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Here we present a multi-scale model to carry out the computation of brittle composite materials reinforced with fibers, and we show its application to standard reinforced concrete. The computation is performed within an operator-split framework on the macro-scale, which allows for different failure mechanisms to develop in separate phases, as both the concrete and the bond-slip exhibit non-linear behavior. The computations on the micro-scale are performed for each constituent separately. The reinforcement is taken to be linear elastic, and the bond-slip is handled as a plastic deformation. The standard elastoplastic procedure is used to compute the bond stress- es, combined with the X-FEM methodology to give the global repre- sentation of slip. The crack development in concrete, on the other hand, is described with a damage model with exponential softening, where ED-FEM is used to represent localized failure. A numerical example is shown to test the developed methodology.

Multi-scale representation of plastic deformation in fiber-reinforced materials: application to reinforced concrete