Volumetric (dilatant) plasticity in geodynamic models and implications on thermal dissipation and strain localization

Abstract

Here, we present a new thermomechanical geodynamic, numerical implementation that incorporates Maxwell viscoelastic rheology accounting for temperature-dependent power-law dislocation creep and pressure-sensitive, non-associated Drucker-Prager brittle failure, as well as for volumetric stresses and strains during viscoplastic flow, a departure from the traditional incompressible assumptions. In solving for energy conservation, we incorporate the heat source term resulting from irreversible mechanical deformations, which embodies viscoelastic and viscoplastic work, and by considering the total stress tensor and total inelastic strain rate tensors, including dilatant plasticity effects for lithospheric-scale applications, instead of only the shear terms as is usually assumed for incompressible materials. This form of the work term thus allows to consider, volumetric deformation and to couple the energy equation to the constitutive description, and hence the stress balance, via the evolving temperature field. Code design enables us to switch individual features of this general rheology ``on or off'' and thus to benchmark this implementation with published numerical experiments of crustal-scale shortening experiments. We investigate whether ``brittle-plastic'' compressibility can promote or inhibit localization of deformation and thermal evolution during compression for crustal, and upper mantle rheology. For both crustal-scale and lithospheric-scale experiments, we establish that the feedback from volumetric dissipation, while contributing to temperature increase along with shear dissipation, can potentially slow down heat production per unit time, depending on the choice of boundary conditions. Our new implementation can be used to address buckling problems and collision tectonics.