Damien Halm

A Model of Anisotropic Damage by Mesocrack Growth; Unilateral Effect:

A three-dimensional model of anisotropic damage by mesocrack growth is first described in its basic version, employing a second-order tensorial damage variable. The model—concerning rate-independent, small strain, isothermal behaviour—allows to take into account residual effects due to damage and reduces any system of mesocracks to three equivalent orthogonal sets. This first version is then extended to account for elastic moduli recovery due to crack closure. Micromechanical considerations impose to employ a fourth-order crack-related tensor when the mesocracks are constrained against opening. Unlike some models which do not avoid (or rectify a posteriori) discontinuities of the stress-strain response, the approach herein ensures a priori the stress continuity and allows to express a convenient macroscopic opening-closure criterion. Nevertheless, the new formulation maintains the orthotropy of the effective properties (instead of an eventual, more general form of anisotropy). Finally, it appears that the extended version does not introduce additional material constants compared to the basic version. The model is tested by simulating the behaviour of Fontainebleau sandstone.

Comparaison des concepts et prédictions des modèles

ABSTRACT Different models presented in this volume are compared. This comparision concerns their concepts and procedures of parameters determination, as well as their predictions.

Computational issues and applications for 3D anisotropic damage modelling: coupling effects of damage and frictional sliding

ABSTRACT The inelastic response for quasi-brittle materials is due to generation and growth of oriented mesocracks. A 3D model taking into account most of effects induced by this kind of damage is outlined. The emphasis is put on the modelling of damage by mesocrack growth and frictional sliding on closed mesocrack lips. From a numerical point if view, a purely implicit local integration scheme has been chosen for both damage and sliding evolutions. This method has been found particularly adapted to the damage modelling at stake here. Although the proposed model couples two dissipative phenomena, the numerical integration is facilitated by a low degree of effective connection between the equations governing each evolution. Simulations of boundary-value problems illustrate the pertinence of the coupled model.

Modelling of coupled effects of damage by microcracking and friction in closed cracks

The paper addresses crucial issues concerning inelastic behaviour of quasi-brittle solids, principally rock-like materials. 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 complex compression-dominated loading paths. Progressive microcracking and frictional blocking/sliding induce anisotropic behaviour, volumetric dilatancy and complex hysteretic effects due to crack opening/closure transition and plasticity-like sliding evolution. These problems are explored and modelled in the framework of rate-type constitutive theory with internal variables. The model is three-dimensional and micromechanically motivated in its essential ingredients. Meanwhile it is built to provide a tool for efficient structural analysis and, as such, represents a continuum damage approach coupled with a form of plasticity. The settlement between apparently conflicting requirements of physical pertinency on the one hand and of applicability of the model on the other hand, is attempted through relative simplicity of the approach (a small number of material constants to identify) and its modular character involving three increasing levels of complexity. The first, ‘basic’ level, concerns modelling of anisotropic degradation by multiple microcrack growth generating volumetric dilatancy and permanent strain. The second level consists in accounting for the ‘normal’ moduli recovery due to crack closure under predominantly compressive loads (unilateral effect). These two levels are outlined briefly at the beginning of the paper. The text focuses on the third level of modelling involving concomitant dissipative phenomena of damage by microcracking and frictional sliding leading to complex hysteretic effects such as inelastic unloading. The interaction of the two phenomena is successfully managed by the coupled model.