ABSTRACT
Considering the limitations of the ideal entropic elasticity models, a micromolecular model for material failure is introduced subsequently as an extension to the micro-sphere model of Miehe et al. (2004). The model is based on a serial connection of a Langevin-type spring representing the energy storage owing to conformational changes induced by deformation, to a bond potential representing the energy stored in the polymer chain due to the interatomic displacement. For the representation of the micro-macro transition in terms of non-affine kinematics, the micro-sphere model is used. The Morse potential is utilized for the interatomic bond, which describes the energetic contribution to rubber-like materials and governs the failure of the polymer chain in terms of bond rupture. Moreover, the model enables uniaxial tension, equi-biaxial tension, pure shear or pure dilatational failure modes, since it is not constructed in terms of a classical volumetric-isochoric split of the free energy function. The coupled representation in terms of the volumetric and isochoric stretches enables the definition a unified failure criterion for all deformation modes. This structure, however, does not prevent the model from showing nearly incompressible behaviour at small to moderate stretches. Unlike the compressible models introduced in the previous subsection, the proposed model attaches the volumetric part to a bond potential where the failure is attained as the
energy barrier and the peak stretch is attained. Therefore, the volumetric deformations are considered to be purely energetic. Further information and algoritmic treatment of the proposed model is documented in Dal & Kaliske (2009).
