Application of the material force method to isotropic continuum damage

Abstract

 The objective of this work is the exploitation of the notion of material forces in computational continuum damage mechanics. To this end we consider the framework of isotropic geometrically non–linear continuum damage and investigate the spatial and material settings that lead to either spatial or material forces, respectively. Thereby material forces essentially represent the tendency of material defects to move relative to the ambient material. In this work we combine an internal variable approach towards damage mechanics with the material force method. Thus the appearance of distributed material volume forces that are conjugated to the damage field necessitates the discretization of the damage variable as an independent field in addition to the deformation field. Consequently we propose a monolithic solution strategy for the corresponding coupled problem. The underlying kinematics, strong and weak forms of the coupled problem will be presented and implemented within a standard Galerkin finite element procedure. As a result in particular global discrete nodal quantities, the so–called material node point (surface) forces, are obtained and are studied for a number of computational examples.