Numerical modeling of shear bands in rocks using FEM and a viscous regularization technique

Resumo

Shear bands are narrow zones of intense shear strain that develop within a broad range of ductile
materials. As these bands precede material failure, their study is fundamental to understand the mechanical
behavior of those materials. In general, the modelling of shear bands is performed through the finite element
method considering constitutive laws which use a non-associative flow rule. Moreover, models for porous
materials such as rocks and soils usually incorporate strain-softening behavior observed in experimental tests. Both
non-associative flow rules and strain-softening can cause loss of well-posedness of the initial-value problem in
classical continuum approaches, leading to mesh dependency and poor convergence during the non-linear solution
process. To overcome such issues, some techniques such as viscous regularization have been proposed. However,
the removal of mesh dependency depends on how the viscous parameter is incorporated into the model. In this
paper, we present simulations of shear bands considering biaxial conditions and including a viscous regularization
technique. The efficiency of that technique is studied considering the onset, width and orientation of the resultant
shear bands in carbonate rocks. We show that despite the use of non-associative flow rules and strain-softening
behavior, the obtained shear band widths converge to finite values upon increasing mesh discretization.