Optimized shock-protecting microstructures

TL;DR

The paper tackles the challenge of protecting objects from repetitive mechanical shocks by designing metamaterial microstructures whose effective stress remains nearly constant over a broad deformation range. It introduces a computational pipeline that combines topology enumeration, a differentiable nonlinear homogenization framework with self-contact, and gradient-based optimization to generate 2D microstructure families that can be extruded for 3D printing. The authors formulate an ideal flat-stress objective, build a one-parameter family of cell topologies P(σ_f), and optimize geometry to match σ_f across multiple strain samples, including non-uniaxial loading via domain rotation. They validate the approach with extensive simulations and physical experiments (compression, drop tests, packaging protection), showing significant improvements over baselines and demonstrating practical applicability, robustness to load direction, and potential for reusable, shock-absorbing packaging and automotive components. The work advances nonlinear metamaterial design by incorporating periodic contact, large deformations, and explicit fabrication-ready geometries, while outlining directions for extension to 3D, multi-axial loading, and dynamic effects.

Abstract

Mechanical shock is a common occurrence in various settings, there are two different scenarios for shock protection: catastrophic protection (e.g. car collisions and falls) and routine protection (e.g. shoe soles and shock absorbers for car seats). The former protects against one-time events, the latter against periodic shocks and loads. Common shock absorbers based on plasticity and fracturing materials are suitable for the former, while our focus is on the latter, where elastic structures are useful. Improved elastic materials protecting against shock can be used in applications such as automotive suspension, furniture like sofas and mattresses, landing gear systems, etc. Materials offering optimal protection against shock have a highly non-linear elastic response: their reaction force needs to be as close as possible to constant with respect to deformation. In this paper, we use shape optimization and topology search to design 2D families of microstructures approximating the ideal behavior across a range of deformations, leading to superior shock protection. We present an algorithmic pipeline for the optimal design of such families combining differentiable nonlinear homogenization with self-contact and an optimization algorithm. These advanced 2D designs can be extruded and fabricated with existing 3D printing technologies. We validate their effectiveness through experimental testing.

Figures (22)

• Figure 1: Model problem setup.
• Figure 2: A cell topology $T$ is annotated with geometric parameters $r$ (a radius and a 2D position for each vertex). The inflator $\Psi$ converts the graph representation into an implicit function, which is then triangulated to obtain a mesh representation $\Bar{q}$ of the cell domain $\Omega$.
• Figure 3: A deformed periodic cell collides with its tiled boundary mesh during homogenization. Accounting for collision is crucial to designing a shock-protecting microstructure family (Figure \ref{['fig:ablation:contact']}).
• Figure 4: Instead of considering the unit cell under non-uniaxial load in (a), we rotate the rest shape and still compress along the Y direction in (b), the compressed shape is shown in (c). The load direction is shown in blue arrows.
• Figure 5: Each microstructure topology (orange, left) is initialized with a default set of positions and radii for each vertex. Before optimization (orange, right) the stress ([per-mode = symbol]) - strain curve is almost linear. After optimization (blue, left) the curve is flat over a large range of deformation (blue, right).