Numerical modeling of rock deformation: 13 FEM 2D Viscous flow Stefan Schmalholz schmalholz@erdw.ethz.ch NO E 61 AS 2008, Thursday 10-12, NO D 11 Numerical modeling of rock deformation: FEM 2D Elasticity. Stefan Schmalholz, ETH Zurich

Closed sys. of eqns: incompressible fluid Conservation of linear momentum, Force balance, Two equations Seven unknowns Conservation of angular momentum, One equation Conservation of mass, One equation Rheology, Three equations Numerical modeling of rock deformation: FEM 2D Elasticity. Stefan Schmalholz, ETH Zurich

Tasks The Matlab script “FEMS_2D_VISCOUS” includes a finite element algorithm that solves the equations of the previous page describing slow viscous flow. The model setup generates single-layer folding under pure shear shortening. After running the finite element code you can visualize the results using the script “Fems_visualization”. The finite element algorithm is described in detail in the PDF-file “FEM_Frehner.pdf”. Document the Matlab scripts for you. Describe the model setup, i.e. boundary conditions, initial geometry, material properties etc. Describe how the deformation of the mesh is done and programmed in the algorithm. Where are the shear stresses “SXZ” highest during folding? Where are the shear strain rates “SRXZ” highest during folding? Where are the horizontal stresses “SXX” highest during folding? Make the model width a factor 3 smaller and a factor 5 larger. What do you observe concerning the fold amplification and the final fold amplitude? Can you explain the result? Numerical modeling of rock deformation: FEM 2D Elasticity. Stefan Schmalholz, ETH Zurich