Topology optimization of pressure dependent elastoplastic energy absorbing structures with material damage constraints

In this study, a density-based topology optimization framework for the design of energy absorbing structures with pressure-dependent yield behavior is presented. The plastic work is maximized while the accumulation of damage is managed through the use of macroscopic fracture constraints. Pressure-sensitive yield behavior is captured by the Drucker-Prager plasticity model and an adjoint method is presented to calculate the path-dependent sensitivities of the objective and constraint functions dependent on this model. Several numerical examples are used to demonstrate the effect of varying the pressure sensitivity of the yield function and the underlying physics is reflected in the final topologies. It is also demonstrated through numerical examples that the use of damage limiting constraints leads to optimal topologies with less damage localization for the same amount of plastic work.