Viscoelastic deformation with damage of quasi-brittle composites: mathematical and computational issues

Abstract

Reversible i) viscoelastic deformation of material samples or engineering structures, caused by external mechanical, thermal, etc. loads, quite diferent under tension and compression in many cases, is accompanied by irreversible ii) damage, starting with the formation of micro-fractured zones and continued with the initiation of propagation of macroscopic cracks. A sufficiently simple, but still interesting model problem covering both i) and ii), motivated by the behaviour of cementitious composites, as fibre-reinforced concrete, is presented in this contribution, together with proper verification of existence of its weak solutions and convergence of appropriate sequences of approximate solutions in finite-dimensional spaces. This is based on the method of discretization in time, on the smeared damage relying on the Eringen regularization and on the extended finite element method, covering macroscopic cracking, open to possible generalizations in several directions.