Topological derivative based optimization of 3D porous elastic microstructures

As an alternative to the well established microstructural optimization techniques, topological derivative based optimization framework has been proposed and successfully implemented for tailoring/optimizing 2D elastic composites recently, Amstutz et al. [1]. In this paper, an optimization framework for 3D porous elastic microstructures is presented which is based on the notion of topological derivative and the computational homogenization of elastic composites. The sensitivity of the homogenized elasticity tensor to the insertion of infinitesimal hollow spheres within the elastic microstructure is used as the measure for the finite element based evolutionary optimization algorithm. The capabilities of the proposed framework, which is free of any regularization parameter, is assessed by means of example problems including some comparisons with analytical bounds.