Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

Abstract

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.

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

“…As mentioned above, Aguiar and Maghous (2018) formulated the homogenized viscoelastic properties for a fractured medium. This approach is based on prior research works developed within the framework of elastic fractured mediums (Maghous et al 2011(Maghous et al , 2014 and the elastic-viscoelastic correspondence principle in the context of non-aging materials.…”

“…Since the paper focus is the study of the computational implementation of the viscoelastic model, only the formulation of the homogenized viscoelastic properties in a medium with isotropically distributed fractures will be shown below in a concise way. The formulation of the elastic properties in a fracture medium, the complete procedure of inverse Laplace-Carson transform and other basic concepts of the theoretical model can be found in Aguiar and Maghous (2018).…”

“…The formulation of non-aging viscoelastic properties of a homogenized medium involves the determination of the fourth-order relaxation tensor  hom  components. This determination relies upon the solution to a viscoelastic Latin American Journal of Solids and Structures, 2019, 16(9), e238 3/33 concentration problem stated on the REV under applied loading  (Aguiar and Maghous, 2018). In such conditions, the homogenized constitutive law for a fractured viscoelastic medium can be defined as…”

“…However, as mentioned above, there are no stress transfer in this type of discontinuities. Subsequently, Nguyen´s analysis was extended by Aguiar and Maghous (2018), who added the fracture behavior studied by Maghous et al (2011).…”

“…In this context, the main objective of the present paper is related to the finite element modeling and implementation within a computational code of the viscoelastic constitutive behavior originally formulated in Aguiar and Maghous (2018) for the fractured medium. It is emphasized that the main novelty of the approach lies in the ability of such a computational tool to allow for effective and accurate analysis of the delayed response of structures built in fractured media.…”