Three-dimensional continental lithosphere extension modeling via particle-in-cell finite element analysis

We extended the two-dimensional particle-in-cell (PIC) finite element code Ellipsis to three-dimensions for application to problems in geodynamics. The particle in cell scheme is a hybrid method which combines a fixed mesh of computational points and a dense arrangement of mobile material points. The fixed Eulerian mesh allows very fast computation (performed in Ellipsis via a multigrid iteration method) whereas the Lagrangian particle reference frame allows the tracking of material interfaces and history dependent properties such as strain history for strain-softening materials. The PIC method is exceptionally useful in very large deformation analyses where purely Lagrangian approaches would be severely hampered by the need for remeshing to minimize element distortion. We apply the Ellipsis particle-in-cell finite element code to a series of problems involving extension of the continental lithosphere. This constitutes one of the first applications of 3D particle-in-cell technology to a problem of geodynamic importance. Specifically, we model a 3 layer lithosphere (with upper crust, lower crust, and upper mantle components), and incorporate phase changes via decompression melting. The extension proceeds in multiple steps, including orientations normal to and oblique to predefined weak zones that serve to aid the onset of localization. The rheological model is viscoplastic (work is continuing on the 3D code s elastic aspect), where the plastic part of the rheology is set to mimic brittle deformation and the viscosity is temperature-dependent. We focus on the distribution of brittle deformation patterns in the upper crust with variable loading schemes, as well as the distribution of melt in the system for realistic parameter values.