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 11 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.