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Computational prediction damage in cementitious composites, as steel fibre reinforced ones, under mechanical, thermal, etc. loads, manifested as creation of micro-fractured zones, followed by potential initiation and evolution of macroscopic cracks, is a rather delicate matter, due to the necessity of bridging between micro-and macro-scales. This short paper presents a relatively simple approach, based on the nonlocal viscoelasticity model, coupled with cohesive crack analysis, using extended finite element techniques. Such model admits proper verification of its existence and convergence results, from the physical and mathematical formulation up to software implementation of relevant algorithms. Its practical applicability is documented on a sequence of representative computational examples.

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Computational prediction of damage in cement-based composites, as steel fibre reinforced ones, under mechanical, thermal, etc. loads, manifested as creation of micro-fractured zones, followed by potential initiation and evolution of macroscopic cracks, is a rather delicatematter, due to the necessity of bridging between micro- and macro-scales. This short paper presents a relatively simple approach, using certain extension of the finite element technique, open to possible generalizations. Such model admits proper verification of its existence andconvergence results, from the physical and mathematical formulation up to software implementation of relevant algorithms. Its practical applicability is documented on computational examples.

The widely used method for solution of impacts of bodies, called the penalty method, is based on the contact force proportional to the length of the interpenetration of bodies. This method is regarded as unsatisfactory by the authors of this contribution, because of an inaccurate fulfillment of the energy conservation law and violation of the natural demand of impenetrability of bodies. Two non-traditional methods for the solution of impacts of bodies satisfy these demands exactly, or approximately, but much better than the penalty method. Namely the energy method exactly satisfies the conservation of energy law, whereas the kinematic method exactly satisfies the condition of impenetrability of bodies. Both these methods are superior in comparison with the penalty method, which is demonstrated by the results of several numerical examples.