Sensitivity analysis of a non‐local, gradient enhanced damage model

Abstract

AbstractThe sensitivities for a non‐local, gradient enhanced damage model are analysed. To model the damage accumulation, a non‐local, gradient enhanced damage model is proposed. Contrary to other approaches, where a local variable is coupled to a non‐local one, see e.g. [1–3], solely a non‐local variable is introduced which is calculated simultaneously with the displacements for each node point. By means of a variational approach, the stiffness matrix as well as the sensitivities, see [4], can be calculated for implementation into the finite element method (FEM) and the minimisation, using sequential quadratic programming (SQP). The framework allows to optimise given geometries with respect to the damage evolution either directly with the damage as the objective function, or indirectly by choosing the damage as a constraint at every finite element node.