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

Abstract

Crucial issues concerning non-linear behaviour of quasi-brittle materials like some rocks, concrete and certain ceramics are addressed in the paper. In fact, inelastic response for this class of solids results from the evolution 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 progressive anisotropic degradation and accounting for frictional sliding over internal crack surfaces is synthesised. The model is three-dimensional and micro-mechanically motivated in its essential ingredients. At 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 one hand and of applicability of the model on the other, is endeavoured through relative simplicity of the approach (a small number of material constants to identify) and its modular character allowing three distinct degrees of complexity. The first `basic' level concerns modelling of the anisotropic degradation by multiple mesocrack growth generating volumetric dilatancy and non-symmetrical strength effects. The second level consists in accounting for the “normal” moduli recovery with respect to mesocrack-sets constrained to close under predominantly compressive loads (unilateral effect). The damage and frictional blocking/sliding coupled effects are dealt with in a non-classical way at the third level allowing thus to treat highly complex loading paths with rotating loading and damage axes (torsional paths for example). Hysteretic effects for loading and unloading due to plasticity-like mesocrack friction are commented. Some computational aspects relative to the model (in its basic, extended and coupled version) are then outlined. It is stressed that a fully implicit integration scheme appears naturally compatible one for a class of damage models 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 sliding is successfully managed by coupled algorithm. The corresponding double integration is facilitated by low interaction degree between damage and sliding criteria. Significant examples are shown illustrating damage and friction induced non-linear behaviour together with complex hysteretic effects for cyclic loading. They illustrate relevancy of the coupled model for quasi-brittle rocks and efficiency of the algorithms employed.