FRACTURE PROPAGATION IN VISCOELASTIC MATERIALS: A MIXED MICRO-MACROSCOPIC APPROACH (Revista Interdisciplinar de Pesquisa em Engenharia, 2017)
This paper presents a theoretical approach to fracture propagation in viscoelastic media, which combines a micromechanical reasoning and macroscopic thermodynamics arguments. 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 and correspondence principle, the first part of the paper is dedicated to assess the exact homogenized behavior of fractured viscoelastic materials. An approximate model for effective viscoelastic properties is also formulated in the framework of Burger model. Based on macroscopic thermodynamics principles, the free energy at macroscopic scale is then formulated, allowing for the analysis of damage propagation. It is shown that the thermodynamic force associated with damage propagation can be computed from the derivative of macroscopic free energy density with respect to fracture density parameter. Expression for the propagation criterion is therefore formulated based on the closed form expression previously obtained for the homogenized viscoleastic relaxation tensor.