A new algorithm for solving large strain deformation problems and its application to fault-propagation folding

We present a new algorithm to solve the problem of rock deformation. The method is based on a ‘classical’ Lagrangian finite element solver in which the connectivity between the nodes of the numerical mesh is updated at the end of each time (or deformation) step. The method, which we term Dynamic Lagrangian Remeshing (DLR), relies on the theory of Delaunay triangulation and produces optimal finite element meshes in the sense that nodes are always connected to their set of nearest neighbour nodes. Because it is based on a Lagrangian method in which the numerical grid is attached to material particles and advected with the deformation, the DLR algorithm is ideally suited to track material boundaries and properly represent free surfaces. In addition, in comparison to ‘classical’ Lagrangian solvers the DLR method is not limited to small strain problems and may be used to model discontinuities such as faults and narrow shear zones. We have used the DLR method to study the evolution of a crustal layer undergoing finite shortening driven by a velocity discontinuity along its base. The numerical model predicts the formation of a large fold that is progressively cut by a fault originating at the velocity discontinuity and propagating through the crustal layer. The model predictions provide support for the fault-propagation folding model of Suppe [I].