Modelling of non-coaxial viscoplastic deformation in geodynamics

The formation of shear bands for time and length scales appropriate for deformation processes in the upper Lithosphere is investigated in plane strain finite element simulations under predominantly uniaxial extension and compression, respectively. The direction of gravity is assumed orthogonal to the extension/compression axis. Mathematically, the formation of shear zones may be explained as a consequence of changes in the type of the governing model equations. Such changes or bifurcations depend strongly on the details of the constitutive relationships such as strain softening, thermal or chemical effects, associated or non-associated—coaxial or non-coaxial flow rules. Here we focus on strain softening and coaxial and non-coaxial flow rules. In the simulations, we consider an initially rectangular domain with the dimensions L0, H0 in the horizontal, vertical directions, respectively. The domain is extended or compressed by prescribing a uniform, horizontal velocity field along one of the vertical boundaries while keeping the opposite boundary fixed. An important global descriptor of the deformation process is the relationship between the horizontal stress resultant (average horizontal stress) and the strain ln(L/L0), where L is the deformed length of the domain. The main goal of this paper is to investigate key factors influencing the phenomenology of the localization process such as flow rule, coaxial, non-coaxial and strain softening. Different origins of the mesh sensitivity of deformations involving localization are also investigated.