Inverse design of growth-inspired disordered metamaterials with programmable nonlinear force deflection responses

Inspired by biological materials, aperiodicity and disorder significantly expand the design freedom of mechanical structures and prove effective in optimizing linear elastic and elastoplastic properties. However, customizing the nonlinear force deflection responses of disordered metamaterials under dynamic impact remains challenging due to the vast design space, irregular structural forms, and complex structure-property relationships. In this work, a novel framework for the design of disordered metamaterials is proposed, consisting of a forward prediction network and an inverse design network, to enable programmable stress-strain behaviors. The disordered metamaterials are generated through a virtual growth program, which assembles predefined building blocks in a stochastic yet controllable manner. Unlike conventional methods, the proposed framework enables diverse equivalent stress-strain responses solely by altering the spatial distribution of building blocks, without changing the generation frequency. In addition, four distinct types of representative structures are identified through investigation of the energy absorption performance of disordered metamaterials. Structural chamber graphs and nodes with different coordination numbers are introduced to elucidate the mechanism by which the spatial distribution of building blocks affects macroscopic mechanical behavior. Furthermore, the inverse design framework generates an energy-absorbing structure that outperforms the maximum-SEA_v sample in the dataset by 8.41%. Finally, dynamic experiments are conducted to validate the effectiveness of the proposed method. This framework provides a new pathway for realizing complex, predefined nonlinear force deflection responses and advances the data-driven design of disordered metamaterials.