In this paper, a coupled elasto-plastic damage model is proposed in multi-laminate framework for modeling coupled plastic flow and damage evolution in geomaterials. In the model micro-macro effects of damage evolution are considered. In macro scale, the effective elastic tensor of damaged material is determined using damage variable and in micro scale, the total plastic strain is considered as the consequence of frictional sliding in sampling planes randomly distributed in the elastic solid matrix.
In most rock materials, two types of inelastic behavior can be generally identified, the plastic deformation related to sliding mechanisms inside the microstructure of rock matrix and material damage induced by growth of micro-cracks. In the case of cohesive geo-materials like rocks and concrete, damage induced by micro-cracks is recognized as an important, even essential, dissipation mechanism of inelastic deformation and failure. Therefore, it is necessary to develop constitutive models taking into account such a coupling in order to better describe fundamental features of mechanical behavior of these materials. The most commonly used theories for modeling of materials are plasticity, fracturebased approaches and continuum damage mechanics (CDM). Though the plasticity models are far superior to elastic approaches in representing hardening and softening characteristics, they fail to address the process of damage due to micro-cracks growth, such as the stiffness degradation, the unilateral effect, etc. Intermingled with classical continuum mechanics in uncoupled manner, fracture mechanics suggests an approach to describe localized damage as to be represented by the ideal or regular discrete cracks with definite geometries and locations, and it has been extensively used in engineering practice . Continuum damage mechanics, which employs some continuum variables to describe the micro-defects, has been an appealing framework for modeling geo-materials. Based on the thermodynamics of irreversible processes, the internal state variable theory and relevant physical considerations (Ju, 1989), CDM provides a powerful and general framework for the derivation of consistent constitutive models suitable for many engineering materials, including geo-materials. Coupled with plasticity or by means of empirical definitions, the irreversible strains due to plastic flow can also be accounted for in elasto-plastic damage theories (see for example [2–11]. In most of these models, the damage variables are defined through a phenomenological way originating from the classical Kachanov's (1958) damage variable . The resulting models consider a scalar variable measuring the ratio between damage and intact surfaces on which the stresses act (d=A/A0 where ‘A0’ is the initial area of undamaged material and ‘A’ intact area of damaged material).
These damage variables are essentially measures of the damage's mechanical effects rather than the microstructure.
the scalar damage ones, where one or several scalars are adopted to characterize the isotropic damage processes;
the tensor damage ones, where secondorder, fourth-order or even eighth-order damage tensor are necessary to account for anisotropic damage effects.