Inverse Design of Metamaterials with Adaptable Force-Displacement Characteristics

Abstract

Metamaterials with tailored force-displacement characteristics hold significant promise for applications ranging from soft robotics and energy dissipation to biomedical devices such as prosthetic sockets, where distinct regions of a structure must simultaneously satisfy fundamentally different mechanical requirements. Existing inverse design frameworks, however, are restricted to single loading conditions and homogeneous desired behaviors, limiting their utility in real-world scenarios where complex, spatially varying mechanical demands must be met within a single continuous material. We present an inverse design method that closes this gap by combining finite element simulation, surrogate optimization, and machine learning within a unified framework. Starting from a fixed unit cell topology governed by eleven geometric shape parameters, we first construct a surrogate model that replaces each unit cell with a polynomial energy density, reducing the metamaterial-scale inverse problem to a tractable optimization over polynomial coefficients. A multi-output multilayer perceptron trained on finite element simulations then maps any required unit cell force-displacement response back to the corresponding shape parameters. We extend the formulation to multi-surface loading, enabling two qualitatively distinct force-displacement targets to be achieved simultaneously in different regions of the same structure. Fabricated prototypes tested under prescribed displacements confirm that the predicted responses, spanning superelastic, bistable, and constant-force behaviors, are reproduced with high fidelity. These results demonstrate a flexible and computationally efficient route to multifunctional metamaterial design under realistic, multi-condition loading environments.