Phase field modeling of general imperfect interfaces

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Material interfaces play an important role in many disciplines such as in engineering or in materials science. Illustrative examples include cracks in quasi-brittle materials or grain boundaries in polycrystals. If the geometry of such interfaces is known in advance, they can be conveniently modeled as sharp interfaces. However, this information is not always available. For instance, the position as well as the geoemtry of cracks are not known beforehand but are part of the boundary value problem to be solved. This type of problems - also referred to as Free Discontinuity Problems - can be effectively modeled by means of phase field theory.Focusing on mechanical loading, several different phase field approximations for sharp interfaces can indeed be found in the literature. However, most of them are based upon severe simplification (Griffith-type models). By way of contrast, the other models are based on relatively simple cohesive zone approaches. Furthermore, thermodynamical aspects are only partly considered and a geometrically linearized setting is adopted. For this reason, a generalization is to be elaborated within this project. To be more precise, the goal of this project is a consistent phase field approximation of complex sharp interface models undergoing large deformations.Concerning sharp interfaces, a framework recently proposed by the applicant represents the starting point. It is the first one allowing to capture arbitrary material symmetries (anisotropy) by simultaneously fulfilling all fundamental balance laws in physics - also in the case of large deformations. This framework is to be approximated by phase field theory. In order to guarantee convergence of the phase field theory to the balance equations of the underlying sharp interface model, a phase field theory recently presented by the applicant will be considered and significantly modified and extended. It is based on a rank-1 decomposition of the deformation gradient and shows higher convergence rates than previous phase field models (towards the sharp interface problem).This project represents the first step towards deriving physically sound constitutive models for phase field approaches. While kinetic effects, i.e., those related to the propagation of interfaces, will be ignored in the submitted proposal, they certainly have to be included in a second step. By doing so, a modeling framework can eventually be established which allows to effectively analyze the interaction between bulk materials and interfaces and finally, to support developing new materials.