Material Force Method. Continuum Damage & Thermo-Hyperelasticity

Abstract

The numerical analysis of material forces in the context of continuum damage and thermo-hyperelasticity constitutes the central topic of this work. We consider the framework of geometrically non-linear 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. Material forces are thus important in the context of damage mechanics and thermo-elasticity, where an evolving damage variable or thermal effects can be understood as a potential source of heterogeneity. Thus the appearance of distributed material volume forces that are due to the damage or temperature gradient necessitates the discretization of the damage or temperature variable as an independent field in addition to the deformation field. Consequently we propose a monolithic solution strategy for the corresponding coupled problem. 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.