Multiscale Modeling of Damage in Micro-Heterogeneous Materials based on incremental variational formulations

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To optimize modern engineering applications the development of innovative materials is of vital importance. For this purpose more and more materials are used that are characterized by a distinct microstructure, e.g. consisting of a matrix with embedded fibers. The simulation of these micro-heterogeneous materials requires the incorporation of the highly nonlinear and irreversible mechanical phenomena at the microscale. In this context direct micro-macro transition approaches based on microscopic Finite-Element calculations of the mechanical fields provide a suitable framework. Of particular interest is the prediction of failure-initializing states that are characterized by microscopic stress concentrations as a result of stiffness reduction (damage). Primary objective of the intended research project is therefore to develop a material model for micro-heterogeneous materials, which is able to represent the damage processes at the microscale numerically. Mainly, the planned formulation is based on discrete microscopic calculations requiring special damage material laws for the individual microscopic components. These have to be developed in the framework of incremental variational formulations. Subsequently, convex hulls are planned to be constructed for the resulting energies, which then lead to mesh-independent solutions of microscopic calculations. This has then to be analyzed in numerical studies where the influence onto homogenized macroscopic stress- and damage quantities is investigated.