A topology optimization method for hyperelastic porous structures subject to large deformation

Porous infill, rather than the solids, can provide high stiffness-to-weight ratio, energy absorption, thermal insulation, and many other outstanding properties. However, porous structure design to date have been majorly performed with topology optimization under small deformation assumption. The effect of porosity control under large deformation is not explored yet. Hence, this paper exploits the topological design method of porous infill structures under large deformational configuration. Specifically, the neo-Hookean hyperelasticity model is adopted to simulate the large structural deformation, and the adjoint sensitivity analysis is performed accordingly with the governing equation and constraint. The maximum local volume fractions before and after deformation are concurrently constrained and especially for the latter, the representative volume points (RVPs) are modeled and tracked for evaluating the local volume fractions subject to the distorted mesh configuration. The local volume constraints are then aggregated with the P-norm method for a global expression. Iterative corrections are made to the P-norm function to rigorously restrict the upper bound of the maximum local volume. Finally, several benchmark cases are investigated, which validate the effectiveness of the proposed method.