Design of composite structures with programmable elastic responses under finite deformations

We systematically design composite metastructures using multi-material topology optimization to precisely achieve tunable elastic responses under finite deformations. We formulate an inverse problem where the errors between the actual (numerical) and the prescribed force–displacement curves are minimized. The framework harnesses multiple hyperelastic materials with distinct constitutive relations, which enlarges the design space of programmable structures compared to the single-material setting. A stress constraint for multi-material structures is proposed to control the levels of stress and deformation in the optimized composite structures with distinct stress limits. Through several numerical design scenarios, we design multi-material structures that achieve a variety of programmed load–displacement curves, some of which are physically unattainable with single materials. The optimized structures exhibit unconventional geometries and multi-material distributions and reveal distinct mechanisms, such as converting deformation modes from flexure-dominated to stretch-dominated. Multiple designs achieving the same target response are identified, demonstrating the effectiveness of the proposed methodology to explore various composite structures with programmable responses.