Modeling and simulation of general imperfect interfaces using phase-field-theory

Mechanical interfaces at the microscale influence the effective macroscopic properties of materials in various forms such as shear bands or grain boundaries in nanomaterials. On the macroscopic scale, interfaces occur, for example, in the form of cracks or boundaries between tectonic plates. Mechanical interfaces can be characterized as coherent interfaces or non-coherent interfaces. While the displacement field is continuous across coherent interfaces, discontinuities occur in the case of non-coherent interfaces. Coherent interfaces can be described by an additional constitutive model depending on the deformation of the interface. A classic example is hyperelasticity. The additional constitutive model allows for jumps in the stress vector as tangent stresses occur in the interface. If the energy of the coherent interface is constant one speaks of perfect interfaces. For perfect interfaces, both, the displacement field and the stress vector are continuous. By way of contrast, non-coherent interfaces can be described as cohesive zone models or generalized interfaces. For cohesive zone models, the interface model only depends on the displacement jump. This allows stress vectors to be transferred across the interface leading to a continuous stress vector field. Generalized interfaces depend on the opening and the deformation of the interface and represent the most general case. Here, discontinuities over the interface occur in the stress vector field as well as in the displacement. In this thesis finite strain phase field approximations for the two latter cases – interface elasticity and cohesive zone models – are presented. By using the phase field method, free boundary problems with evolving interfaces can be described and solved without an exact description and parametrization of the interface’s geometry. In contrast to sharp interface formulations, the interface is approximated as a diffuse volume with an order parameter – the phase field – and an internal length scale. With vanishing internal length the phase field description converges towards the sharp interface formulation in the sense of Γ-convergence. Furthermore, the nucleation and evolution of interfaces is included within the method without any additional cost. The wide range of capabilities of the novel descriptions are highlighted by numerical examples.