Topology Optimization of Energy-Dissipating Plastic Structures with Shear Modified Gurson–Tvergaard–Needleman Model

Abstract

This paper presents a density-based topology optimization framework for designing energy-dissipating plastic structures. In order to mitigate the material damage during the plastic energy dissipation process, the total material volume in a design is minimized while subjected to a minimum plastic work constraint and a maximum damage constraint. The Gurson–Tvergaard–Needleman (GTN) model with shear damage modifications is adopted to simulate the physics of ductile-damage mechanisms under various stress states. Path-dependent design sensitivities are analytically derived using the adjoint method within the framework of nonlinear finite element analysis. The effectiveness of the proposed framework is demonstrated by a series of numerical examples that shows the proposed framework can successfully limit damage in optimized plastic designs under the prescribed threshold by reconfiguring structural topologies. More notably, compared to the designs obtained with the von Mises plasticity model, damage constrained plastic designs with the GTN model have overall better ductility, higher load carrying capacity, and higher plastic work dissipation before failure initiation.