Optimized Shock-protecting Microstructures

Abstract

We use shape optimization and topology search to design families of microstructures approximating the ideal shock-protecting behavior. We present an algorithmic pipeline for the optimal design of such families combining differentiable nonlinear homogenization with self-contact and an optimization algorithm. We fabricate the designs with existing 3D printing technologies and validate their effectiveness through experimental testing.

Results

Five optimized patterns: initial shape, rest shape, deformed shape, compression experiments and force-strain plots

Five optimized patterns validated in physical experiments. From left to right: initial shapes, optimized rest shapes, deformation of the optimized shapes, compression experiments, and force (N) against strain (%) for the experiments (blue) and the periodic simulations (orange).

Drop tests, simulated and physical

A duck falling down a slope on un-optimized microstructures, with Von Mises stress shown

Maximum Von Mises stress over time for the optimized and initial microstructures

Drop experiment: a glass ball survives on the microstructure but shatters on a solid cube

Full simulation and fabricated sample of the optimized sheared pattern

A duck falls down a slope, here on un-optimized microstructures — compare the optimized version in the teaser above. Optimizing cuts peak Von Mises stress by 72%. In the physical drop test, a glass ball filled with 200 g of metal balls reaches 50% compression and survives on the microstructure, but shatters on a solid cube. The last panel compares a full simulation with the fabricated sample.

Comparisons with prior work

Stress-compression curves for the baseline pattern, its optimized geometry and our connectivity

Comparison against transient shape optimization: stress, stress norm and acceleration

Left: the topology and geometry of [Joodaky 2020] (A) is considerably extended by optimizing its geometric parameters (B); our family has a different connectivity (C) giving an even wider flat response. Right: against transient shape optimization [Huang et al. 2024], our result absorbs 47% more total impulse during the shock while taking less time and memory to optimize.

Method

A material that protects well against shock has a highly non-linear elastic response: its reaction force should stay as close to constant as possible while it deforms. We search for 2D microstructure families with that property, then extrude and 3D print them.

1. Homogenize. We formulate the effective stress–strain dependence of a non-linear periodic structure under large displacement, with self-contact and a non-linear base material law. Contact is not optional here — a pattern optimized without it develops much higher stress than predicted once the cells touch.

2. Optimize the shape. The homogenization is differentiable, so the cell geometry (up to 80 parameters) is optimized directly against the target constant stress. Optimizing the cell rather than a full multi-cell structure gets a better result in less time and memory.

3. Search topologies. An extensive search over 105 candidate connectivities finds those that can hold a flat response, yielding a family parametrized by the target stress. Symmetric tiles are excluded: they buckle into energetically equivalent configurations, which destabilizes large tilings.

The resulting family holds a flat response up to 75% compression, against 57% for the previously known structure of [Joodaky 2020], and can be used directly to design and print shock absorbers.

Citation

@article{10.1145/3687765, author = {Huang, Zizhou and Panozzo, Daniele and Zorin, Denis}, title = {Optimized shock-protecting microstructures}, journal = {ACM Trans. Graph.}, volume = {43}, number = {6}, articleno = {181}, numpages = {21}, year = {2024}, month = nov, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, issn = {0730-0301}, doi = {10.1145/3687765}, url = {https://doi.org/10.1145/3687765} }