Zusammenfassung

This thesis deals with three-dimensional modeling of heterogeneous cohesive materials. The investigations focus exemplarily on concrete and fiber-reinforced concrete as composite materials, which exhibit highly non-linear material behavior. Micro-mechanical failure phenomena like delamination of fibers in a matrix as well as microcracks and micropores in concrete result in narrow failure zones where strains localize and energy dissipation occurs. The elastic material stiffness is reduced due to localized damage and discrete evolving cracks. The width of the failure process zone is typically several orders of magnitude smaller than the structural dimensions, which implies displacements of multiple scales. Resolving these displacements and the high gradients in the solution functions requires either a very fine discretization or an enhancement of the approximation space. The main part of this study concentrates on a detailed numerical analysis of delamination in fiber-reinforced composites and crack evolution in concrete by means of the extended finite element method. In the second part a two-scale method is proposed that incorporates the effect of fine scale failure phenomena in the macroscopic structural behavior.

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