Anisotropic damage in quasi-brittle solids: modelling, computational issues and applications

Crucial issues concerning non-linear behaviour of quasi-brittle materials l ike some rocks, concrete and certain ceramics are addressed in the paper. I n fact, inelastic response for this class of solids results from the evolut ion of a large number of micro- and mesocracks accompanied with frictional effects regarding closed cracks for compressive loading paths. Progressive microcracking produces volumetric dilatancy, induced anisotropy and further pressure sensitivity on the macroscale. A continuum damage model attempting to capture salient Features of progress ive anisotropic degradation and accounting for frictional sliding over inte rnal crack surfaces is synthesised. The model is three-dimensional and micr o-mechanically motivated in its essential ingredients. Al the same time it is built to provide a tool for structural analysis purpose. The settlement between apparently conflicting requirements of physical pertinency on the o ne hand and of applicability of the model on the other, is endeavoured thro ugh relative simplicity of the approach (a small number of material constan ts to identify) and its modular character allowing three distinct degrees o f complexity. The first 'basic' level concerns modelling of the anisotropic degradation b y multiple mesocrack growth generating volumetric dilatancy and non-symmetr ical strength effects. The second level consists in accounting for the "nor mal" moduli recovery with respect to mesocrack-sets constrained to close un der predominantly compressive loads (unilateral effect). The damage and fri ctional blocking/sliding coupled effects are dealt with in a non-classical way at thr third level allowing thus to treat highly complex loading paths with rotating loading and damage axes (torsional paths for example). Hyster etic effects for loading and unloading due to plasticity-like mesocrack fri ction are commented. Some computational aspects relative to the model (in its basic, extended an d coupled version) are then outlined. It is stressed that a fully implicit integration scheme appears naturally compatible one for a class of damage m odels as it is for the model at stake (in spite of its specific features). The frictional sliding evolution is dealt with in a way close to plasticity integration algorithms. Concomitant, growth of damage and frictional slidi ng is successfully managed by coupled algorithm. The corresponding. double integration is facilitated by low interaction degree between damage and sli ding criteria. Significant examples are shown illustrating damage and friction induced non -linear behaviour together with complex hysteretic effects for cyclic loadi ng. They illustrate relevancy of the coupled model for quasi-brittle rooks and efficiency of the algorithms employed. (C) 2000 Elsevier Science S.A. A ll rights reserved.