Multiscale structural optimization for prescribed deformations in the nonlinear elastic regime

In this paper, a multiscale structural optimization framework capable of efficiently designing two-scale structures with prescribed displacements in the nonlinear elastic regime is presented. In contrast to previous multiscale structural optimization frameworks, which are founded upon the assumptions of linear elasticity, the present framework is capable of efficiently operating within the nonlinear elastic regime. At the core of the present framework is a parameterized microscale geometry, which through the straightforward manipulation of the microscale parameters provides direct access to both positive and negative Poisson's ratios. The microscale model is concurrently coupled to the macroscale model such that only the microscale parameter space traversed by the optimizer is resolved during the optimization procedure, leading to a significant reduction in the computational expense of analysis. To demonstrate the capability of this framework, three prescribed deformation profiles are targeted by three distinct optimization procedures. In all instances, the deformation profile is successfully targeted. To verify the accuracy of the optimized structures, high-fidelity single-scale simulations are performed. In each case, excellent agreement is noted between the high-fidelity simulations and the corresponding optimized macroscale displacement fields, with errors of less than 10%.