Gurson–Tvergaard–Needleman model guided fracture‐resistant structural designs under finite deformations

Abstract

AbstractA finite strain shear modified Gurson–Tvergaard–Needleman (GTN) model based on multiplicative elastoplasticity, together with its implementation details, is presented. This GTN model which can simulate the loss of load‐carrying capacity of porous metals through nucleation, growth, shearing, and coalescence of voids is incorporated in an optimization framework for designing structures with optimal plastic energy dissipation capacity while satisfying prescribed constraints on material usage and damage. An adjoint method‐based analytical path‐dependent sensitivity analysis is presented that can be used with gradient‐based optimization algorithms. Using the proposed topology optimization formulations, the optimized designs exhibit well‐constrained fracture at the design displacements. Ultimate performance analyses of the optimized designs demonstrate that the fracture‐resistant designs can have higher ductility, ultimate strength as well as improved energy dissipation, as compared to the designs guided by von Mises plasticity where no fracture mechanisms are modeled. Moreover, due to finite deformations, a fracture can initiate at multiple locations and critical fracture locations can change during the loading process. In addition, different failure modes are revealed from different optimized designs under large deformations.