Continuum damage mechanics applied to quasi-brittle materials

The dissipative behaviour of quasi-brittle solids (rocks, concrete, ceramics, etc.), inherent to the evolution of a number of micro- and mesocracks within the material, has been one of privileged fields of Continuum Damage Mechanics (CDM). It is however relatively recently that the full extent of complex mechanisms relevant to progressive microcracking was approached with some success with the CDM methodology and with micromechanical modelling tools. This is because the inelastic behaviour relative to multiple microcracking comprises specific anisotropic effects, volumetric dilatancy and some complex hysteretic phenomena (non-compatible with the scope of the classical plasticity theory). The latter phenomena are known to be induced by complementary dissipation due to frictional resistance and sliding closely connected to opening/closure transition for microcracks. In such a manner progressive, oriented microcracking and frictional resistance and sliding over some defects should be simultaneously controlled for a large range of compression-dominated loading paths. The paper, and the corresponding lecture, present an attempt on an unified approach concerning the field at stake. The phenomena involved require reliable control of damage growth, of opening/closure transition for mesocracks and of plasticity-like sliding evolution on closed-crack sets. These problems are approached in the framework of rate-type constitutive theory with internal variables. The different model segments are three-dimensional and micromechanic ally motivated in their essential ingredients. Still, they are built to provide tools for efficient structural analysis for engineering problems. The essential part of the modelling synthesised represents a continuum damage model coupled with a form of sliding-related plasticity. The interaction of the two phenomena is efficiently conducted, allowing for reasonably menageable identification of material constants and numerical implementation. Further problems related to interaction of a primary material anisotropy with a damage-induced one and to microcrack interaction effects are discussed in the final part of the paper.