Computational approach to localization using global energy minimization

Damage localization induced by strain softening can be predicted by the direct minimization of a global energy function [Baker G, Hunt GW. In: Bazant ZP, et al., editors. Damage of Quasi-brittle Structures. London: E and FN Spon, 1994. p. 387–94; Hunt GW, Baker G. J Mech Phys Solids 1995;43(7):1127–50]. This article concerns the computational strategy for implementing this principle for softening materials such as concrete. Instead of using heuristic global optimization techniques, our strategies are a hybrid of local optimization methods with a path-finding approach to ensure a global optimum. With admissible nodal displacements being independent variables, it is easy to deal with the geometric (mesh) constraint conditions. The direct search optimization methods recover the localized solutions for a range of softening lattice models which are representative of the quasi-brittle structures.