Summary The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions.

Assessing the overall instantaneous behavior and strength properties of jointed materials have been the subject of important investigations in the last decades, including phenomenological or micromechanics-based contributions. However, less attention has been dedicated to delayed component of deformation in such media. This issue is addressed in this paper, which is devoted to the formulation of a micromechanical approach to effective viscoelastic properties of jointed rocks with consideration of constituents aging. At the scale of representative elementary volume (REV), the joints are modeled as planar interfaces whose behavior is described by means of generalized viscoelastic state equations under normal and shear loading conditions. Closed-form expressions for the homogenized creep tensor are derived from solving an appropriate viscoelastic concentration problem stated on the REV. The local strain and displacement jump fields are analyzed by extending the concept of strain concentration to relate the components of joint displacement jump to macroscopic strain. Main features of the theoretical overall creep behavior, such as the anisotropy associated with the privileged joint orientations, are highlighted through explicit formulations in some particular configurations of the jointed medium. Finally, the ability of the approach to accurately reproduce the creep behavior of jointed media is assessed by comparison with experimental data as well as with finite element solutions derived in the context of multilayered stratified composite modeling.

The constitutive behavior of geomaterials is generally affected by the presence at different scales of discontinuity surfaces with different sizes and orientations. According to their mechanical behavior, such discontinuities can be distinguished as cracks or fractures. Fractures are interfaces that can transfer normal and tangential stresses, whereas cracks are discontinuities without stress transfer. Regarding the formulation of the behavior of materials with isotropic distribution of micro-cracks or fractures, previous works had essentially focused on their instantaneous response induced by structural loading. Few research works have addressed time-dependent (delayed) behavior of such materials. The present contribution describes the formulation and computational implementation of a micromechanics-based modeling for viscoelastic media with an isotropic distribution of micro-fractures. The homogenized viscoelastic properties are assessed by implementing a reasoning based on linear homogenization schemes (Mori-Tanaka) together with the correspondence principle for non-aging viscoelastic materials. It is shown that the homogenized viscoelastic behavior can be described by means of a generalized Maxwell rheological model. The computational implementation is developed within the finite element framework to analyze the delayed behavior of geomaterials with the presence of isotropically distributed micro-fractures under plane strain conditions. Several examples of applications are presented with the aim to illustrate the performance of the finite element modeling. The assessment of the approach accuracy and the corresponding code verification are performed by comparing the numerical predictions with analytical solutions for simple and complex geo-structures.

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.

No abstract