A simple computer program for calculating stress and strain rate in 2D viscous inclusion-matrix systems

Abstract

Computer-based numerical solutions of geomechanical problems are important to understand the processes forming rock structures as well as to quantify the associated pressure, stresses and strain rates. However, the development of such computer programs and the underlying mathematical methods are commonly not taught in a standard structural geology curriculum. Here, we present a simple computer program to calculate the stress, pressure, velocity and strain rate fields for two-dimensional (2D) viscous inclusion-matrix systems under pure shear and simple shear. The main aim of our contribution is to explain this computer program in a simple and transparent way, so that it can be used for introductory courses on geomechanical numerical modelling in structural geology. We present the governing equations of 2D viscous deformation and program the equations in the same order and style, so that the equations are still recognizable in the computer program. The computer program can treat stiff and weak inclusions of any shape and considers both linear and power-law viscous flow laws. We present numerical calculations for various inclusion-matrix scenarios. The program is written with the software MATLAB, is provided as supplementary material, and can also be run with the freely available software GNU Octave.