MICROMECHANICAL APPROACH TO VISCOELASTIC BEHAVIOR OF FRACTURED MEDIA (Revista Interdisciplinar de Pesquisa em Engenharia, 2017)
This paper presents a micromechanical approach to overall viscoelastic properties of randomly fractured media. Unlike cracks, fractures can be viewed as interfaces that are able to transfer efforts. Their specific behavior under shear and normal stresses is a fundamental component of the deformation and fracture in brittle materials such as geomaterials. Based on the implementation of the Mori-Tanaka linear homogenization scheme, the first part of the analysis is dedicated to derive close-form expressions for the homogenized elastic stiffness tensor of the fractured medium. The effective viscoelastic behavior is then assessed from the elastic homogenization in Laplace framework and making use of the correspondence principle. In this context, a specific procedure for performing the inverse of Carson-Laplace transform is developed, allowing for the analytical derivation of homogenized relaxation and creep tensors. It is shown that the viscoelastic behavior can generally be described by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximation of the effective behavior by a Burger”“like model is formulated in the last part of the paper.