Biological Computation for Digital and Fabrication

A biologically-informed !nite element approach to structural performance and material optimization of robotically deposited !bre structures

Neri Oxman1, Jared Laucks2, Markus Kayser3, Carlos David Gonzalez Uribe4, Jorge Duro-Royo5 Massachusetts Institute of Technology, Media Lab, Mediated Matter, USA http://matter.media.mit.edu [email protected], [email protected], [email protected], [email protected], [email protected]

Abstract. mori silkworm is explored as a computational approach for shape and material context of an architectural design installation. We demonstrate that in the absence -driven strategy for material computation. Keywords.

INTRODUCTION

Form-generation and Optimization in Nature Biological systems can be characterized as entities is typically de!ned by the extreme set of external that “compute” material organization according to conditions acting as the “environment”. The system’s external performance criteria. Bone tissue, for in- overall form and mechanical properties are derived stance, alters between states of compact tissue and from processes of shape and material optimization spongy tissue as a function of the applied structural respectively, maximizing compatibility between the load and the requirement for blood circulation (Ox- system’s innate material properties, its external en- man, 2010). Similarly, spider silk alters its mechanical vironment and its desired performance criteria (Ox- properties as a function of its use: spiral silk is used man et al., 2012). As a result natural systems typically for capturing prey while cocoon silk is used for pro- exhibit high levels of integration between shape, tective egg sacs (Nova et al., 2010). The range of vari- structure and material making Nature’s ation in material distribution and physical properties highly e"cient and e#ective forms of “computation”.

Chapter - Computation and Performance - eCAADe 31 | 1 Form-generation and Optimization in structural and environmental stimuli (Brady, 1985; Digital Design Colorni et al., 1996). Consider the optimal shape of Unlike the biological world in which there exist high tree branches or animal tissue morphology. These levels of integration between shape and material shapes and their material composition express an distribution (Benyus, 2009), digital design protocols e#ective use of as well as an e"cient are typically divided into processes of form-gen- thermodynamic operation for an environment-inter- eration and processes of performance-based op- acting system. These processes can be used both as timization, the former being a precondition for the models by which to explain and predict other natu- latter (Mitchell and Oxman, 2010). Finite element ral processes but also as computations in their own methods for example, implemented in order to op- right (Brady, 1985; Colorni et al., 1996; Sha#er and timize shape, material properties and distribution, Small, 1997). are applied only after the form has been generated Research into the use of biological processes as (Brenner and Carstensen, 2004). Another distinction forms of computation the can inform design genera- between biological and digital optimization is the tion are found for example in the use of slime molds ability in the Natural world to produce combinations in order to model real-world infrastructural networks of property and morphological variation of isotropic (Tero et al., 2010). Here problems are described as in- structures (Benyus, 2009). In digital design, optimi- stances of the distributed growth dynamics of the zation processes are typically divorced from mate- resulting in the encoding of a general rial organization since most fabrication materials are linear programming (LP) language. Results prove anisotropic in property (Oxman et al., 2012). Given that the model converges to the optimal solutions the advantages of biological shape-generation and of the LP (Ibid.). Captured in a biologically inspired optimization protocols, can processes of biological mathematical computation, this research can poten- optimization be used to inform and compute de- tially guide network construction in other domains. sired structural and environmental performance of man-made structures? The Silk Pavilion – General Background Given almost any 3D entity, a broad suite of Inspired by optimization processes in Nature like techniques in computational design exists that sup- that of the slime mold described above, the Silk ports form-generation and optimization processes Pavilion is an architectural structure fabricated by within parametric environments (Kolarevic and digital fabrication technologies combined with the Klinger, 2008). Examples of such techniques include deployment of live silkworms. It explored the rela- particle systems, multi-agent systems, network anal- tionship between digital and biological fabrication ysis, and ! nite element methods (Haroun Mahdavi on product and architectural scales. The primary and Hanna, 2004). Replacing such computational structure is created of 26 polygonal panels made processes with biological ones allows informing of silk threads laid down by a CNC (Computer- shape-generation processes as well as spatial mate- Numerically Controlled) machine. Inspired by the rial organizations within a single (biological) system. silkworm’s ability to generate a 3D cocoon out of a single multi-property silk thread (1km in length), BACKGROUND the overall geometry of the pavilion is created using an that assigns a single continuous thread Biological Computation for Digital Design across patches providing various degrees of density. and Fabrication Overall density variation is informed by the silk- Numerous forms in Nature achieve their shape and worm itself deployed as a biological “printer” in the structure through local optima processes, as mate- creation of the secondary structure. A swarm of 6500 rial organization and composition are informed by silkworms were positioned at the bottom rim of the

2 | eCAADe 31 - Computation and Performance - Chapter Figure 1 Composite image of com- pleted Silk Pavilion installation and Bombyx mori silkworms spinning on the CNC fabri- cated super-structure.

sca#old spinning %at non-woven silk patches as they Bombyx mori silkworm as a computational schema !ll the gaps across the CNC deposited silk ! bres. for determining shape and material optimization of Following their pupation stage the silkworms are !bre-based surface structures. This biological form removed. Resulting moths can produce 1.5 million of “computation” can potentially exclude the need eggs with the potential of constructing up to 250 for Finite Element methods. additional pavilions (Figure 1). A#ected by spatial and environmental condi- AIMS AND GOALS tions such as geometrical density and variation in Fibre-based structures are ubiquitous in both archi- natural light and heat the silkworms were found to tectural and biological systems. Robust structural migrate to denser and darker areas. Desired light performance involves the balancing of force-and- e#ects informed variations in material organization response in order to achieve material morphologies across the surface area of the structure. A season- that are structurally e"cient and environmentally speci!c sun path diagram mapping solar trajectories e#ective (Oxman, Tsai et al. 2012). Typically this pro- in the space dictated the location, size and density of cess involves a step-wise process including com- apertures within the structure in order to lock in rays putational modeling, ! nite-element analysis and of natural light entering the pavilion from South and digital fabrication. Biological !bre-based structures East elevations. The central oculus is located against such as the silkworm’s cocoon however may provide the East elevation and may be used as a sun-clock. for the uni!cation of these three media through The construction process of the Silk Pavilion the use of the silkworm’s path as an optimization was inspired by basic research experiments reported “tool path” and a fabrication “technology”. The guid- herein that informed processes of modeling, analy- ing assumption here is that the silkworm’s ability sis and fabrication. This paper reports upon experi- to generate ! bre structures with varying degrees mental work considering biological forms of com- of density based on its environment has been per- putation for digital design modeling, analysis and fected through evolutionary pressure. We also as- fabrication. Speci!cally, we explored the formation sume that the cocoon is an optimal structure which of non-woven ! bre structures generated by the itself is based on the idea that optimization-seeking

Chapter - Computation and Performance - eCAADe 31 | 3 Figure 2 Placement of a Bombyx mori silkworm on top of a !at surface-spinning platform.

processes are omnipresent in Nature. Having been appeared to have spun a % at silk patch instead of developed without top-down control this case may the anticipated 3-D cocoon structure. This was due represent a scalable approach for !bre-based struc- to the lack of a physical vertical pole/axis against tural design based on optimization. Our main goal which the silkworm would otherwise construct its is to determine whether these structures are likely cocoon. The experiment con!rmed that the Bombyx to yield reasonably e"cient solutions to combinato- mori silkworm would spin silk as a %at patch in the rial optimization challenges such as load informed absence of vertical surface features (Figure 3). !bre-density distribution in membrane structure. The Dice Series METHODOLOGY AND EXPERIMENTAL Following, we began introducing a central ver- SET!UP tical axis of varying heights to determine (1) at The experimental set-up consisted of a series of which height point would the 3D cocoon structure surface patches measuring 80X80mm in surface emerge, and (2) how might !bre distribution be af- area with varying sectional con!gurations. A live fected by the relative location of the vertical axis and silkworm was positioned on top of the surface and its height. A family of tent-like structures consisting left to spin. We hypothesized that spinning con!gu- of a rectangular surface patch with a single vertical rations and !bre density distribution would vary ac- axis (“1-dice section” per Figure 4) was set up. cording to the morphological features of the “host- Varying axes heights of 3mm, 6mm, 9mm, ing environment” (Figure 2). 12mm, 15mm, 18mm, 21mm, 24mm, and 27mm were implemented (Figure 5). Initial Experimentation to Determine The experiments demonstrated the following: Fibre-Density Variation in Flat-spun Silk (1) a 3D cocoon structure emerged only at a section- The !rst experiment consisted of a %at surface patch al height of 21mm height below which a tent-like with no additional surface features. The silkworm structure in the form of a rectangular pyramid was

4 | eCAADe 31 - Computation and Performance - Chapter Figure 3 A Bombyx mori silkworm com- pleting the deposition of ap- proximately 1km of !at-spun silk. The research con"rms that given the absence of a vertical axis the silkworm will spin a !at silk patch.

Figure 4 Comparison of two 1-dice con"gurations with a 3mm and a 21mm vertical axis illus- trating the di#erence between !at spinning (su$ciently short vertical axis) and a cocoon spinning (su$ciently long vertical axis).

Figure 5 Series of one-dice platforms ranging in vertical axis height from 3mm to 27mm each with 3mm increments.

spun. Given the dimensions of the natural cocoon we as a function of the distance from the central verti- assume that a minimum height of ~21mm account- cal pole to the surface boundary. This may point to a ing for the longitudinal axis of the cocoon must be local optima condition requiring the least amount of provided in order for a 3D structure to emerge. In energy for the construction of a strong stable struc- the absence of this height, a non-enclosed surface ture within a given timeframe (Figure 6); (3) bound- patch will be spun; (2) !bre density typically varied ary contours were typically denser. We assume this is

Chapter - Computation and Performance - eCAADe 31 | 5 Figure 6 18mm one-dice platforms illustrating higher density deposition along the shortest distances from the geo- metrical center to the surface boundary contour.

Figure 7 Series of (15) rectangular FEM-dice platforms ranging from 10mm to 15mm in pole heights.

due to the silkworm’s constant search for a vertical FEM representations were computed as hy- pole tall enough to allow for cocoon construction. pothetical static-force studies for anticipated ! bre Additional experiments followed exploring in- variation in a membrane tent-like structure accomo- depth relations between topographical surface fea- dating the environment given by the patch. Linear tures and !bre density. These include the Rectangu- Elastic Isotropic 101 Nylon with an elastic modulus lar FEM-Dice Series, the Pentagonal FEM-Dice Series, of 1000000000 N/M^2 was used to represent the the Thrust Vault Series, and the Maltese-cross series. membrrane material. The results of the study con- Their descriptions are given below. !rm general correlation between anticipated Stress- Strain calculations (computed using the SolidWroks The Rectangular FEM-Dice Series environment) and the resulting ! bre-structure as The series included a set of 15 %at 80X80mm surface spun by bombyx mory silkworm. See a typical exam- patches in di#erent dice-face con!gurations. Poles ple in Figure 8. of 10-15mm height were used to de!ne the planar con!rgruation and the sectional hiehgt of the patch The Polygonal FEM-Dice Series (Figure 8). A live silkworm was then positioned in This series is analogous to the previous one (FEM- each patch to spin a typical 1km long !lament. The Dice Series) containing four models based on a po- assumption was that the variation in ! bre density lygonal patch as the base environment (Figure 9). and organization would re%ect the morpolohgical The results of the study con!rm general cor- constrains given by the “environment” (i.e. the sir- relation between anticipated Stress-Strain calcula- face patch). tions (using the SolidWroks environment) and the

6 | eCAADe 31 - Computation and Performance - Chapter Figure 8 4-Dice face con"gurations. L to R: Digital representa- tion of anticipated stress for membrane structure based on 4 poles calculated within SolidWorks; physical model with digital representation as base. The silkworm is shown to the right; physical model juxtaposed with silk "bre by the Bombyx mori silkworm. Denser "bres appear between poles along boundaries as anticipated by the FEM model.

resulting ! bre-structure as spun by bombyx mory peared): a typical model demosntrates increased silkworm. See a typical example in Figure 10 below !bre density along the boundaries. In addition, a demonstrating ! bre distribution along regions of circula patch appears at the center of the patch highest stress around the central vertical axis of the marking the silkwrm’s attempt to form a 3D cocoon patch 10. between the two planes that make up the section (Figure 12). The Thrust Vault Series Unlike the two previous series, the Thrust Vault Se- The Maltese-cross Series ries is comprised of non-%at 80X80mm patches vary- The !nal series introduces variations in both plan and ing in topographical features. Sectional height var- sectional con!gurations. The plan con!guration in ies across 5mm and 20mm with 5mm increments; this series is no longer constraint to a completely %at each model is repeated twice to validate the consist- rectangular, polygonal or circular surface patch but ency of the resulting morphology. Color annotations rather it is oriented in a Maltese-cross con!guration. represent variation in curvature with the color green The variation in section height introduces spatial typically representing anticlastic curvature and blue ‘gaps’ to the silkworm’s movement as it spins its silk representing synclastic curvature (Figure 11). in circular motion. Sectional height varies between The assumption was that the variation in ! bre 5mm and 20mm with 5mm increments; each model density and organization would re%ect the mor- is repeated twice to validate the consistency of the polohgical constraitns given by the environment. resulting morphology. Colour annotations represent Indeed, our results con!rm this correlation below variation in curvature with the colour green typically 20mm height (above this heigh the 3D cocoon ap- representing anticlastic curvature and blue repre-

Chapter - Computation and Performance - eCAADe 31 | 7 Figure 9 Series of polygonal FEM-Dice platforms.

Figure 10 One-dice polygonal platforms showing greater density of silk deposition in areas of higher Stress-Strain.

senting synclastic curvature (Figure 13). RESULTS AND DISCUSSION As anticipated, the results re%ect the correlation In this paper we have shown that the silkworm Bom- between !bre density and surface features demon- byx mori forms !brous silk networks on %at patches. strating a combination between the %at-dice-series Fibre density distribution appears to be su"ciently and the thrust-vault series. similar to the anticipated !bre density variation that was computationally generated for a prescribed

8 | eCAADe 31 - Computation and Performance - Chapter Figure 11 Series of three-dimensional thrust vault spinning plat- forms.

Figure 12 20mm tall thrust vault spin- ning platform demonstrat- ing the silkworm’s spinning behavior.

Figure 13 Series of three-dimensional Maltese-cross spinning platforms.

membrane structure of the same mass and surface inspired mathematical model that may be useful for area. We conclude that the Bombyx mori silkworm anticipating ! bre density and organizational varia- itself may be used as a biological “tool” with which tion in !brous membrane structures exposed to well to “compute” !bre distribution within small-scale 1:1 de!ned local loading conditions. structures, or as scaled representations of larger archi- By collecting qualitative and quantitative data tectural structures constructed with !brous materials. from live silkworms spinning on top of pre-fabricat- This work is still in its early stages. The core ed %at patches we successfully predicted a correla- mechanisms required for ! brous network forma- tion between the nature of material distribution and tion can be further captured within a biologically the geometrical characteristics of the patch. These

Chapter - Computation and Performance - eCAADe 31 | 9 results, combined with future research currently un- for hard combinatorial optimization problems.” Inter- der way, have signi!cant implications for structural national Transactions in Operational Research 3(1): analysis protocols of !bre-based systems. Addition- 1-21. ally this work may also carry implications for biologi- Haroun Mahdavi, S. and S. Hanna (2004). “Optimising con- cally inspired digital design and fabrication. Here, tinuous microstructures: a comparison of gradient- the relationship between the global, top-down based and stochastic methods.” design of a constricting “environment” designed Kolarevic, B. and K. R. Klinger (2008). Manufacturing mate- arti!cially by the designer informs its local, bottom- rial e#ects: rethinking design and making in architec- up material manifestation as portrayed by the bio- ture, Routledge New York. logical (the silkworm). Finally, the Bombyx Mitchell, W. J. and N. Oxman (2010). Material-based design mori silkworm may be considered as an autono- computation, Massachusetts Institute of Technology. mous agent in processes of design optimization. As Nova, A., S. Keten, et al. (2010). “Molecular and nanostruc- this research has shown, this project opens up new tural mechanisms of deformation, strength and tough- possibilities for the use of biological processes as ness of spider silk ! brils.” Nano Letters 10(7): 2626- forms of computation. 2634. Oxman, N. (2010). Material-based design computation, ACKNOWLEDGEMENTS Massachusetts Institute of Technology. Research and Design by the Mediated Matter Re- Oxman, N., E. Tsai, et al. (2012). “Digital anisotropy: A vari- search Group at the MIT Media Lab in collabora- able elasticity rapid prototyping platform: This paper tion with Prof. Fiorenzo Omenetto (TUFTS Univer- proposes and demonstrates a digital anisotropic fabri- sity) and Dr. James Weaver (WYSS Institute, Harvard cation approach by employing a multi-material print- University). Mediated Matter researchers include ing platform to fabricate materials with controlled gra- Markus Kayser, Jared Laucks, Carlos David Gonzalez dient properties.” Virtual and Physical Prototyping 7(4): Uribe, Jorge Duro-Royo and Neri Oxman (Director). 261-274. Sha#er, R. E. and G. W. Small (1997). “Peer Reviewed: Learn- References ing Optimization From Nature: Genetic Benyus, J. M. (2009). Biomimicry, HarperCollins e-books. and Simulated Annealing.” Analytical Chemistry 69(7): Brady, R. (1985). “Optimization strategies gleaned from bio- 236A-242A. logical evolution.” Nature 317(6040): 804-806. Tero, A., S. Takagi, et al. (2010). “Rules for biologically in- Brenner, S. C. and C. Carstensen (2004). “Finite element spired adaptive network design.” Science Signalling methods.” Encyclopedia of Computational Mechanics. 327(5964): 439. Colorni, A., M. Dorigo, et al. (1996). “Heuristics from nature

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