On the nonlocal computational modelling of damage in brittle and quasi-brittle materials

Computational prediction of progressive micro-cracking, observed namely in brittle and quasi-brittle materials, resulting in their softening behaviour, needs some regularization approach. Its social relevance increases with the massive application of steel fibre-reinforced concrete and similar composites in buildings and engineering structures. However, most approaches contain ad hoc computational procedures and tricks, without a proper mathematical existence and convergence analysis for the time development of damage. This paper demonstrates the possibility of such analysis, at least for a simplified model problem of structural dynamics, with numerous references to available generalizations and some application examples.