ⁄ ⁄ Lx = L and Ly = H (10) 𝐿 =𝐿and 𝐿 =𝐻 (10) L = 2l cos θ and H = h + 2l sin θ (11) 𝐿 = 2𝑙 cos 𝜃 and 𝐻=ℎ+2𝑙sin𝜃 (11) where Ex and Ey are the Young moduli in x and y axial directions; Fx and Fy is the applied forces in where 𝐸 and 𝐸 are the Young moduli in x and y axial directions; 𝐹 and 𝐹 is the applied x and y directions that needed to produce a unit displacement; Lx is the width of the element along forces in x and y directions that needed to produce a unit displacement; 𝐿 is the width of the x-direction and Ly is height of the element along y-direction; Ax and Ay are the areas of the element element along x-direction and 𝐿 is height of the element along y-direction; 𝐴 and 𝐴 are the along the x and y directions. Ux and are the displacements in x and y directions. areas of the element along the x and y directions. 𝑈 and 𝑈 are the displacements in x and y directions.

Another elastic component, such as 𝑣, 𝑣, is the Poisons ratio x, and y axial directions can be defined from the following equation:

Symmetry 2019, 11, 1398 9 of 15

Another elastic component, such as vxy, vyx, is the Poisons ratio x, and y axial directions can be deﬁned from the following equation:

Symmetry 2019, 11, x FOR PEER REVIEW εy εx 9 of 15 vxy = and vyx = , (12) − εx −εy 𝑣 =− and 𝑣 =− , (12) where εx, εy are x and y axial directional strains. The shear modulus Gxy is defined as follows: where 𝜀,𝜀 are x and y axial directional strains. The shear modulus 𝐺 is defined as follows: Shear stressxy Gxy = . (13) 𝐺=Shear strainxy. (13) We can conclude that the proposed interior design and the geometry of the patterns, as well as material properties, make our 3D fabrications more flexible.flexible. The proposed interior design combines flexibilityflexibility andand lowlow weight,weight, which which are are valuable valuable physical physical properties properties for for 3D 3D fabrications. fabrications. Additionally, Additionally, we weexamined examined the flexibilitythe flexibility of samples of samples fully fully filled fill withed thewith homogenous the homogenous honeycomb honeycomb structures structures and sparse and sparsehomogenous homogenous honeycombs, honeycombs, as can beas seencan be in seen Figure in8 Figure. 8.

(a) (b) (c) (d)

Figure 8. Compression eeffectsffects on on the the models models filled filled with with the the homogenous homogenous honeycomb honeycomb structure, structure, the sizethe sizeof bunny of bunny models models is 1 0is cm1 0 cm8 × cm 8 cm2 × cm, 2 cm, the the size size of of the the cube cube model model is is 10 10 cm cm ×10 10 cm cm ×5 5 cm,cm, ((aa))the the × × × × bunny model with fully filledfilled homogenous honeycomb, it is tested with aa metallicmetallic stick,stick ( b)) the box model filledfilled with homogenoushomogenous honeycomb,honeycomb, itsits backsidebackside isis testedtested withwith aa metallicmetallic stick,stick ((cc))the the bunny model with sparse homogenous honeycomb,honeycomb, itsits backfront side side is is tested tested with with a a metallic metallic stick, stick. (d ) the bunny model with sparse homogenous honeycomb, its front side is tested with a metallic stick. As depicted in Figure 8, we applied y-directional compression load with a metallic stick, which is heavierAs depicted than a pen in Figure to provide8, we appliedmore sufficient y-directional compression compression load loadfor the with samples a metallic that stick,are fully which filled is withheavier the than homogenous a pen to provide honeycomb more su structures.fficient compression Despite loadthe elastic for the samplesproperties that of are soft fully 3D filled printing with materials,the homogenous a very honeycomb slight bending structures. effect Despitewas ob theserved elastic at propertiesthe top of of models. soft 3D printingHere, homogenous materials, a veryhoneycomb slight bending structures effect are was non-orthotropic. observed at the The top co ofmpression models. Here, strength homogenous of the bunny honeycomb model structureswas only 40N,are non-orthotropic. which backs up The the compressionabove statement. strength It is of less the flexible bunny modelcompared was to only the 40N, bunny which model backs with up our the proposedabove statement. interior Itdesign is less and flexible the patterns. compared to the bunny model with our proposed interior design and theFurther, patterns. we have experimented with samples that are filled with the sparse honeycomb patterns, as shownFurther, in Figure we have 8. experimentedHere, the pattern with is samples derived that from are the filled homogenous with the sparse honeycomb honeycomb structure. patterns, To determineas shown inthe Figure flexibility8. Here, of the the samples pattern we is derived carried fromout a thetest homogenouswhere the samples honeycomb were subjected structure. to To y- directionaldetermine thecompression flexibility load of the with samples a metallic we carriedstick. The out metallic a test where stick was the samplesused in order were subjectedto provide to a y-directionalstronger compression compression load. load We withobserved a metallic that stick.it is still The less metallic flexible stick than was our used proposed in order honeycomb to provide pattern.a stronger However, compression it was load. slightly We observed better compared that it is stillto the less samples flexible thanwith our fully proposed filled homogenous honeycomb pattern.honeycomb However, structures. it was From slightly the curre betternt examination, compared to we the can samples conclude with that fully the filledinterior homogenous filled with thehoneycomb homogenous structures. honeycomb From the structures current examination, are less flexible we can concludecompared that to the our interior proposed filled withpattern. the Moreover,homogenous our honeycomb patterns structurescan be flexible are less in flexible two directions compared tobecause our proposed they are pattern. based Moreover,on the non- our patternshomogenous can be honeycomb flexible in structures, two directions which because enables they to areposition based the on columns the non-homogenous of patterns vertically honeycomb and horizontallystructures, which with enablesthe entire to positionelements the by columns our method. of patterns vertically and horizontally with the entire elements by our method. 5. Soft Printing Materials Thermoplastic polyurethane (TPU) The mechanical properties of TPU are dependent on its chemical consistency, as we described earlier. We further focused on the hardness scale. The Shore hardness of TPU is important because it is a measurement that describes TPU properties. Generally, the Shore hardness of TPU begins from A to D. The category A denotes a flexible type of TPU, while the category D refers to more rigid TPU, the relationship between categories and the TPU and TPE hardness range is depicted in Figure 9.

Symmetry 2019, 11, 1398 10 of 15

5. Soft Printing Materials Thermoplastic polyurethane (TPU) The mechanical properties of TPU are dependent on its chemical consistency, as we described earlier. We further focused on the hardness scale. The Shore hardness of TPU is important because it is a measurement that describes TPU properties. Generally, the Shore hardness of TPU begins from A to D. The category A denotes a ﬂexible type of TPU, while the category D refers to more rigid TPU, the relationshipSymmetry 2019, between11, x FOR PEER categories REVIEW and the TPU and TPE hardness range is depicted in Figure9. 10 of 15

Figure 9. ThermoplasticThermoplastic polyurethane polyurethane (TPU) (TPU) categories categories and and its its with with thermoplastic thermoplastic elastomer elastomer (TPE) (TPE) hardness range.

Thermoplastic elastomer (TPE) Similarly, withwith TPU, TPU, TPE TPE materials materials have have a variety a variety level of level flexibility of flexibility and softness and that softness is determined that is bydetermined its chemical by blends.its chemical Because blends. of the Because elastic propertiesof the elastic of TPEproperties users can of fabricateTPE users soft can and fabricate flexible soft 3D fabrications,and flexible 3D which fabrications, are also durable.which are The also printing durable. process The printing can be process challenging can be for challenging TPE compared for TPE to TPUcompared because to TPU of several because factors of several as the factors printing as speed, the printing temperature speed, andtemperature settings. Toand avoid settings. inaccuracy, To avoid it isinaccuracy, recommended it is recommended to set the lower to printing set the lower speed printing at 5 to 30 speed mm/ s.at 5 to 30 mm/s. As mentioned above, the characteristic of soft 3D printing materials is determined by Shore hardness. This hardnesshardness scalescale allowsallows usersusers to to fabricate fabricate with with a a required required level level of of flexibility. flexibility. The The level level of flexibilityof flexibility can can be be determined determined according according to theto the hardness hardness scale scale table table in Tablein Table2. 2.

Table 2.2. Hardness scale.

HardnessHardness scale (Shore(Shore A) A) No.No. CategoryCategory of Objects of Objects Hardness Hardness 1.1. ShoppingShopping cartwheel cartwheel 100A 100A Hard Hard 2.2. Phone Phone cord cord 90A 90A Medium Hard Medium Hard 3.3. LeatherLeather belt belt 85A 85A Medium Soft Medium Soft 4.4. Tire Tire tread tread 60 A 60 A 5. Pencil eraser 40A 5. Pencil eraser 40A Soft 6. Rubber band 20A Soft 6. Rubber band 20A In this study, TPU printed 3D fabrications with the Shore 80 A and TPE printed 3D fabrication In this study, TPU printed 3D fabrications with the Shore 80 A and TPE printed 3D fabrication with the hardness scale is 60A were used. with the hardness scale is 60A were used. 6. Experimental Results 6. Experimental Results As mentioned in the introduction, soft printing materials come in a variety of chemical As mentioned in the introduction, soft printing materials come in a variety of chemical consistencies consistencies and different levels of hardness. Therefore, we printed our outputs with different soft and diﬀerent levels of hardness. Therefore, we printed our outputs with diﬀerent soft printing materials, printing materials, such as TPU and TPE, to conduct a comparison test between these outputs to such as TPU and TPE, to conduct a comparison test between these outputs to determine the physical determine the physical properties of 3D fabrications. properties of 3D fabrications. Moreover, we consider how the materials impact the flexibility and additionally stretchability of the soft 3D printed fabrications. The mechanical performance of our outputs was measured under compression using the UTM machine INSTRON – 5690 (USA, Instron). Tension test results The results for the conducted tension test are provided in the Table 3. We conducted tensile stress tests for different soft printing materials. From the results of our experiment we can conclude that soft 3D printed fabrications are impacted by factors as the pattern type and the material.

Table 3. Results of tension test.

Tension Strength

Material No. Model TPU TPE

Symmetry 2019, 11, 1398 11 of 15

Moreover, we consider how the materials impact the ﬂexibility and additionally stretchability of the soft 3D printed fabrications. The mechanical performance of our outputs was measured under compression using the UTM machine INSTRON-5690 (USA, Instron). Tension test results The results for the conducted tension test are provided in the Table3. We conducted tensile stress tests for diﬀerent soft printing materials. From the results of our experiment we can conclude that soft 3D printed fabrications are impacted by factors as the pattern type and the material.

Table 3. Results of tension test.

Tension Strength No. Model Material TPU TPE Box 1 778N 1400N 10 cm 5 cm 1.5 cm × ×

The tension experiment showed varying results for TPU and TPE printed samples because of their material properties. The most stretchable sample is a 3D print made of TPE. The current experiment veriﬁes the technical characteristics of TPE and TPU regarding their stretchability. Compression test results The experimental test results for the compression test are shown in Table4. The compression test was done to reveal the compression strength of our proposed patterns. When a compression load was applied, the linear elastic deformation is occurred by causing the patterns elements to bend.

Table 4. Results of compression test.

Compression Strength No. Model Material X-Directional Y-Directional Box Model with honeycomb patterns 1 TPU 503N 122N 10 cm 10 cm 5 cm × ×

The results of the test revealed that the compressive strength of a pattern directly depends on the elastic properties of its material, as well as on the geometrical shape of its infill pattern. The experiment verified the flexibility of our patterns where loading conditions were conducive to buckling. Flexural Test In Table5 has shown the results of flexure test. As it is known from the physics that flexible materials have lower flexural strengths compared to rigid materials; therefore, we have lower flexural strengths for 3D printed models with TPE and the higher strengths for samples with TPU. Besides, the pattern topology impacts their flexural strengths.

Table 5. Results of ﬂexural test.

Flexural Strength No. Model Honeycomb Pattern Hexagonal Trapezoid Box with TPU 1 212N 343N 10 cm 10 cm 5 cm × × Box with TPE 2 75N 216N 10 cm 10 cm 5 cm × × Symmetry 2019, 11, 1398 12 of 15

Weight comparison In addition to determining the optimal pattern for flexibility, we have included a weight comparison of the fabricated 3D objects. This part of the experiment allows us to determine the cost-effectiveness of our method. We measured the weight of each presented model to reveal the lightest interior for soft 3D printed fabrications. These results are shown in Table6. As it can be seen, there are three di fferent patterns presentedSymmetrySymmetry 2019 2019 with, ,11 11, , thex x FOR FOR proposed PEER PEER REVIEW REVIEW interior design. The experiment reveals that the lightest1212 model of of 15 15 is the fish model with the hexagonal interior, which weighs 47 g. The second lightest is the model with SymmetrySymmetry Symmetry 2019 2019, 11, , 2019 11x FOR, x, FOR11 PEER, x PEERFOR REVIEW PEER REVIEW REVIEW 12 of12 15of 1215 of 15 the hexagonal trapezoid interior.

TableTable 6. 6. Weight Weight of of fish fish models. models. SymmetrySymmetry 2019 2019, ,11 11, ,x x FOR FOR PEER PEER REVIEW REVIEW 1212 of of 15 15 Table 6. Weight of ﬁsh models. TableTable 6.Table Weight6. Weight 6. Weight of offish fish models.of models.fish models.Weight Weight

ModelModel WeightWeightWeightWeight No.No.No. Honeycomb-likeHoneycomb-like pattern pattern Hexagonal Hexagonal trapezoid trapezoid Grid Grid pattern pattern ModelModelModel Model No.No. No. Honeycomb-likeHoneycomb-likeHoneycomb-likeHoneycomb-like patternpattern pattern pattern TableTable 6.6. Hexagonal Weight Weight Hexagonal Hexagonal Hexagonal of of fish fishtrapezoid trapezoid trapezoidmodels. models. trapezoid Grid Grid pattern Grid pattern pattern

WeightWeight

ModelModel No.No. Honeycomb-likeHoneycomb-like patternpattern Hexagonal Hexagonal trapezoidtrapezoid Grid Grid patternpattern TPUTPUTPU Printed Printed Printed TPU 2DTPU FishPrintedTPU Printed Printed 1. 2D2D Fish Fish 14 cm 2D2D Fish8 cmFish2D Fish × × 1.1. 1414 cm cm2 cm× × 8 8 cm cm × × 1. 1. 14 1. 14 cm cm ×14 8 × cmcm 8 cm ×× 8 × cm × 22 cm 2cm cm 2 cm TPUTPU PrintedPrinted 4747 g g 51 51 g g 6060 g g 4747 47gg g 47 g 51 51g51 g g 51 g 60 60g g 6060 g 2D2D FishFish Non-HomogenousNon-HomogenousNon-HomogenousNon-HomogenousNon-Homogenous Based Based Based Based Based Non-Homogenous Based Honeycomb PatternHomogenousHomogenousHomogenousHomogenousHomogenous Homogenous Honeycomb Honeycomb Honeycomb Honeycomb Honeycomb Based Based PatternBased BasedPatternBased Based Pattern Pattern Pattern Pattern 1.1. 1414 cmcm ×× 88 cmcm ×× HoneycombHoneycombHoneycombHoneycomb Pattern Pattern Pattern Pattern Pattern 22 cmcm 4747 gg 51 51 gg 6060 gg Non-HomogenousNon-Homogenous BasedBased HomogenousHomogenous HoneycombHoneycomb BasedBased PatternPattern TPUTPUTPU Printed PrintedTPU Printed Printed HoneycombHoneycomb PatternPattern TPUTPU Printed Printed 2D2D2D Bunny Bunny Bunny2D Bunny 2. 2. 2. 2.2D2D Bunny Bunny 1010 cm 10cm cm ×108 8 cm× cmcm 8 cm ×× 8 × cm × 2.2. × × 1010 cm cm22 cm ×cm 2× 8 cm8 cm cm2 cm × × 22 cmTPU TPUcm PrintedPrinted 22 22g g 22 g 26 26g g 26 g 2D2D BunnyBunny 2.2. 2222 g g 2626 g g In1010 InTable cmcmTableIn ×× Table6, 88 cm6,cmwe we ××6,also alsowe tested alsotested testedhomogenous homogenous homogenous an and dnon-homogenous annon-homogenousd non-homogenous honeycombs honeycombs honeycombs regarding regarding26 regarding g their their their weights.weights.weights. It isIt shownis Itshown is shown that that our thatour honeycomb honeycombour honeycomb pattern pattern pattern is lighteris lighter is lighter than than the than the homogenous homogenousthe homogenous based based honeycombbased honeycomb honeycomb InIn TableTable22 cmcm 6,6, wewe alsoalso testedtested homogenoushomogenous anandd non-homogenousnon-homogenous honeycombshoneycombs regardingregarding theirtheir weights.structure.weights.structure.structure. It It is is shown shown that that our our honeycomb honeycomb pattern pattern is is lighter lighter than than the the homogenous homogenous based based honeycomb honeycomb 22 g In Tablestructure.structure.6, weIn InTable also Table In 7, Table tested we7, we compared 7, compared we homogenous compared different different different sizes and sizes2222 of sizes g non-homogenousg ofthe the honeycomb of honeycomb the honeycomb pattern pattern pattern honeycombs with with the with the standard standard the standard regarding grid grid2626 pattern. g g grid pattern. theirpattern. weights. It is shownThe thatThe lightestInIn ourThelightest Table Table Inlightest honeycombIn soft 7,Table softTable7, we3D we soft3D printedcompared 6,compared6, printed 3D wewe printed pattern fabricationalsoalso fabrication different different testedtested fabrication is is lighterhomogenous homogenous theissizes sizes the bunny is bunnyofthe of than the the bunnymodel honeycomb model honeycombanan thed dmodelwith non-homogenous homogenousnon-homogenouswith the with the patternweight pattern weightthe weight of with with of22 based honeycombs 22honeycombsg. theof theg. 22 standard standard honeycombg. regardingregarding grid grid pattern. pattern. structure. theirtheir weights.weights. ItIt isis shownshown thatthat ourour honeycombhoneycomb patternpattern isis lighterlighter thanthan thethe homogenoushomogenous basedbased honeycombhoneycomb In TableTheThe7, lightest welightest comparedTable softTable soft 7. Table3D 3DWeight7. Weightprinted printed di7. Weight comparisonﬀ comparisonerent fabrication fabrication comparison sizes of bunnyof bunny of is ofis models bunnythethe models bunny bunny honeycomb models wi thwi thdifferentmodel model widifferentth different with patternswith pattern patterns the thepatterns and weight andweight with patterns patternsand theof patternsof size. 22 22 size. standard g.g. size. grid pattern. structure.structure. The lightest soft 3D printed fabrication is the bunny model with the weight of 22 g. NoNo NoModelModelInTableInModel Table Table Table 7. 7. 7, Weight 7,Weight we we compared compared comparison comparison different different of of bunny bunny sizes sizes models models of of the the wi Weighthoneycomb wihoneycombthWeightth different differentWeight pattern pattern patterns patterns with with and and the thepatterns patterns standard standard size. size. grid grid pattern. pattern. . . . TheThe lightestlightest softsoft 3D3D printedprintedHoneycomb-like fabricationfabricationHoneycomb-likeHoneycomb-like isis thethe Pattern Pattern bunnybunny Pattern modelmodel withwith thethe weightweight Grid ofof Grid 22 22Pattern Grid g.Patterng. Pattern NoNo TableModelModel 7. Weight comparison of bunny models with diﬀWeighterentWeight patterns and patterns size. . Table 7. Weight comparison of bunny models with different patterns and patterns size. . TableTable 7. 7. Weight Weight comparison comparisonHoneycomb-likeHoneycomb-like of of bunny bunny models models Pattern Pattern wi with th different different patterns patterns and and patterns patterns Grid Grid size. size. Pattern Pattern Weight No. NoNo Model ModelModel WeightWeight Honeycomb-like Pattern Grid Pattern TPU.. TPU PrintedTPU Printed Printed Honeycomb-likeHoneycomb-like PatternPattern Grid Grid PatternPattern 2D 2D Bunny Bunny 2D Bunny 1. 1. 101. 10cm cm ×10 8 × cmcm 8 cm ×× 8 × cm × TPUTPU Printed Printed 2 cm2 cm 2 cm

2D 2D Bunny Bunny TPU Printed 24 24g g 24 g 22 22g g 22 g 60 60g g 60 g 1.1. 1010 cm cm ×TPU TPU× 8 8 cm cm PrintedPrinted × × 1. In2D InTable BunnyTableIn Table8 we8 we have8 havewe donehave done adone comparisona comparison a comparison test test for testfor 3D 3Dfor models models3D models from from differentfrom different different categories. categories. categories. The The The 22 cm cm2D2D BunnyBunny experiment10experiment cmexperiment8 cm was was 2carried cm wascarried carried out out by outby measuring measuringby measuring their their we their weightight we one ightone by oneby one. one.by The one.The lightest Thelightest lightest interior interior interior is isthe the is the 1. ×10 cm × 8 cm × hexagonal1.1.hexagonal hexagonal1010 cmcmpattern. ×pattern.× 88 cmcmpattern. Hexagonal ×× Hexagonal Hexagonal 24patterns24 patternsg g patterns are are the arethe most themost efficientmost efficient 22efficient22 g patternsg patterns patterns regarding regarding regarding their their cost-their 60cost-60 g g cost- 22 cmcm effectivenesseffectivenessInIneffectiveness TableTable and 88and weweflexibility and flexibility havehave flexibility donedoneincluding including aincludinga comparisoncomparison stress-susta stress-susta stress-susta inability.testtest inability. forforinability. 3DTherefore,3D Therefore, modelsmodels Therefore, they fromtheyfrom arethey are different different widely arewidely widely used categories.categories.used inused in in The The 22 g 60 g experimentdifferentexperimentdifferentdifferent applications. applications. waswas applications. carriedcarried outout byby measuring24measuring2424 g gg theirtheir weweightight oneone222222 by g gbyg one.one. TheThe lightestlightest interiorinterior6060 g g isis thethe hexagonalhexagonal InIn pattern. pattern. TableTable 88 Hexagonal weHexagonalwe havehave donedone patternspatterns aa comparisoncomparison areare thethe test testmostmost forfor efficient efficient3D3D modelsmodels patternspatterns fromfrom different differentregardingregarding categories.categories. theirtheir cost-cost- TheThe TableTable 8.Table Weight8. Weight 8. Weight comparison comparison comparison of models.of models. of models. effectivenesseffectivenessexperimentexperiment andand was was flexibilityflexibility carriedcarried includingoutoutincluding byby measuringmeasuring stress-sustastress-susta theirtheirinability.inability. weweightight one oneTherefore,Therefore, byby one.one. they ThetheyThe lightestarelightestare widelywidely interiorinterior usedused isis theinthein In Table8 wehexagonalhexagonal have done pattern.pattern. a comparison HexagonalHexagonal test patternspatterns for 3D areare models thethe mostmost fromWeight efficientWeightefficient diWeightff erent patternspatterns categories. regardingregarding The theirtheir experiment cost-cost- NoNodifferentdifferentNo ModelModel applications. applications.Model Material Material Material effectivenesseffectiveness andand flexibilityflexibility includingincluding stress-sustastress-sustainability.inability. Therefore,Therefore,HexagonalHexagonal Hexagonaltheythey Trapezoid are areTrapezoid widelyTrapezoidwidely usedused inin was carried. . out. by measuring their weight Honeycomb-like oneHoneycomb-likeHoneycomb-like by one. Pattern The Pattern Pattern lightest interior is the hexagonal pattern. Hexagonal patternsdifferentdifferent are applications.applications. the most efficientTableTable patterns8. 8. Weight Weight comparison comparison regarding of of theirmodels. models. cost-e ffectiveness and flexibility including stress-sustainability. Therefore, theyTableTable 8. are8. Weight Weight widely comparison comparison used of inof models. models. diWeightWeightfferent applications. NoNo ModelModel MaterialMaterial HexagonalHexagonal Trapezoid Trapezoid . . Honeycomb-likeHoneycomb-like Pattern Pattern WeightWeight NoNo ModelModel MaterialMaterial HexagonalHexagonal TrapezoidTrapezoid .. Honeycomb-likeHoneycomb-like PatternPattern

Symmetry 2019, 11, 1398 13 of 15

Table 8. Weight comparison of models.

Weight No. SymmetrySymmetryModel 2019 ,2019 11, x, 11FOR, x FORPEER PEER REVIEW Material REVIEW 13 of 1315 of 15 SymmetrySymmetry 2019 ,2019 11, x, 11FOR, x FORPEER PEER REVIEW REVIEW 13 of 1315 of 15 SymmetrySymmetry 2019SymmetrySymmetry ,2019 11, x, 2019 112019FOR, x, , 11 FOR11PEER, ,x x FOR FORPEER REVIEW PEER PEER REVIEW REVIEW REVIEW Honeycomb-like Pattern Hexagonal Trapezoid131313 of of of 15 1513 15 of 15

2D Bear 1. 2D Bear2D Bear 2D2D BearBear TPU 1. 141. cm2D1.1. 8 Bear2D cm Bear 2 cm 1. 1. 14 cm×14 ×cm 81414 cm × cmcm 8 × cm × × 88 cm×cm ××TPU TPU TPUTPU 14 cm14 ×cm 8 cm× 8 ×cm × TPUTPU 2 cm2 cm22 cmcm 2 cm2 cm 2 cm2 cm 4141 gg 34 g34 34 g gg 4141 g41 g 34 g 41 g41 g

3D Box 3D3D BoxBox 2. TPU 10 cm 2.3D2.10 Box cm3D1010 cmBoxcm5 cm×10×10 cmcm ×× TPUTPU ×3D Box3D × Box 2. 2.10 cm10 ×10cm cm×105 5 × cm cm cm × TPUTPU 2. 2.10 cm10 ×10cm ×10cm ×cm × TPUTPU 5 cm5 cm 6666 gg 103103 gg 5 cm5 cm 5 cm5 cm 66 g66 g 103 g103 g 66 g66 66 g 103103 g103g g

3D3D BoxBox

3.3.3D Box1010 cm cm ×10×10 cmcm ×× TPUTPU 3. TPU 10 cm 3D10 Box cm3D Box555 cm cm cm 3D Box3D Box 3. 3.10 cm×10 ×10cm cm×10× ×cm × TPUTPU 3. 3.10 cm10 ×10cm ×10cm ×cm × TPUTPU 6262 gg 7979 gg 5 cm5 cm 5 cm5 cm 5 cm5 cm

62 g62 gg 7979 g79 g 62 g 79 g79 g

3D 3D BoxBox TPETPE

1010 cm cm ×10×10 cmcm ×× 4.4. 5 cm 5 cm 3D3D Box 3D Box TPETPE 4. 3D Box3D Box TPETPE TPE 6060 gg 8080 gg 10 10 cm cm1010 ×10cm cm cm×105 × cm × 4. 4.10 cm×10 ×10cm ×10cm× ×cm × 4. 4. 5 cm5 cm 4. 4. 5 7.cm7. ConclusionsConclusions5 cm 5 cm5 cm 60 g60 g 80 g80 g InIn thisthis study,study, wewe havehave presentedpresented aa specificspecific60 ginteriorinterior designdesign targetedtargeted forfor softsoft80 g3D3D80 printedgprinted 60 g60 60 g 80 g80 g fabricationsfabrications alongalong withwith speciallyspecially designeddesigned flexibleflexible ininfillfill patterns.patterns. ItIt waswas donedone toto fabricatefabricate 3D3D objectsobjects 7. Conclusions7. Conclusionswith improved physical properties by focusing on their flexibility and additionally stretchability with 7. Conclusions7. Conclusionswith improved physical properties by focusing on their flexibility and additionally stretchability with 7. Conclusions In thisconsiderationInconsideration thisstudy, study, we for for material wehavematerial have presented and and presented cost cost reduction. reduction. a specific a specific More More interiorover,over, interior we we design described described design targeted the the targeted flexibility flexibility for for softof of the the soft3D developed developed 3Dprinted printed In thisIninfillinfill thisstudy, patternspatterns study, we andand wehave highlightedhighlighted have presented presented howhow athethe specific followingafollowing specific interiorinterior fafa ctorsinteriorctors designdesignsuchsuch design asas thetargetedtargetedthe patterntargetedpattern forfor typetype forsoftsoft andand soft3D3D thethe 3D printedprinted elasticelastic printed fabricationsfabrications along along with with specially specially designed designed flexible flexible infill in patterns.fill patterns. 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In tension addition, In addition, and our flexure ourmethod method loadsis specifical is specifical on infilllyly targetedtargetedly patterns. targeted forfor thethefor In FDMFDMthe this FDM 3D3D paper, printingprinting3D printing we technology.technology. did technology. not consider WeWe We recognizerecognizechosenchosen these these alonglimitationsalong limitations withwith anan of appropriateappropriate our of ourstudy. study. pattern patternWe fabricatedWe typetype fabricated accoacco samplesrdingrding samples toto theirbytheir using by elasticelastic using Flashforge properties.properties. Flashforge Finder WeWe Finder believebelieve FDM FDMthisthis 3D 3D recognizerecognizestudystudy these these bringsbrings limitations limitations newnew innovationsinnovations of our of ourstudy. intointo study. softWesoft 3DWefabricated3D printing printingfabricated samples byby providing providingsamples by using by thesethese using Flashforge meaningfulmeaningful Flashforge Finderinsightsinsights Finder FDM intointo FDM thethe 3D 3D experimentsprinter ofprinter overhanging (Zhejiang (Zhejiang Flashforge3D models Flashforge3D and technology models technology with Co., Co., diLTD,China).ff erentLTD,China). thicknesses. The Thepresented presented In addition, method method proved our proved method its its printerprinter (Zhejiangdesigndesign (Zhejiang process.process. Flashforge3D Flashforge3D technology technology Co., Co., LTD,China). LTD,China). The Thepresented presented method method proved proved its its is specificallyefficiency targetedefficiency in a forin number a the number FDM of theof 3D theconducted printing conducted experime technology. experiments. nts.From We From recognizethe thestudy study investigations, these investigations, limitations it can it ofcanbe our be efficiencyefficiency in ain number a number of theof theconducted conducted experime experiments. nts.From From the thestudy study investigations, investigations, it can it canbe be study. We fabricatedconcludedconcluded that samples thatour ourmethod by method using is an is effective Flashforgean effective structural structural Finder design FDM design concept 3D concept printer in which in which (Zhejiang materials materials are Flashforge3D properlyare properly concludedconcluded that thatour ourmethod method is an is effective an effective structural structural design design concept concept in which in which materials materials are properlyare properly chosenchosen along along with with an appropriate an appropriate pattern pattern type type acco accordingrding to their to their elastic elastic properties. properties. We Webelieve believe this this technology Co.,chosenchosen LTD, along China).along with with an The appropriate an presentedappropriate pattern method pattern type type proved acco according itsrding to e ffitheir tociency their elastic elastic in properties. a number properties. We of the Webelieve conductedbelieve this this studystudy brings brings new new innovations innovations into intosoft soft3D printing3D printing by providing by providing these these meaningful meaningful insights insights into intothe the experiments.study Fromstudy brings brings the new study new innovations innovations investigations, into into soft soft3D it printing3D can printing be by concluded providing by providing these that these meaningful our meaningful method insights isinsights an into eff into theective the designdesign process. process. structural designdesigndesign process. concept process. in which materials are properly chosen along with an appropriate pattern type according to their elastic properties. We believe this study brings new innovations into soft 3D printing by providing these meaningful insights into the design process.

Symmetry 2019, 11, 1398 14 of 15

Author Contributions: Conceptualization, K.C.; Funding acquisition, S.-M.C.; Investigation, K.C.; Methodology, K.C.; Project administration, S.-M.C.; Software, K.C.; Supervision, S.-M.C.; Validation, S.-M.C.; Visualization, K.C.; Writing—original draft, K.C.; Writing—review & editing, K.C. and S.-M.C. Funding: This research was funded by Ministry of Science and ICT, Korea: IITP-2019-2016-0-00312. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Liu, X.; Lin, L.; Wu, J.; Wang, W.; Yin, B.; Wang, C.C.L. Generating sparse self-supporting wireframe models for 3D printing using mesh simplification. Graph. Models 2018, 98, 14–23. [CrossRef] 2. Lee, M.; Fang, Q.; Cho, Y.; Ryu, J.; Liu, L.; Kim, D.S. Support-free hollowing for 3D printing via Voronoi diagram of ellipses. Comput. Aided Des. 2018, 101, 23–36. [CrossRef] 3. Hu, J.; Wang, S.; Wang, Y.; Li, F.; Luo, Z. A lightweight methodology of 3D printed objects utilizing multi-scale porous structures. Vis. Comput. 2019.[CrossRef] 4. Feng, J.; Fu, J.; Lin, Z.; Shang, C.; Li, B. A review of the design methods of complex topology structures for 3D printing. Vis. Comput. Ind. Biomed. Art 2018, 1.[CrossRef] 5. Li, D.; Dai, N.; Zhou, X.; Huang, R.; Liao, W. Self-supporting interior structures modeling for buoyancy optimization of computational fabrication. Int. J. Adv. Manuf. Technol. 2017, 95, 825–834. [CrossRef] 6. Wadbro, E.; Niu, B. Multiscale design for additive manufactured structures with solid coating and periodic infill pattern. Comput. Methods Appl. Mech. Eng. 2019, 357, 112605. [CrossRef] 7. Wei, X.R.; Zhang, Y.H.; Geng, G.H. No-infill 3D Printing. 3D Res. 2016, 7.[CrossRef] 8. Moradi, M.; Meiabadi, S.; Kaplan, A. 3D Printed Parts with Honeycomb Internal Pattern by Fused Deposition Modelling; Experimental Characterization and Production Optimization. Met. Mater. Int. 2019.[CrossRef] 9. Kim, J.H.; Kim, G.H. Effect of rubber content on abrasion resistance and tensile properties of thermoplastic polyurethane (TPU)/rubber blends. Macromol. Res. 2014, 22, 523–527. [CrossRef] 10. Grady, B.P.; Cooper, S.L.; Robertson, C.G. Thermoplastic Elastomers. In The Science and Technology of Rubber; Academic Press: Cambridge, MA, USA, 2013; pp. 591–652. 11. Awale, R.; Ali, F.; Azmi, A.; Puad, N.; Anuar, H.; Hassan, A. Enhanced Flexibility of Biodegradable Polylactic Acid/Starch Blends Using Epoxidized Palm Oil as Plasticizer. Polymers 2018, 10, 977. [CrossRef][PubMed] 12. Available online: https://ninjatek.com (accessed on 11 November 2019). 13. Available online: https://www.sainsmart.com (accessed on 11 November 2019). 14. Available online: https://fillamentum.com (accessed on 11 November 2019). 15. Available online: https://www.facebook.com/MadeSolid (accessed on 11 November 2019). 16. Bates, S.R.; Farrow, I.R.; Trask, R.S. Compressive behaviour of 3D printed thermoplastic polyurethane honeycombs with graded densities. Mater. Des. 2018.[CrossRef] 17. Hedayati, R.; Sadighi, M.; Mohammadi Aghdam, M.; Zadpoor, A. Mechanical Properties of Additively Manufactured Thick Honeycombs. Materials 2016, 9, 613. [CrossRef][PubMed] 18. Amiri Moghadam, A.A.; Alaie, S.; Deb Nath, S.; Aghasizade Shaarbaf, M.; Min, J.K.; Dunham, S.; Mosadegh, B. Laser Cutting as a Rapid Method for Fabricating Thin Soft Pneumatic Actuators and Robots. Soft Robot. 2018, 5, 443–451. [CrossRef][PubMed] 19. Martínez, J.; Dumas, J.; Lefebvre, S. Procedural voronoi foams for additive manufacturing. ACM Trans. Graph. 2016, 35, 1–12. [CrossRef] 20. Martínez, J.; Song, H.; Dumas, J.; Lefebvre, S. Orthotropic k-nearest foams for additive manufacturing. ACM Trans. Graph. 2017, 36, 121. [CrossRef] 21. Available online: https://ultimaker.com/en/products/ultimaker-cura-software (accessed on 11 November 2019). 22. Available online: http://www.kisslicer.com/ (accessed on 11 November 2019). 23. Available online: https://slic3r.org/ (accessed on 11 November 2019). 24. Chynybekova, K.; Choi, S.M. Multilevel Design for the Interior of 3D Fabrications. Symmetry 2019, 11, 1029. [CrossRef] 25. Wang, W.; Wang, T.Y.; Yang, Z.; Liu, L.; Tong, X.; Tong, W.; Deng, J.; Chen, F.; Liu, X. Cost-effective printing of 3D objects with skin-frame structures. ACM Trans. Graph. 2013, 32, 177:1–177:10. [CrossRef] 26. Lu, L.; Sharf, A.; Zhao, H.; Wei, Y.; Fan, Q.; Chen, X.; Savoye, Y.; Tu, C.; Cohen-Or, D.; Chen, B. Build-to-last: Strength to weight 3D printed objects. ACM Trans. Graph. 2014, 33, 97:1–97:10. [CrossRef] Symmetry 2019, 11, 1398 15 of 15

27. Sa, A.M.; Mello, V.M.; Rodriguez Echavarria, K.; Covill, D. Adaptive Voids Primal and Dual Adaptive Cellular Structures for Additive Manufacturing. Vis. Comput. 2015, 31, 799–808. 28. Li, D.; Dai, N.; Jiang, X.; Jiang, X.; Chen, X. Interior structural optimization based on the density-variable shape modeling of 3D printed objects. Int. J. Adv. Manuf. Technol. 2016, 83, 1627–1635. [CrossRef] 29. Nguyen, D.S.; Vignat, F. A method to generate lattice structure for Additive Manufacturing. In Proceedings of the 2016 IEEE International Conference on Industrial Engineering Engineering Management (IEEM), Bali, Indonesia, 4–7 December 2016. [CrossRef] 30. Chen, Y. A Mesh-Based Geometric Modeling Method for General Structures. In Proceedings of the 26th Computers and Information in Engineering Conference, Philadelphia, PA, USA, 10–13 September 2006. [CrossRef] 31. Tang, Y.; Kurtz, A.; Zhao, Y.F. Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing. Comput. Aided Des. 2015, 69, 91–101. [CrossRef] 32. Aremu, A.O.; Brennan-Craddock, J.P.J.; Panesar, A.; Ashcroft, I.A.; Hague, R.J.; Wildman, R.D.; Tuck, C. A voxel-based method of constructing and skinning conformal and functionally graded lattice structures suitable for additive manufacturing. Addit. Manuf. 2017, 13, 1–13. [CrossRef] 33. Wu, J. Continuous Optimization of Adaptive Quadtree Structures. In Proceedings of the TU Delft. Solid and Physical Modeling-SPM 2018, Bilbao, Spain, 11–13 June 2018. 34. Wu, J.; Clausen, A.; Sigmund, O. Minimum compliance topology optimization of shell–infill composites for additive manufacturing. Comput. Methods Appl. Mech. Eng. 2017, 326, 358–375. [CrossRef] 35. Wu, J.; Wang, C.C.L.; Zhang, X.; Westermann, R. Self-supporting rhombic infill structures for additive manufacturing. Comput. Aided Des. 2016, 80, 32–42. [CrossRef] 36. Tim, A.; Puentesa, J.; Kattingerb, J. Fused filament fabrication melting model. Addit. Manuf. 2018, 22, 51–59. 37. Rosenthal, M.; Henneberger, C.; Gutkes, A.; Bues, C.T. Liquid Deposition Modeling—A promising approach for 3D printing of wood. Eur. J. Wood Wood Prod. 2018, 76, 797–799. [CrossRef] 38. Heimbs, S.; Schmeer, S.; Middendorf, P.; Maier, M. Strain rate effects in phenolic composites and phenolic-impregnated honeycomb structures. Compos. Sci. Technol. 2007, 67, 2827–2837. [CrossRef] 39. Mukhopadhyay, T.; Adhikari, S. Equivalent in-plane elastic properties of irregular honeycombs: An analytical approach. Int. J. Solid Struct. 2016, 91, 169–184. [CrossRef]

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