Numerical implementation of a micromechanics-based viscoelastic model for geomaterials with isotropically distributed micro-fractures

Abstract

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.

Micromechanical approach to effective viscoelastic behavior of jointed rocks

“…The main advantage of the approach based on homogenization lies precisely on the fact it becomes unnecessary to operate with intricate geometry discretizations (finite element meshes). In line of a recent work dedicated to computational implementation of micromechanics-based viscoelastic model for geomaterials with distributed micro-fractures, 91 the incorporation of the homogenized creep behavior within a finite element tool is the matter of ongoing research.…”

“…[82][83][84][85][86] As far as the formulation of overall viscoelastic properties of jointed materials is concerned, the approaches relying upon micromechanics techniques have essentially addressed the case of a matrix with embedded micro-cracks or micro-fractures under the assumption of nonaging linear viscoelasticity for the constituents. [87][88][89][90][91] The main interest consists in tacking advantage of the classical results established within the context of elasticity in conjunction with the elastic-viscoelastic correspondence principle. The theoretical framework of random media upscaling 92 is commonly used to evaluate the effective elastic properties in the Laplace-Carson space by resorting to the Eshelby-based homogenization schemes.…”

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

“…In addition, the average of concentration tensor over entire REV   should ensure Eq. ( 4), leading to  =  for both situations [51].…”

“…However, most of these studies restrict the mechanical behavior of the discontinuities to cracks [33][34][35][36][37][38][39][40][41][42][43][44], thereby limiting the applicability of the obtained formulation to open discontinuities. 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].…”

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

“…The pioneering works of 1–4 studied several aspects regarding to the propagation of fractures, developing the classic bases of discrete fracture mechanics. The extension of these analyzes to continuous fracture models, which is relevant for densely fractured materials, arose naturally through phenomenological/damage approaches, micromechanics, or other methodologies that lead to similar results (see for instance 5–27 ). The first difficulty commonly faced in these approaches is related to the assessment of the representative constitutive models for the fractures and the intact material separately by relying mainly on experimental identification.…”