Material forces for inelastic models at large strains: application to fracture mechanics

Elastomeric materials show a wide range of different elastic and inelastic properties. Additionally, this class of materials is subjected to large deformations. Considering all these effects, fracture mechanical investigations are very challenging tasks and cannot be performed with standard approaches. Effects of inhomogeneities and discontinuities such as cracks can be investigated with the so-called material force approach in an efficient and elegant way. For comprehensive investigations of inelastic materials, the complete balance of the material motion problem has to be formulated. In this case, the material volume forces depend on the internal history variables which are required for the inelastic constitutive model. This paper derives a general formulation for rate-dependent and rate-independent inelastic materials based on a multiplicative split of the deformation gradient to cover viscoelastic and elastoplastic materials at finite deformations.