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.