FINITE ELEMENT NUMERICAL IMPLEMENTATION OF A MICROMECHANICS-BASED VISCOELASTIC MODEL FOR FRACTURED GEOMATERIALS

Resumo

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 transmit normal and tangential stresses, whereas cracks are discontinuities without stress transfer.
As far as the formulation of the behavior of materials with isotropic distribution of micro-cracks or
fractures is concerned, 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 micro-fractured media. The effective 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 presence of isotropically distributed
micro-fractures under plane strain conditions. Several examples of applications are presented with the
aim to illustrate the performances of the finite element modeling. The accuracy of the approach is also
assessed by comparing the numerical predictions with analytical solutions.