Disordered Continuity: Programming Resolution-Independent Stochastic Metamaterials with Differentiable Anisotropic Property Distribution

Abstract

Nature-inspired stochastic metamaterials with disordered and multiscale architectures have shown great promise towards extraordinary functionalities, including high mechanical resilience, stress modulation and biased stiffness reinforcement. As a special type of functionally graded metamaterial, programming multiscale stochastic metamaterial to achieve required functional property is computationally demanding due to the iterative simulation process, and thereby often intuitively implemented by filling a predefined subset of functional units into rasterized design space of fixed resolution, which restricts the flexibility and effectiveness of the designed functionality. To mitigate the computational complexity introduced by the multiscale architecture, we proposed a two-stage approach to programming stochastic metamaterials towards customized mechanical response. Instead of directly optimizing stochastic microstructures, the proposed approach first optimizes a differentiable physical property distribution, e.g. stiffness that targets desired functionality, and then generates spinodal architected microstructures to realize such property distribution under resolution-independent rasterization. The key enabler is the incorporation of spherical harmonics to represent, modulate and interpolate anisotropic stiffness distribution, which then serves as a non-uniform distribution function for the generation of anisotropic spinodal infills with high continuity. The test results demonstrated effective design of stochastic metamaterials with programmed functionalities to enable stress modulation, texture encoding and mechanical cloaking.