Computational Tools for 3D Printing
Ariel Shamir
Bernd Bickel
Wojciech Matusik

Part 3: Design and Fabricationof Deformable Objects
Bernd Bickel

Deformable Objects[Festo][shapeways.com][RBO Hand, TU Berlin]

From Functional 2 Direct Specification

Base Materials
Fabrication

Search &Simulation
Virtual Object

OutputManufacturing Deformable Materials

intrinsic[Hiller and Lipson 2009][Bickel et al. 2010][Skouras et al. 2013][Chen et al. 2013][Schumacher et al. 2015][Panetta et al. 2015][Martínez et al. 2016]

extrinsic[Bickel et al. 2012][Chen et al. 2014]

From Functional 2 Direct Specification

Base Materials
Fabrication

Search &Simulation
Target ObjectOutput

Material Representation
Stress-Strain relationship in 1D– Strain– StressLinear Representations Do Not Work
• Stress-strain relationship is non-linear
Choice of material model• Linear Elastic• Hyperelastic• Plasticity• Creep

Acquiring mechanical properties
Option 1: “Standard” Material Tests

Typical specimen shapeTensile test machine• Common types of tests: Uniaxial
Tension, Uniaxial Compression, Biaxial
Tension, Torsion• “Simple” to construct stress-strain curve• Fitting material parameters easy
• Intuitive inspection of experimental data
and material parameter fits
• Requires specific shape of specimen

Acquiring mechanical properties
Option 2: Acquire Force/Displacement Pairs..

..

Materialsample• Capturing boundary conditions
accurately
can be challenging• Requires solving an inverse problem[Schnur and Zabaras 1992; Becker andTeschner 2007; Bickel et al. 2009; Leeand Lin 2012] (elastic), [Kauer et al. 2002;
Gao et al. 2009] (viscoelastic), [Kajbergand Lindkvist 2004] (plasticity)From Functional 2 Direct Specification

Base Materials
Fabrication

Search &Simulation
Target Object

OutputManufacturing Deformable Materials

intrinsic[Hiller and Lipson 2009][Bickel et al. 2010][Skouras et al. 2013][Schumacher et al. 2015][Panetta et al. 2015][Martínez et al. 2016][Chen et al. 2013]

extrinsic[Bickel et al. 2012][Chen et al. 2014]

GoalApproach 1: Topology Optimization[Sigmund 2009][Schumacher et al. 2015]

Approach 1: Topology Optimization𝛼𝑖𝑶 𝜶 = 𝑪𝒈𝒐𝒂𝒍 − 𝑪 𝜶𝟐𝑭+𝑹Approach 1: Topology Optimization

𝑶 𝜶 = 𝑪𝒈𝒐𝒂𝒍 − 𝑪 𝜶𝟐𝑭+𝑹Approach 2: Systematic Topology Enumeration?

[Panetta et al. 2015]

Approach 2: Systematic Topology Enumeration[Panetta et al. 2015]

Topology Sweep[Panetta et al. 2015]

Microstructure Shape Optimization• Thickness and offset parameters continuously control
microstructure’s shape, 𝜔• Fit the microstructure to an elasticity tensor:[Panetta et al. 2015]

Shape Optimization Results[Panetta et al. 2015]

Shape Optimization Results[Panetta et al. 2015]

Manufacturing Deformable Materials

intrinsic

extrinsic[Hiller and Lipson 2009][Bickel et al. 2010][Skouras et al. 2013][Schumacher et al. 2015][Panetta et al. 2015][Martínez et al. 2016][Chen et al. 2013][Bickel et al. 2012][Chen et al. 2014]

From Functional 2 Direct Specification
Input• Shape with assigned
Material Parameters• Deformation Specification

Output• Spatially-varying
material structureFrom Functional 2 Direct Specification
Input

Output• Shape with assigned
Material Parameters
mapping• Deformation Specification• Spatially-varying
material structureChallenge: Find optimal combinations[Schumacher et al. 2015]

Challenge: Find optimal combinations[Schumacher et al. 2015]

Periodic Tiling: Challenges• Mapping? Possible, but difficult.

• Gradation? Possible, but transitions?

?

Hexahedral-dominant meshing[Sokolov et al. 2015][Schumacher et al. 2015] – solves an optimization
problem for finding compatible tilingsProcedural Synthesis for Fabrication

F(x,y,z)

SliceFill with microstructure[Martínez et al. 2016]

Procedural Synthesis for Fabrication

Printed with Autodesk Ember[Martínez et al. 2016]

Procedural Synthesis for Fabrication:
Result Cute Octopus

Printed with B9 Creator[Martínez et al. 2016]

From Functional 2 Direct Specification
Input• Shape with assigned
Material Parameters

Output• Spatially-varying
material structure• Deformation Specification
optimization

Problem Formulation

DesignParameters
𝐸 𝐱, 𝐩 = 𝐸𝑚𝑎𝑡𝑐ℎ 𝐱, 𝐱 𝑡𝑎𝑟𝑔𝑒𝑡

subject to𝐟 𝑡𝑜𝑡𝑎𝑙 𝐱, 𝐩 = 0

Problem Formulation

DesignParameters
𝐸 𝐱, 𝐩 = 𝐸𝑚𝑎𝑡𝑐ℎ 𝐱, 𝐱 𝑡𝑎𝑟𝑔𝑒𝑡

subject to𝐟 𝑡𝑜𝑡𝑎𝑙 𝐱, 𝐩 = 0

Optimization Strategies:• Discrete ([Bickel et al. 2010])• Continuous ([Skouras et al. 2013])

Discrete Optimization: Material Search Tree

[Bickel et al. 2010]

Discrete Optimization: Material Search Tree

[Bickel et al. 2010]

Pruning the Search Space• Bounds from physical constraints

Too SoftToo Hard[Bickel et al. 2010]

Pruning the Search Space• Clustering at each level

SimilarToo SoftToo Hard[Bickel et al. 2010]

Result[Bickel et al. 2010]

Ready to Wear

[Bickel et al. 2010]

Problem Formulation

DesignParameters
𝐸 𝐱, 𝐩 = 𝐸𝑚𝑎𝑡𝑐ℎ 𝐱, 𝐱 𝑡𝑎𝑟𝑔𝑒𝑡

subject to𝐟 𝑡𝑜𝑡𝑎𝑙 𝐱, 𝐩 = 0

Optimization Strategies:• Discrete ([Bickel et al. 2010])• Continuous ([Skouras et al. 2013])

Continuous Material Distribution Optimization

softstiff[Skouras et al. 2013]

Material Distribution Optimization

Material Distribution Optimization

Results

Rest Pose

Stiff
Target PoseSoft

Manufacturing Deformable Materials

intrinsic[Hiller and Lipson 2009][Bickel et al. 2010][Skouras et al. 2013][Chen et al. 2013][Schumacher et al. 2015][Panetta et al. 2015]

extrinsic[Bickel et al. 2012][Chen et al. 2014]

Thickness Optimization• Works with a single base material• Idea: modulate local stiffness by modifying the skin thickness

Target surface

Undeformed bar[Bickel et al. 2013]

Thickness Optimization• Minimization problem,
𝐩, 𝐱 = argmin 𝐸𝑚𝑎𝑡𝑐ℎ 𝐱, 𝐱 𝑡𝑎𝑟𝑔𝑒𝑡
𝐩,𝐱

,
1 𝜕𝑊
+ 𝛾|
2
𝜕𝐱 𝐱,𝐩2

Physical consistency,,[Bickel et al. 2013]

Thickness Optimization

Rest shapeForehead inner side

Target geometry

Results

Simulation

Robotic headSpec2Fab• Spec2Fab processes use a similar structure• Small set of common components

Branch and Bound
Linear Solver
QP
Simulated Annealing
SPSA

ReducedParameters

Simulation

Optimization

Comparison

Subsurface Scattering
Caustics
Shadows
Deformation
Image Distances
Mesh Distances
Curve Distances[Chen et al. 2013]

Common Components

ReducedParameters

Simulate

Optimization

Compare to goal

Reducer Tree

Tuner Network[Chen et al. 2013]

Spec2Fab for Deformation and Texture

Input
Shape

Goal: deformation

Tuner

Stratum
TextureVoxel

Goal: texture

Material Material… MaterialPrint[Chen et al. 2013]

Conclusion• Summary– Control at various levels– Techniques could be combined– Interactive vs. Specification-Based Design• Limitations / Future Work– Scaling– Non-linear material behavior can be very complex– Fabrication constraints often quite specifc– 3D printer• Durability of materials• Handling of materials

Thank you!
Acknowledgements
Melina Skouras, Jeremie Dumas, Sylvain Lefebvre, and Julian Panetta for providing slides/image material.

References

Bickel, B., Bächer, M., Otaduy, M. A., Lee, H. R., Pfister, H., Gross, M., & Matusik, W. (2010). Design and fabrication of materials withdesired deformation behavior. ACM Transactions on Graphics (TOG), 29(4), 63.
Bickel, B., Kaufmann, P., Skouras, M., Thomaszewski, B., Bradley, D., Beeler, T., ... & Gross, M. (2012). Physical face cloning. ACM
Transactions on Graphics (TOG), 31(4), 118.
Chen, D., Levin, D. I., Didyk, P., Sitthi-Amorn, P., & Matusik, W. (2013). Spec2Fab: a reducer-tuner model for translating specifications to3D prints.ACM Transactions on Graphics (TOG), 32(4), 135.
Panetta, J., Zhou, Q., Malomo, L., Pietroni, N., Cignoni, P., & Zorin, D. (2015). Elastic textures for additive fabrication. ACM Transactions
on Graphics (TOG),34(4), 135.
Schumacher, C., Bickel, B., Rys, J., Marschner, S., Daraio, C., & Gross, M. (2015). Microstructures to control elasticity in 3D
printing. ACM Transactions on Graphics (TOG), 34(4), 136.

Skouras, M., Thomaszewski, B., Coros, S., Bickel, B., & Gross, M. (2013). Computational design of actuated deformablecharacters. ACM Transactions on Graphics (TOG), 32(4), 82.
Martínez, J., Dumas, J., & Lefebvre, S. (2016). Procedural voronoi foams for additive manufacturing. ACM Transactions on Graphics(TOG), 35(4), 44.