Adaptive methods in the mechanics of heterogeneous materials

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A use of heterogeneous materials such as composites is very attractive in the sense of a lightweight construction, thus becoming more common in industrial practice. The growing demands on a computer simulation of such materials are not only related to a more profound theoretical treatment, but also to the associated high computational cost. This motivates the development of adaptive methods in this thesis for balancing the accuracy and the numerical efficiency of such simulations in a systematic and automated manner. Our attention is limited to a two-scale Cauchy and a micromorphic continuum, respectively in micromechanics and generalized mechanics. We handle both linear elastic and elastoplastic material behavior within a small strain theory. The adaptive procedures are mainly developed on the basis of goal-oriented error estimates, aiming at errors in a user-defined quantity of interest representing the goal of a simulation. Therewith, we control both model and discretization errors of the finite element method. For homogenization of physically nonlinear heterogeneous materials, an adaptive procedure based on an effective empirical indicator is additionally proposed.