Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting

The concern of this work is a consequent exploitation of the notion of material forces for the application within hyperelastostatic fracture mechanics. Contrary to physical forces, material forces act on the material manifold, thus essentially representing the tendency of defects like cracks or inclusions to move relative to the ambient material. Based on the formulation of the appropriate quasi-static balance laws in the material space we aim at a fresh look onto classical aspects of hyperelastostatic fracture mechanics. Operating throughout within the geometrically nonlinear setting we emphasize on the one hand the duality of the direct and the inverse motion description and on the other hand we re-establish the classical path integrals from elementary equilibrium considerations in the material space.