Consistent tangent stiffness for nonlocal damage models

This paper deals with the computational analysis of strain localization problems using nonlocal continuum damage models of the integral type. The general framework for a consistent derivation of the “nonlocal” tangent stiffness is presented. The properties of the tangent stiffness matrix are discussed and the corresponding assembly procedure is described. The quadratic rate of convergence of the Newton–Raphson iteration procedure is demonstrated and the efficiency of the proposed technique is compared to the standard approach based on the secant or elastic stiffness matrices. In this context, performance of direct and iterative solvers for the linearized equilibrium equations is also examined.