Developing a deep understanding of magmatic processes, such as the ascent of magmatic melts through the lithosphere, is a notoriously complex interdisciplinary task that involves contributions from various branches of geosciences. Here, we focus on the implementation of mode-1 plasticity, which is highly relevant for the modeling of dyke propagation through the brittle crust under an excess of fluid (melt) pressure, as part of a nonlinear elasto-visco-plastic rheology that is also appropriate for modeling the ductile-brittle transition in the upper mantle.

For this, we adopt a coupled poro-elasto-visco-plastic description of the strain localization process to capture the onset and advance of vertical dykes originating from magma reservoirs located at various depth. We mostly aim to investigate the hydro-mechanical interactions of such a system (e.g. permeability increase and elastic modulii degradation with increasing plastic strain, and influence of fluid pressure on both total stresses and on the yield surface). Thermal effects are essentially ignored, apart from the background geothermal gradient. The reservoir is represented as a cavity subjected to an increased fluid pressure.

We describe the brittle deformation using multi-surface plasticity models in the framework of the flow plasticity theory. A number of challenging problems are usually encountered in this case from an algorithmic viewpoint, including a lack of convexity and continuity of both the yield surface and flow potential, spurious elastic domains, singularity points and loss of convergence. We address these issues by using a relatively simple Perzyna-type visco-plastic model that consists of a linear Drucker-Prager shear failure envelop, and a circular tensile cap. Both surfaces are combined with each other in a way that enforces dimensional consistency, convexity, and continuity throughout the entire stress space.

Finally, we discuss the algorithmic details of the model which is incorporated in an implicit finite element code and demonstrate the  application results.