Design of composite structures with programmable elastic responses under finite deformations

We systematically design composite structures using multi-material topology optimization to 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 enlarge 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 exure-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.