A micromechanics‐based approach to damage propagation criterion in viscoelastic fractured materials regarded as homogenized media

Abstract

This paper aims to formulate a damage propagation criterion in microfractured viscoelastic materials, relying upon a micromechanics reasoning together with thermodynamics concepts. The fracture density is regarded as damage parameter at macroscopic scale. The equivalent behavior of the heterogeneous material (solid matrix + fractures) is first formulated within the framework of viscoelastic homogenization theory. In this context, relevant relationships relating local fields to macroscopic fields are derived, thus allowing a clear micromechanical interpretation of quantities involved in the upscaling process, such as the residual or viscous strains. Based on thermodynamic concepts, the energy dissipation and the free energy of the homogenized viscoelastic material are deduced at the macroscopic scale. The formulation of an energetic-based criterion for damage propagation in viscoelastic fractured materials is then achieved by viewing the macroscopic energy release rate as the thermodynamic force responsible for propagation. Due to the delayed deformation component, the formulation is time-dependent. Since it is formulated directly at the homogenized material level, the main advantage of the approach developed in this work is the rigorous determination of the energy release rate expression, without neglecting any residual term. In the last part of the paper, several numerical applications are performed to illustrate the main features of the modeling and to provide comparison with available simplified formulations. Finally, the proposed damage propagation criterion is applied to give qualitative insights on fracturing process of sedimentary layered rocks at geological times scale viewed as a long-term mechanical damage problem, emphasizing the viscosity effects in preventing fracture propagation.

Upscaling modeling of effective elastic properties and anisotropic damage propagation in fractured materials regarded as homogenized media

“…A smaller number of studies investigate the mechanical behavior by treating the discontinuities as fractures [45][46][47][48][49][50][51][52]. In addition to determining the equivalent behavior, some studies have also demonstrated success in using micromechanics theory to estimate propagation criteria and damage evolution models of the material at the macroscopic scale based on microscopic parameters of fractures and the solid material [53][54][55][56][57][58][59]. It is important to note, however, that only a few studies address the anisotropic distribution/propagation of cracks by using micromechanics [39,[60][61][62][63].…”