Finite Element Modeling in the Design Process of 3D Printed Pneumatic Soft Actuators and Sensors

robotics

Article Finite Element Modeling in the Design Process of 3D Printed Pneumatic Soft Actuators and Sensors

Charbel Tawk 1,2 and Gursel Alici 1,2,*

1 School of Mechanical, Materials, Mechatronic and Biomedical Engineering, and Applied Mechatronics and Biomedical Engineering Research (AMBER) Group, University of Wollongong, Northﬁelds Ave, Wollongong, NSW 2522, Australia; [email protected] 2 ARC Centre of Excellence for Electromaterials Science, University of Wollongong Innovation Campus, North Wollongong, NSW 2500, Australia * Correspondence: [email protected]

Received: 27 May 2020; Accepted: 6 July 2020; Published: 7 July 2020

Abstract: The modeling of soft structures, actuators, and sensors is challenging, primarily due to the high nonlinearities involved in such soft robotic systems. Finite element modeling (FEM) is an effective technique to represent soft and deformable robotic systems containing geometric nonlinearities due to large mechanical deformations, material nonlinearities due to the inherent nonlinear behavior of the materials (i.e., stress-strain behavior) involved in such systems, and contact nonlinearities due to the surfaces that come into contact upon deformation. Prior to the fabrication of such soft robotic systems, FEM can be used to predict their behavior efficiently and accurately under various inputs and optimize their performance and topology to meet certain design and performance requirements. In this article, we present the implementation of FEM in the design process of directly three-dimensional (3D) printed pneumatic soft actuators and sensors to accurately predict their behavior and optimize their performance and topology. We present numerical and experimental results to show that this approach is very effective to rapidly and efficiently design the soft actuators and sensors to meet certain design requirements and to save time, modeling, design, and fabrication resources.

Keywords: additive manufacturing; ﬁnite element modeling; design optimization; soft robotics; soft sensors; soft actuators; 3D printing

1. Introduction Soft robots are ideal to interact safely with humans and operate in highly dynamic environments since they are made of excessively deformable and stretchable materials [1,2]. The development of these soft systems is inspired by soft biological structures present in nature, such as an elephant trunk, octopus arm, squid tentacles, and worms that are made mostly of compliant materials and liquids [3]. The structures, actuators, sensors, electronics, and power sources of a soft robotic system should primarily be made of soft materials [4]. However, the realization of completely soft robots remains a great challenge for scientists and engineers. The soft actuators and sensors involved in every soft robotic system are the major and critical components that make such systems functional and useful. Soft robots demand dexterous soft actuators that can generate relatively low and high forces (i.e., controllable forces) to facilitate soft and adaptive interaction with their environments [5]. In addition, soft robots require robust ﬂexible, stretchable, or compressive soft sensors that can sustain large deformations repeatedly over sustained periods, while providing consistent output signals [6]. Such reliable and stable sensors are essential for soft robots to develop reliable feedback control systems [7,8].

Robotics 2020, 9, 52; doi:10.3390/robotics9030052 www.mdpi.com/journal/robotics Robotics 2020, 9, 52 2 of 14

The soft robotics field has grown hugely in recent years during which many untethered soft robots have been developed [9]. In addition to being safe to interact directly with humans and delicate objects, soft robots have multiple advantages compared to conventional robotic systems. First, soft robots are made of low-cost soft materials that make them accessible and affordable [1]. Second, soft robots are made of soft monolithic bodies. Therefore, these systems require minimal or no assembly processes in some cases. Third, soft robots can be directly fabricated using various three-dimensional (3D) printing technologies in addition to conventional manufacturing techniques [10–14]. Fourth, soft robotic systems can be used and implemented in diverse robotic applications, such as locomotion robots, adaptive grippers, artificial muscles, parallel manipulators, prostheses, robotic hands, human-machine interfaces, and many others [5]. Finally, the compliance of soft robots makes them ideal for handling extreme external mechanical deformations [15] without any damage and for manipulating delicate and fragile objects without damaging them [16]. In general, the development of soft robots relies heavily on experimental results and prototyping [17,18]. Although the soft robotics field has several advantages to offer various solutions to applications requiring human-robot interaction, this field still faces limitations in terms of modeling, design optimizing, and fabricating soft bodies, especially when it comes to designing automation tools [19]. Modeling is critical for the design and development of novel soft robots [10]. Since it is very challenging to derive analytical models [20] for soft robots, due to nonlinearities, numerical methods are used instead [10]. Finite element modeling (FEM) is one approach to model and simulate soft robotic components. For instance, the mechanical and/or electrical behavior of soft sensors [21,22] can be predicted and/or optimized using FEM. However, the implementation of FEM can be challenging. The main reason is that the FEM of soft robotic actuators and sensors involves multiple nonlinearities, including geometric nonlinearities, material nonlinearities, and contact nonlinearities, resulting from different surfaces coming into contact upon deforming a soft body. Additionally, soft robots are usually made of complex geometries (i.e., complicated topologies). The FEM of soft systems is used for several important reasons [23]. First, the behavior of soft robotic systems can be accurately predicted under a specific input (i.e., pressure, displacement, etc.). Second, the performance of soft robotic systems can be quickly predicted and optimized accurately before their fabrication [24,25]. Therefore, the simulations save huge amounts of time and potential fabrication resources. Third, the geometry or topology of soft robotic devices can be optimized and modified to meet certain design or performance requirements [23]. Fourth, the simulations can be used to iterate rapidly and efficiently between several designs to optimize their behavior and performance. Finally, FEM can be efficiently used to accurately control soft robotic systems [8,26] in real-time [27,28]. There are several FEM software that use hyper-elastic material models to perform highly nonlinear simulations to predict and optimize the performance of soft robots, such as SOFA [29], Abaqus (Dassault Systèmes Simulia Corp., Waltham, MA, USA) [30], COMSOL Multiphysics® [31] and ANSYS (ANSYS Inc., Canonsburg, PA, USA) [32]. In addition, there are several other methods to model soft robotic systems, including lumped parameter modeling [33], point-lattices connected by linear beam elements [34], and Cosserat elements [35]. In this work, FEM is used in the design process of directly 3D printed soft pneumatic actuators and sensors to efficiently and accurately predict their behavior under various inputs and to optimize their performance and geometry to meet certain design and performance requirements before their fabrication. This work focuses specifically on how a commercial FEM tool can be used to design and optimize soft and 3D printable pneumatic actuators and sensors. A hyper-elastic materials model is developed for use in FE simulations, based on the experimental stress-strain data of the soft 3D printable material used to 3D print the actuators and sensors. The FEM results, in all cases, are validated using experimental data and only the final optimized designs are presented. This work presents a roadmap on how to implement FEM in the design process of soft pneumatic actuators and sensors using a commercially available FE analysis software. In addition, it presents the challenges encountered Robotics 2020, 9, 52 3 of 14 in simulating soft bodies and provides some useful recommendations for successfully simulating suchRobotics bodies. 2020, 9, x FOR PEER REVIEW 3 of 14

2. Design Process The designdesign processprocess starts starts with with modeling modeling the the 3D 3D computer-aided computer–aided design design (CAD) (CAD) models models of the of softthe actuatorssoft actuators and sensors,and sensors as shown, as shown in Figure in Figure1. The 1. structures The structures are designed are designed so that theyso that can they be 3D can printed be 3D usingprinted aﬀ usingordable affordable and accessible and accessible fused deposition fused deposition modeling modeling (FDM) 3D (FDM) printers 3D withoutprinters usingwithout support using materialssupport materials and postprocessing. and postprocessing. Additionally, Additionally the soft material, the soft used material to 3D print used the to soft 3D printactuators the and soft sensorsactuators is and characterized sensors is tocharacterized extract its stress-strainto extract its data stress that–strain can bedata used that to can develop be used a hyper-elasticto develop a materialhyper-elastic model material for use model in FE simulations. for use in FE Afterwards, simulations. the Afterward designeds CAD, the modelsdesigned are CAD imported models to theare FEMimported software to the along FEM withsoftware the material along with model the material developed model to simulate developed the to soft simulate actuators the and soft sensors actuato tors predictand sensors their to behavior predict andtheir optimize behavior their and optimize performance. their Basedperformance. on the FEMBased results, on the theFEM CAD results models, the areCAD modiﬁed, models and are their modified, simulation and is their repeated simulation accordingly is repeated until the desired accordingly performance until the is achieved desired beforeperformance their fabrication. is achieved Once before the desired their fabrication. or optimized Once performance the desire isd obtained, or optimized the 3D performance CAD models is areobtained sliced, inthe 3D 3D printing CAD models commercial are sliced slicing in software 3D printing where commercial the printing slicing parameters software are optimizedwhere the toprinting fabricate parameters airtight and are functional optimized soft to fabricate actuators airtight and sensors. and functional Finally, the soft fabricated actuators prototypes and sensors. are characterizedFinally, the fabricated to assess prototypes their experimental are characterized performance to assess and to their compare experimental it with its performance FEM counterpart and to verifycompare and it validatewith its theFEM simulation counterpart results. to verify and validate the simulation results.

Figure 1. The design process for simulating and fabricating airtight and optimized soft 3D printable pneumatic actuators and sensors.sensors.

3. Materials and Methods

3.1. Materials, Models, and 3D Printing Technology 3.1. Materials, Models, and 3D Printing Technology A thermoplastic poly(urethane) (TPU) (TPU),, known commercially as NinjaFlex (NinjaTek, (NinjaTek, Manheim, Pennsylvania, PA, PA, U.S.A. U.S.A.),), was was used used to to 3D 3D print print the the soft soft pneumatic pneumatic actuators actuators and andsensors sensors using using low- low-costcost and andopen open-source-source FDM FDM 3D 3Dprinters printers (FlashForge (FlashForge Creator Creator Pro; Pro; FlashForge FlashForge Inventor, Inventor, FlashForge Corporation,Corporation, Hangzhou,Hangzhou, ZheJiang Province, China). The actuators and sensors were modeled using CAD software software (Dassault (Dassault Syst Syèstèmes,mes, SOLIDWORKS SOLIDWORKS Corp., Corp. Waltham,, Waltham, Massachusetts, Massachusetts, MA, U.S.A.; MA, U.S.A.Fusion; 360,Fusion Autodesk 360, Autodesk Inc., San Inc.Rafael,, San CA, Rafael, U.S.A.). CA, The U.S.A.). 3D CAD The models 3D CAD were models sliced usingwere asliced commercially using a availablecommercially slicer available (Simplify3D, slicer Simplify3D(Simplify3D, Inc., Simplify3D Cincinnati, Inc. OH,, Cincinnati U.S.A.)., OH, The U.S.A.) 3D printing. The 3D parameters printing wereparameters optimized were in optimized the slicer in to the 3D printslicer completelyto 3D print airtight,completely reliable, airtight, and reliable, functional and softfunctional pneumatic soft actuatorspneumatic and actuators sensors and [32 ,sensors36–38]. [32,36–38].

3.2. TPU Stress–Strain Data The stress–strain relationship of the TPU used was extracted to assess its behavior using an experimental uniaxial tensile test. Eight TPU samples were printed using a longitudinal infill pattern and another eight samples were printed using a crosswise infill pattern to assess the effect of different

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Robotics 2020, 9, x FOR PEER REVIEW 4 of 14 3.2. TPU Stress-Strain Data infillThe patterns stress-strain on the relationshipbehavior of the of theTPU. TPU The used two wasinfill extracted patterns had to assess an insignificant its behavior effect using on anthe experimentalaverage stress uniaxial–strain tensiledata of test.the TPU, Eight as TPU shown samples in Figure were 2. printed using a longitudinal infill pattern and anotherThe tests eight were samples conducted were printedon the TPU using samples a crosswise, according infill pattern to the toISO assess 37 standard, the effect where of diff erentall the infillsamples patterns were on stretched the behavior by 800% of the at a TPU. rate Theof 100mm/s two infill using patterns an electromechanical had an insignificant Instron effect Universal on the averageTesting stress-strain machine (Instron8801 data of the, Instron, TPU, as Norwood, shown in FigureMA, U.S.A.).2.

FigureFigure 2. 2.Experimental Experimental stress-strain stress–strain data data of theof t TPUhe TPU used used to 3D to print 3D print the soft the pneumaticsoft pneumatic actuators actuators and sensors.and sensors. Inset: Inset: Longitudinal Longitudinal sample sample (top) and(top) crosswise and crosswise sample sample (bottom). (bottom).

4. 3TheD Printable tests were Soft conducted Actuators on and the Sensors TPU samples, according to the ISO 37 standard, where all the samples were stretched by 800% at a rate of 100mm/s using an electromechanical Instron Universal Testing4.1. Bending machine Soft (Instron8801, Vacuum Actuators Instron, (SOVA) Norwood, MA, U.S.A.). Bioinspired bending soft vacuum actuators are developed for use in diverse soft robotic 4. 3D Printable Soft Actuators and Sensors applications, including locomotion robots, adaptive grippers, artificial muscles, and modular soft 4.1.robotic Bending pneumatic Soft Vacuum hinges Actuators [32]. A single (SOVA) SOVA is shown in Figure 3. The SOVA actuators are activated using negative pressure (i.e., 90% vacuum). When negative pressure is applied to the actuator, consistingBioinspired of five bending pneuma softtic bending vacuum hinges actuators, it generates are developed a bending for motion, use in as diverse shown soft in Figure robotic 3. applications,The objective including of the FE simulations locomotion was robots, to design adaptive a single grippers, chamber artificial that could muscles, achieve and a modularbending angle soft robotichigher pneumatic than 80° when hinges 90% [32 vacuum]. A single was SOVA applied. is shown The geometry in Figure of3. a The single SOVA chamber actuators was are modified activated and usingoptimized negative to achieve pressure this (i.e., bending 90% angle vacuum). when When 90% vacuum negative wa pressures applied. is applied to the actuator, consisting of five pneumatic bending hinges, it generates a bending motion, as shown in Figure3. The objective of the FE simulations was to design a single chamber that could achieve a bending angle higher than 80◦ when 90% vacuum was applied. The geometry of a single chamber was modified and optimized to achieve this bending angle when 90% vacuum was applied.

4.2. Linear Soft Vacuum Actuators (LSOVA) Similarly, linear soft vacuum actuators are developed for use in diverse soft robotic applications, including locomotion robots, adaptive grippers, artificial muscles, parallel manipulators, and soft prosthetic fingers [36,37]. A single LSOVA actuator, consisting of five pneumatic chambers, is shown in FigureFigure4. The 3. Bending objective soft of vacuum the FE actuators simulations (SOVA). was The to design initial position a single of chamber a single SOVA that could actuator generate when a maximum(a) no linear vacuum displacement is applied and under (b) its an corresponding applied negative final pressureposition when (i.e., 95.7%90% vacuum vacuum). is applied. The thickness of the thin walls and the topology of a single chamber were optimized to achieve the desired performance.4.2. Linear Soft The Vacuum wall thicknessActuators (LSOVA) played an important role in the design process since it is directly related to the airtightness of the 3D printed LSOVA actuators. Similarly, linear soft vacuum actuators are developed for use in diverse soft robotic applications, including locomotion robots, adaptive grippers, artificial muscles, parallel manipulators, and soft prosthetic fingers [36,37]. A single LSOVA actuator, consisting of five pneumatic chambers, is shown in Figure 4. The objective of the FE simulations was to design a single chamber that could generate a

Robotics 2020, 9, x FOR PEER REVIEW 4 of 14 infill patterns on the behavior of the TPU. The two infill patterns had an insignificant effect on the average stress–strain data of the TPU, as shown in Figure 2. The tests were conducted on the TPU samples, according to the ISO 37 standard, where all the samples were stretched by 800% at a rate of 100mm/s using an electromechanical Instron Universal Testing machine (Instron8801, Instron, Norwood, MA, U.S.A.).

Figure 2. Experimental stress–strain data of the TPU used to 3D print the soft pneumatic actuators and sensors. Inset: Longitudinal sample (top) and crosswise sample (bottom).

4. 3D Printable Soft Actuators and Sensors

4.1. Bending Soft Vacuum Actuators (SOVA) Bioinspired bending soft vacuum actuators are developed for use in diverse soft robotic applications, including locomotion robots, adaptive grippers, artificial muscles, and modular soft robotic pneumatic hinges [32]. A single SOVA is shown in Figure 3. The SOVA actuators are activated using negative pressure (i.e., 90% vacuum). When negative pressure is applied to the actuator, consisting of five pneumatic bending hinges, it generates a bending motion, as shown in Figure 3. The objective of the FE simulations was to design a single chamber that could achieve a bending angle higherRobotics 2020than, 9 80°, 52 when 90% vacuum was applied. The geometry of a single chamber was modified5 and of 14 optimized to achieve this bending angle when 90% vacuum was applied.

Robotics 2020, 9, x FOR PEER REVIEW 5 of 14 maximum linear displacement under an applied negative pressure (i.e., 95.7% vacuum). The thickness of the thin walls and the topology of a single chamber were optimized to achieve the desired performance.Figure 3. Bending BendingThe wall soft soft thickness vacuum vacuum actuators actuatorsplayed an(SOVA). (SOVA). important The initial initial role position positionin the designof of a a single single process SOVA SOVA sinceactuator it iswhen directly related(a) tono thevacuum airtightness is applied of and the ( b3D) its printed corresponding LSOVA ﬁnalfinal actuators. positionposition whenwhen 90%90% vacuumvacuum isis applied.applied.

Figure 4. LinearLinear soft soft v vacuumacuum actuators actuators (LSOVA). (LSOVA). The initial position of a a single single LSOVA LSOVA actuator when (a) no vacuum is applied andand ((b)) itsits correspondingcorresponding ﬁnalfinal positionposition whenwhen 95.7%95.7% vacuumvacuum isis applied.applied.

4.3. Soft Pneumatic Sensing Chambers (SPSC) Soft pneumatic sensing chambers (SPSCs (SPSCs),), that are sensitive to the four main mechanical input modalities of of compression, compression, bending, bending, torsion, torsion, and and rectilinear rectilinear displacement displacement,, are are developed developed for for use use in indiverse diverse robotic robotic applications applications,, such such as soft as softtouch touch human human-machine–machine interfaces, interfaces, soft softwearable wearable gloves, gloves, soft softcontrollers controllers and andthrottles, throttles, and andsoft bending soft bending sensors. sensors. The distinct The distinct SPSCs SPSCs are shown are shown in Figure in Figure 5. The5. Themain main objective objective of the of theFE FEsimulations simulations was was to tomodify modify and and optimize optimize the the topology topology of of the the various various SPSCs to obtain a linear relationship between the applied input mechanical loads and the output change in their internal volume [38] [38].. This This linearity linearity means means that that the the sensors sensors can can be be directly directly 3D 3D printed printed and and used. used. The relationship between the input displacement and output pressure can be obtained by using two experimental data points and and,, consequently consequently,, can be used consistently since the SPSCs are stable over time, reliable, and repeatable. Therefore, Therefore, there there is is no no need for an empirical formula that requires an experimental evaluation using a specific speciﬁc experimental setup to obtain and describe the relationship between the inputinput displacementdisplacement andand the the output output pressure pressure for for each each 3D 3D printed printed SPSC. SPSC. Linearity Linearity is oneis one of theof the desired desired performance performance metrics metrics for for actuators actuators and and sensors. sensors.

Figure 5. Soft pneumatic sensing chambers (SPSCs). 3D printed (a) Push Button (i.e., touch sensor), (b) Linear Sensor, (c) Bending Sensor, and (d) Torsional Sensor.

5. Finite Element Modeling The FE diagram that shows and describes all the steps involved in a single simulation of a soft pneumatic actuator or sensor is shown in Figure 6.

Robotics 2020, 9, x FOR PEER REVIEW 5 of 14 maximum linear displacement under an applied negative pressure (i.e., 95.7% vacuum). The thickness of the thin walls and the topology of a single chamber were optimized to achieve the desired performance. The wall thickness played an important role in the design process since it is directly related to the airtightness of the 3D printed LSOVA actuators.

Figure 4. Linear soft vacuum actuators (LSOVA). The initial position of a single LSOVA actuator when (a) no vacuum is applied and (b) its corresponding final position when 95.7% vacuum is applied.

4.3. Soft Pneumatic Sensing Chambers (SPSC) Soft pneumatic sensing chambers (SPSCs), that are sensitive to the four main mechanical input modalities of compression, bending, torsion, and rectilinear displacement, are developed for use in diverse robotic applications, such as soft touch human–machine interfaces, soft wearable gloves, soft controllers and throttles, and soft bending sensors. The distinct SPSCs are shown in Figure 5. The main objective of the FE simulations was to modify and optimize the topology of the various SPSCs to obtain a linear relationship between the applied input mechanical loads and the output change in their internal volume [38]. This linearity means that the sensors can be directly 3D printed and used. The relationship between the input displacement and output pressure can be obtained by using two experimental data points and, consequently, can be used consistently since the SPSCs are stable over time, reliable, and repeatable. Therefore, there is no need for an empirical formula that requires an experimental evaluation using a specific experimental setup to obtain and describe the relationship betweenRobotics 2020 the, 9 ,input 52 displacement and the output pressure for each 3D printed SPSC. Linearity is6 one of 14 of the desired performance metrics for actuators and sensors.

FigureFigure 5. SoftSoft pneumatic pneumatic sensing sensing chambers chambers (SPSC (SPSCs).s). 3D 3D printed printed ( (aa)) Push Push Button Button (i.e., (i.e., touch touch sensor), sensor), ((b)) Linear Linear Sensor, Sensor, (c) Bending Sensor, andand ((dd)) TorsionalTorsional Sensor.Sensor.

5.5. Finite Finite Element Element Modeling Modeling TheThe FE FE diagram that that shows shows and and describes describes all all the the steps steps involved involved in in a a single single simulation simulation of of a a soft soft pneumaticRobotics 2020 actua actuator, 9, x FORtor PEERor sensor REVIEW is shown in Figure 6 6.. 6 of 14

FigureFigure 6. 6.Finite Finite elementelement simulationssimulations diagram for pneumatic pneumatic soft soft actuators actuators and and sensors. sensors.

5.1.5.1. FEM FEM Software Software TheThe FE FE simulations simulations were we performedre performed in ANSYS in ANSYS Workbench Workbench (ANSYS (ANSYS Inc.) using Inc.) a using“Static a Structural “Static Analysis”.Structural Analysis”. The 3D CAD The models3D CAD of models the soft of actuators the soft actuators and sensors and (i.e.,sensors geometries) (i.e., geometries) were directly were importeddirectly to imported ANSYS “Designto ANSYS Modeler”. “Design Here, Modeler”. ANSYS Here, was used ANSYS to performwas used the FEto simulationsperform the of FE the softsimulations actuators of and the sensorssoft actuators presented, and sensors since it presented oﬀers various, since hyper-elasticit offers various materials hyper-elastic models materials and it is idealmodels for performingand it is ideal static for performing structural simulations static structural using simulations hyper-elastic using materials. hyper-elastic materials.

5.2.5.2. Material Material Model Model TheThe average average experimental experimental stress-strainstress–strain datadata of the TPU w wereere imported imported and and used used in in a amanually manually defineddefined material material (i.e., (i.e., NinjaFlex)NinjaFlex) inin thethe “Engineering“Engineering Data”. The The data data were were imported imported as as “Uniaxial “Uniaxial TestTest Data” Data” for for the the “Hyperelastic “Hyperelastic ExperimentalExperimental Data”.Data”. The TPU TPU wa wass modeled modeled using using a afive five-parameter-parameter Mooney-RivlinMooney–Rivlin hyper-elastic hyper-elastic material material model model that thatfitted fitted its average its average stress-strain stress– data.strain The data. five-parameter The five- parameter Mooney–Rivlin model was chosen since it best fitted the TPU experimental data compared to other available models, such as Neo–Hookean, Yeoh, and Ogden. The parameters of the material model are listed in Table 1. The model was fitted to the experimental stress–strain data using the available curve fitting tools in ANSYS.

Table 1. TPU hyper-elastic material model constants.

Hyper-elastic Material Model Material Constant Value (Unit) C10 −0.233 (MPa) C01 2.562 (MPa) Five-parameter(chenchen) C20 0.116 (MPa) Mooney-Rivlin C11 −0.561 (MPa) C02 0.900 (MPa) Incompressibility Parameter D1 0.000MPa−1

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Mooney-Rivlin model was chosen since it best fitted the TPU experimental data compared to other available models, such as Neo-Hookean, Yeoh, and Ogden. The parameters of the material model are listed in Table1. The model was fitted to the experimental stress-strain data using the available curve fitting tools in ANSYS.

Table 1. TPU hyper-elastic material model constants.

Hyper-Elastic Material Model Material Constant Value (Unit) C10 0.233 (MPa) − C01 2.562 (MPa) Five-parameter C20 0.116 (MPa) Mooney-Rivlin C11 0.561 (MPa) − C02 0.900 (MPa) 1 Incompressibility Parameter D1 0.000 MPa−

5.3. Meshing The CAD models of the soft actuators and sensors are meshed using an adaptive mesh with higher-order tetrahedral elements. A sizing function is applied when necessary to obtain a mesh with a speciﬁc element size. The mesh used in all cases is suitable for hyper-elastic materials. Since such materials can undergo large deformations, a very ﬁne mesh is not recommended. A relatively coarse mesh is desired for convergence. The mesh size is carefully studied and selected to ensure that the solution is not dependent on it.

5.4. Analysis Settings The “Large Deformation” option is activated in all the performed simulations to account for the large deﬂections exhibited by the soft structures upon activation. Additionally, a speciﬁc number of “Substeps” of 20 is imposed in each simulation to apply the loads gradually. This is an important parameter to consider since it prevents the load from being applied in one step which, in most cases, results in convergence issues, especially when dealing with soft materials that have a relatively low Young’s modulus.

5.5. Contacts Frictional contact pairs are deﬁned between all the surfaces that come into contact upon deformation. The behavior of the contacts is set to “Symmetric” to minimize penetration, which results in more accurate results and realistic behavior. The “Augmented Lagrange” formulation is used since it is suitable for frictional and self-contacts.

5.6. Boundary Conditions In addition to the contact pairs defined in all the structures, for SOVA, a “Fixed Support” boundary condition is applied to their base to fix them and a negative pressure (up to 90% vacuum) is applied to the internal surfaces of their hollow chambers. Similarly, for LSOVA, a “Fixed Support” is applied to their base and a negative pressure (up to 95.7% vacuum) is applied to the internal surfaces of their hollow chambers. The FEM and experimental boundary conditions applied to the various SPSCs are shown in Figure7. A “Fixed Support” is defined on one side of each structure and an appropriate “Displacement Support” (i.e., a linear or rotational displacement) is imposed on their opposite ends to simulate the mechanical deformations applied for each mode of deformation, as shown in Figure7. Robotics 2020, 9, x FOR PEER REVIEW 7 of 14 a specific element size. The mesh used in all cases is suitable for hyper-elastic materials. Since such materials can undergo large deformations, a very fine mesh is not recommended. A relatively coarse mesh is desired for convergence. The mesh size is carefully studied and selected to ensure that the solution is not dependent on it.

5.4. Analysis Settings The “Large Deformation” option is activated in all the performed simulations to account for the large deflections exhibited by the soft structures upon activation. Additionally, a specific number of “Substeps” of 20 is imposed in each simulation to apply the loads gradually. This is an important parameter to consider since it prevents the load from being applied in one step which, in most cases, results in convergence issues, especially when dealing with soft materials that have a relatively low Young’s modulus.

5.5. Contacts Frictional contact pairs are defined between all the surfaces that come into contact upon deformation. The behavior of the contacts is set to “Symmetric” to minimize penetration, which results in more accurate results and realistic behavior. The “Augmented Lagrange” formulation is used since it is suitable for frictional and self-contacts.

5.6. Boundary Conditions In addition to the contact pairs defined in all the structures, for SOVA, a “Fixed Support” boundary condition is applied to their base to fix them and a negative pressure (up to 90% vacuum) is applied to the internal surfaces of their hollow chambers. Similarly, for LSOVA, a “Fixed Support” is applied to their base and a negative pressure (up to 95.7% vacuum) is applied to the internal surfacesRobotics 2020 of, 9their, 52 hollow chambers. The FEM and experimental boundary conditions applied to8 ofthe 14 various SPSCs are shown in Figure 7.

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5.7. FEM Results Figure 7. The applied boundary conditions on each SPSC. ( a)) The p pushush button is activated through a solidVarious rotating important crank that res pushes ults can through be effectively its soft deformable used to assess wall. and( b) The interpret linear sensor the simulation is attached of to a soft bodya, motoras shown that in generates Figure a 6. rectilinear The total stroke.deformation ( (cc)) The The isbending bending the result sensor sensor of theis is attached attached load applied to to a a soft to flexure flexurea soft bodyjoint and it showsthat generates generateshow the bodya a bending bending is deformed angle angle between between at different 0° 0 and◦ and 90°stages 90 when◦ when of a the tendon a tendonload is applied pulled is pulled using, as usingshown a linear a linearin motor. Figure motor. (d 8.) This deformation(Thed) The torsional torsional can sensorbe sensordirectly is attached is attached compared to a to servo a servowith motor motorits thatexperimental that generates generates an counterpart anangular angular displacement displacementto verify betweenit. betweenThe volume0° changeand0◦ and 90°. of 90the ◦. various SPSC was assessed at different stages of the applied load to obtain a relationship between this change and the applied mechanical load, as shown in Figure 9. As stated 5.7. FEMA “Fixed Results Support” is defined on one side of each structure and an appropriate “Displacement earlier, the aim was to obtain a linear relationship between the applied mechanical loads and the Support” (i.e., a linear or rotational displacement) is imposed on their opposite ends to simulate the changeVarious in their important internal results volume. can Ideally, be effectively a relationship used to assess exists and between interpret the the change simulation in the of internal a soft mechanicalbody, as shown deformations in Figure applied6. The totalfor each deformation mode of deformation, is the result ofas shown the load in appliedFigure 7. to a soft body volume (V1/V2) of the soft chambers and the experimental pressure change (P1V1 = P2V2), obtained anddue itto shows the mechanical how the bodydeformation is deformed applied. at di fferent stages of the load applied, as shown in Figure8. This deformationAdditionally can, the be blocked directly force compared, which with is itsthe experimental reaction force counterpart obtained towhen verify the it. actuators The volume are changeactivated of the but various restricted SPSC from was assessed moving at at di ff botherent sides stages, can of the be applied computed load to and obtain compared a relationship to its betweenexperimental this change counterpart and the to appliedverify it mechanical, as shown load,in Figure as shown 10. This in Figurereaction9. Asforce stated is a earlier,measure the of aim the wasoutput to obtainforce that a linear a soft relationshipactuator can betweengenerate. the applied mechanical loads and the change in their internalFinally, volume. the Ideally,stresses a and relationship strain resulting exists between from the the load change applied in the can internal be assessed volume as (V presented1/V2) of the in softTable chambers 2. These and two the parameters experimental are pressure very important change (P since1V1 = theyP2V should2), obtained be minimized due to the asmechanical much as deformationpossible to enhance applied. the lifetime of the soft actuators and sensors developed.

FigureFigure 8.8. FEMFEM deformed deformed shape shape for fo (ra )(a SOVA) SOVA when when 90% 90% vacuum vacuum is applied is applied and (band) LSOVA (b) LSOVA when 95.7%when vacuum95.7% vacuum is applied. is applied.

Figure 9. FEM deformed shape for (a) the push button when 24.5° remote rotating displacement is applied on the crank which not shown for visual purposes, (b) linear sensor when a 10 mm displacement is applied, (c) bending sensor when a 90° bending angle is applied by pulling the tendon, and (d) torsional sensor when a 90° remote rotating displacement is applied on its end.

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5.7. FEM Results Various important results can be effectively used to assess and interpret the simulation of a soft body, as shown in Figure 6. The total deformation is the result of the load applied to a soft body and it shows how the body is deformed at different stages of the load applied, as shown in Figure 8. This deformation can be directly compared with its experimental counterpart to verify it. The volume change of the various SPSC was assessed at different stages of the applied load to obtain a relationship between this change and the applied mechanical load, as shown in Figure 9. As stated earlier, the aim was to obtain a linear relationship between the applied mechanical loads and the change in their internal volume. Ideally, a relationship exists between the change in the internal volume (V1/V2) of the soft chambers and the experimental pressure change (P1V1 = P2V2), obtained due to the mechanical deformation applied. Additionally, the blocked force, which is the reaction force obtained when the actuators are activated but restricted from moving at both sides, can be computed and compared to its experimental counterpart to verify it, as shown in Figure 10. This reaction force is a measure of the output force that a soft actuator can generate. Finally, the stresses and strain resulting from the load applied can be assessed as presented in Table 2. These two parameters are very important since they should be minimized as much as possible to enhance the lifetime of the soft actuators and sensors developed.

RoboticsFigure2020, 9 8., 52 FEM deformed shape for (a) SOVA when 90% vacuum is applied and (b) LSOVA when9 of 14 95.7% vacuum is applied.

Figure 9. FEM deformed shape for (a) the push button when 24.5° remote rotating displacement is Figure 9. FEM deformed shape for (a) the push button when 24.5◦ remote rotating displacement is appliedapplied on on the the crank crank which which not shown not shown for visual for purposes, visual purposes, (b) linear ( sensorb) linear when sensor a 10 mmwhen displacement a 10 mm

isdisplacement applied, (c) bendingis applied, sensor (c) bending when a sensor 90◦ bending when angle a 90° isbending applied angle by pulling is applied the tendon, by pulling and the(d) torsionaltendon, and sensor (d) whentorsional a 90 sensor◦ remote when rotating a 90° displacementremote rotating is applieddisplacement on its end.is applied on its end.

Additionally, the blocked force, which is the reaction force obtained when the actuators are activated but restricted from moving at both sides, can be computed and compared to its experimental counterpart to verify it, as shown in Figure 10. This reaction force is a measure of the output force that a soft actuator can generate. Robotics 2020, 9, x FOR PEER REVIEW 9 of 14

Figure 10. 10. SOVASOVA and and LSOVA LSOVA blocked blocked force. force. (a) SOVA (a) SOVA FEM deformedFEM deformed shape results shape (i.e., results SOVA (i.e., behavior SOVA whenbehavior both when horizontal both upperhorizontal and lower upper faces and at lower both faces ends areat both fixed ends and restricted are fixed from and movingrestricted using from a fixedmoving support). using a (fixedb) SOVA support). experimental (b) SOVA blocked experimental force setup, blocked where force two setup, actuators where are two placed actuators and fixed are facingplaced eachand other.fixed facing (c) LSOVA each deformed other. (c) shape LSOVA results deformed (i.e., LSOVA shape behaviorresults (i.e., when LSOVA both horizontal behavior upperwhen andboth lowerhorizontal faces upper at both and ends lower are fixedfaces andat both restricted ends are from fixed moving and restricted using a fixedfrom support).moving using (d) LSOVA a fixed experimentalsupport). (d) LSOVA blocked experimental force setup. blocked force setup.

Finally,Table the 2. Stress stresses–Strain and FEM strain results resulting when the from maximum the load input applied load is can applied be assessed to each structure. as presented in Table2. These two parameters are very important since they should be minimized as much as possible Structure Equivalent Elastic Stress (von-Mises) (MPa) Equivalent Elastic Strain (von-Mises) (mm/mm) to enhanceSOVA the lifetime of the soft actuators2.724 and sensors developed. 0.185 LSOVA 6.193 0.300 Push Button 25.276 0.10378 Linear Sensor 3.0933 0.222 Bending Sensor 8.456 0.656 Torsional Sensor 1.174 0.099

6. Verification of FEM Results The FE results, in terms of total deformation and output blocked force for SOVA and LSOVA, were compared to their experimental counterparts to assess their validity. In addition, the relationship between the input mechanical loads and the change in the air pressure was obtained experimentally to verify that this relationship is linear, as the FE simulations of the SPSCs predicted.

6.1. Total Deformation The experimental total deformation of SOVA and LSOVA actuators were obtained and compared with their FEM counterparts. The difference between the experimental bending angle of SOVA of 265.50° and its FEM bending angle of 269.63° is 1.56%. Similarly, the difference between the experimental linear displacement of LSOVA of 35.03 mm and its FEM linear displacement of 39.47 mm is 12.67% (this difference is higher due to the printing artifacts in LSOVA that interfered with its linear displacement [36]). These differences verify that the FEM results can accurately predict the deformation of the soft pneumatic bending and linear actuators.

6.2. Blocked Force Likewise, the experimental blocked force of SOVA and LSOVA actuators were obtained and compared with their FEM counterparts. The difference between the experimental blocked force of SOVA of 10.72N and the FEM blocked force of 12.33N is 15.02%. This difference is higher since, at higher pressures, the force sensor moved slightly, which reduced the experimental blocked force of SOVA and the two actuators did not perfectly align, as shown in Figure 10b in the experimental setup,

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Table 2. stress-strain FEM results when the maximum input load is applied to each structure.

Equivalent Elastic Stress Equivalent Elastic Strain Structure (von-Mises) (MPa) (von-Mises) (mm/mm) SOVA 2.724 0.185 LSOVA 6.193 0.300 Push Button 25.276 0.10378 Linear Sensor 3.0933 0.222 Bending Sensor 8.456 0.656 Torsional Sensor 1.174 0.099

6. Veriﬁcation of FEM Results The FE results, in terms of total deformation and output blocked force for SOVA and LSOVA, were compared to their experimental counterparts to assess their validity. In addition, the relationship between the input mechanical loads and the change in the air pressure was obtained experimentally to verify that this relationship is linear, as the FE simulations of the SPSCs predicted.

6.1. Total Deformation The experimental total deformation of SOVA and LSOVA actuators were obtained and compared with their FEM counterparts. The difference between the experimental bending angle of SOVA of 265.50◦ and its FEM bending angle of 269.63◦ is 1.56%. Similarly, the difference between the experimental linear displacement of LSOVA of 35.03 mm and its FEM linear displacement of 39.47 mm is 12.67% (this difference is higher due to the printing artifacts in LSOVA that interfered with its linear displacement [36]). These differences verify that the FEM results can accurately predict the deformation of the soft pneumatic bending and linear actuators.

6.2. Blocked Force Likewise, the experimental blocked force of SOVA and LSOVA actuators were obtained and compared with their FEM counterparts. The difference between the experimental blocked force of SOVA of 10.72N and the FEM blocked force of 12.33N is 15.02%. This difference is higher since, at higher pressures, the force sensor moved slightly, which reduced the experimental blocked force of SOVA and the two actuators did not perfectly align, as shown in Figure 10b in the experimental setup, compared to the simulation [32]. Although ultimate attention was provided to fabricate two identical SOVA actuators, there were differences in their mechanical output under the same pressure. Similarly, the difference between the experimental blocked force of LSOVA of 27.66N and its FEM blocked force of 28.66N is 3.62%. These differences verify, again, that the FEM results can accurately predict the blocked force of the soft pneumatic bending and linear actuators.

6.3. Volume Change Linearity The change in the internal volume of the various SPSCs changed linearly with the applied load [38]. The experimental load was ramped up and down by a step of 10°, as shown in Figure 11, where at each step enough time (i.e., 5 s) was given for the various SPSCs to ensure that the pressure value recorded was the final steady-state value. This change was verified experimentally by obtaining a linear relationship between the internal pressure change in the various SPSCs and the corresponding applied load, as shown in Figure 7, since a relationship exists between the change in the internal volume (V1/V2) and the experimental pressure change (P1V1 = P2V2). V1 is the initial volume of single SPSC and V2 is the internal volume at a corresponding input displacement. V1 is computed from the initial CAD models of the SPSCs and V2 is computed from the deformed CAD models, resulting from theRobotics FE 2020simulations., 9, 52 Figure 11a shows the experimental linear relationship between the 11 input of 14 displacement and the output pressure for the bending sensor and its corresponding FEM linear relationship between the same input displacement and the output volume change. The linear fit of 2 bothboth relationships resultedresulted inin a a coe coefficientfficient of of determination determination of of R R=2 0.995= 0.995 for for the the experimental experimental data data and 2 andR = R0.9882 = 0.988 for thefor FEMthe FEM data. data. Similarly, Similarly, Figure Figure 11b shows 11b shows the experimental the experimental linear relationship linear relationship between betweenthe input the displacement input displacement and the output and pressure the output for the pressure torsional for sensor the and torsional its corresponding sensor and FEM its correspondinglinear relationship FEM between linear relationship the same input between displacement the same input and the displacement output volume and the change. output The volume linear 2 change.fit of both The relationships linear fit of both resulted relationships in a coeffi resultedcient of determinationin a coefficient ofof Rdetermination= 0.996 for the of R experimental2 = 0.996 for 2 thedata experimental and R = 0.997 data for and the R FEM2 = 0.997 data. for These the FEM results data. show These that results the FEM show predicted that the FEM the behavior predicted of the the behaviorphysical bendingof the physical and torsional bending sensors and torsional accurately. sensors accurately.

FigureFigure 11. 11. FEMFEM versus versus experimental experimental results results for for ( (aa)) a a soft soft bending bending sensor sensor and and ( (bb)) a a soft soft torsional torsional sensor. sensor.

6.4. Stress-Strain Results The stress and strain results were obtained to assess the regions of each structure that experience high stresses and large strains, as presented in Table2. High stress and strain values led to a significantly shorter lifetime due to the failure of the material (i.e., separation of the printed layers). However, it is important to note that, although in some regions the stress values might be high, they might not have a significant effect on the lifetime or performance of the structure, since they do not lead to the failure of the actuator or sensor. For instance, for the push button, the high stress leads to a shorter lifetime compared with the lifetime of the remaining SPSCs [38]. The push button sustained 60,000 activation cycles, while the bending sensor, which exhibits higher stresses and strains, sustained more than 150,000 activation cycles, since these high stresses and strains occurred on the top of the sensor in the groove area, which is far from the thin walls. However, for the LSOVA, since the stress concentration occurs on the corners of the thin walls, their lifetime was significantly shorter (~20,000 activation cycles) compared to the SOVA, which sustained more than 120,000 cycles. The stress and strain data were taken into consideration in the design process to minimize them and to ensure that they minimally affected the lifetime of the soft actuators and sensors. Robotics 2020, 9, 52 12 of 14

7. Discussion

7.1. Challenges and Recommendations One challenge encountered is the distortion of some elements in the FE model due to the large mechanical deformations. However, this issue was alleviated by incorporating a coarser mesh, when needed, that was suitable for hyper-elastic materials. The mesh used in each case was selected to verify that the results were accurate and mesh independent. Another possible challenge was the difficulty to achieve convergence (i.e., solution) due to the multiple contacts involved in each structure. The reason is that the “Symmetric” frictional contacts imposed imply that no penetration is allowed between the surfaces that come into contact. Although in the contact settings, the “Penetration Tolerance” is set to “Program Controlled”, in some cases it is recommended to put a reasonable manual value to relax this constraint to achieve convergence. This tolerance should be chosen such that the simulations must be realistic where no excess penetration is allowed. Another recommendation for simulating pneumatic soft bodies successfully is that there is no need to include all the details involved in the real geometry in the simulation. However, the simulated geometry must be simplified as much as possible as long as it can be still considered as the real body and captures the most significant features. This simplification will eliminate several problems that might be encountered during meshing and solving to save considerable amounts of computing power and time. For instance, for SOVA and LSOVA, the holes connecting the different chambers were ignored in the simulated body, since they have an insignificant effect on the final solution. Similarly, the input holes in the different SPSCs are ignored in the simulated bodies, as shown in Figures5 and9.

7.2. An Effective Solution to a Soft Robotic Challenge Developing soft pneumatic actuators and sensors for soft robotic systems using various manufacturing techniques and technologies is both time and material consuming. As stated earlier, although the modeling of soft actuators and sensors is an indispensable part of the soft robotics field, it is a very challenging problem, due to nonlinearities. However, in this study, we showed that FEM can be effectively used to handle the nonlinearities involved in modeling soft robotic actuators and sensors to optimize and predict their behavior accurately. Therefore, this study has effectively presented a roadmap for efficiently designing and modeling soft pneumatic actuators and sensors.

7.3. Future Work In future work, various materials can be considered to fabricate various soft actuators and sensors using different manufacturing technologies with different geometries where their appropriate material models can be developed for use in simulations. Additionally, coupled simulations that account for fluid-structure interaction can be used for both actuators, and sensors and dynamic simulations can be performed to assess their behavior under dynamic conditions where inertial forces are significant. Finally, FEM is not limited to soft actuators and sensors that are made of TPU or silicone materials that are not responsive (i.e., cannot be controlled) to external stimuli. Smart materials (e.g., shape memory alloys, dielectric, ionic polymer-metal composites, coiled polymer fibers, hydrogels, humidity-responsive materials, magnetic responsive structures, etc.) that can be excited by external stimuli can be used as actuators and sensors in some cases and, therefore, can be also simulated.

8. Conclusions The modeling of soft and highly deformable robotic structures and systems is challenging, due to nonlinearities, such as geometric, material, and contact nonlinearities. Although the modeling of such soft robotic systems is challenging, it should be integrated into the design process of these systems before their fabrication to eﬃciently and accurately predict their behavior and to optimize their performance and topology to meet certain design and performance requirements. Soft pneumatic Robotics 2020, 9, 52 13 of 14 actuators and sensors that can be directly 3D printed using open source and low-cost FDM 3D printers can be optimized in terms of performance and topology using FEM that predicts their behavior and performance accurately. This means that tremendous amounts of time and resources can be saved, and that FEM can be eﬃciently used to handle the nonlinearities involved in modeling soft robotic actuators and sensors, which are essential elements of soft robotic systems.

Author Contributions: Conceptualization, G.A. and C.T.; methodology, G.A. and C.T.; software, C.T.; validation, G.A. and C.T.; writing—original draft preparation, C.T.; writing—review and editing, G.A.; visualization, C.T.; supervision, G.A.; project administration, G.A. All authors have read and agreed to the published version of the manuscript. Funding: This research has been supported by ARC Centre of Excellence for Electromaterials Science (Grant No. CE140100012) and the University of Wollongong, Australia. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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