Topology optimization of nonlinear periodically microstructured\n materials for tailored homogenized constitutive properties

Abstract

A topology optimization method is presented for the design of periodic\nmicrostructured materials with prescribed homogenized nonlinear constitutive\nproperties over finite strain ranges. The mechanical model assumes linear\nelastic isotropic materials, geometric nonlinearity at finite strain, and a\nquasi-static response. The optimization problem is solved by a nonlinear\nprogramming method and the sensitivities computed via the adjoint method.\nTwo-dimensional structures identified using this optimization method are\nadditively manufactured and their uniaxial tensile strain response compared\nwith the numerically predicted behavior. The optimization approach herein\nenables the design and development of lattice-like materials with prescribed\nnonlinear effective properties, for use in myriad potential applications,\nranging from stress wave and vibration mitigation to soft robotics.\n