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Simulation of fracture in heterogeneous elastic materials with cohesive zone models
In brittle composite materials, failure mechanisms like debonding of the matrix-ﬁber interface or ﬁber breakage can result in crack deflection and hence in the improvement of the damage tolerance. More generally it is known that high values of fracture energy dissipation lead to toughening of the material. Our aim is to investigate the inﬂuence of material parameters and geometrical aspects of ﬁbers on the fracture energy as well as the crack growth for given load scenarios. Concerning simulations of crack growth the cohesive element method in combination with the Discontinuous Galerkin method provides a framework to model the fracture considering strength, stiffness and failure energy in an integrated manner. Cohesive parameters are directly determined by DFT supercell calculations. We perform studies with prescribed crack paths as well as free crack path simulations. In both cases computational results reveal that fracture energy depends on both the material parameters but also the geometry of the ﬁbers. In particular it is shown that the dissipated energy can be increased by appropriate choices of cohesive parameters of the interface and geometrical aspects of the ﬁber. In conclusion, our results can help to guide the manufacturing process of materials with a high fracture toughness.