A phase-field approach for crack modelling of elastomers

The description of a problem related to an evolving interface or a strong discontinuity requires to solve partial differential equations on a moving domain, whose evolution is unknown. Standard computational methods tackle this class of problems by adapting the discretized domain to the evolving interface, and that creates severe difficulties especially when the interface undergoes topological changes. The problem becomes even more awkward when the involved domain changes such as in mechanical problems characterized by large deformations. In this context, the phase-field approach allows us to easily reformulate the problem through the use of a continuous field variable, identifying the evolving interface (i.e. the crack in fracture problems), without the need to update the domain discretization. According to the variational theory of fracture, the crack grows by following a path that ensures that the total energy of the system is always minimized. In the present paper, we take advantage of such an approach for the description of fracture in highly deformable materials, such as the so-called elastomers. Starting from a statistical physics-based micromechanical model which employs the distribution function of the polymer’s chains, we develop herein a phase-field approach to study the fracture occurring in this class of materials undergoing large deformations. Such a phase-field approach is finally applied to the solution of crack problems in elastomers.