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The design of specified nonlinear mechanical responses into a structure ormaterial is a highly sought after capability, which would have a significantimpact in areas such as wave tailoring in metamaterials, impact mitigation,soft robotics, and biomedicine. Here, we present a topology optimizationapproach to design structures for desired polynomial nonlinear behavior,wherein we formulate the problem in such a way as to decouple the nonlinearresponse from the stiffness. We show results across qualitatively differentpolynomial behaviors while achieving a high degree of precision, creating apath toward analytically tractable nonlinear dynamical systems. The approachenables access to previously difficult to design for, or hitherto unachieved,nonlinear behavior via optimized structures, which can furthermore beincorporated as unit cells of designer materials with tailored nonlinearproperties.

Tailoring high precision polynomial architected material constitutive responses via inverse design