Inelastic deformation in crystalline rocks

The elasto-plastic behavior of crystalline rocks, such as evaporites, igneous rocks, or metamorphic rocks, is highly dependent on the behavior of their individual crystals. Previous studies indicate that crystal plasticity can be one of the dominant micro mechanisms in the plastic deformation of crystal aggregates. Deformation bands and pore collapse are examples of plastic deformation in crystalline rocks. In these cases twinning within the grains illustrate plastic deformation of crystal lattice. Crystal plasticity is governed by the plastic deformation along potential slip systems of crystals. Linear dependency of the crystal slip systems causes singularity in the system of equations solving for the plastic slip of each slip system. As a result, taking the micro-structure properties into account, while studying the overall behavior of crystalline materials, is quite challenging. To model the plastic deformation of single crystals we use the so called `ultimate algorithm' by Borja and Wren (1993) implemented in a 3D finite element framework to solve boundary value problems. The major advantage of this model is that it avoids the singularity problem by solving for the plastic slip explicitly in sub steps over which the stress strain relationship is linear. Comparing the results of the examples to available models such as Von Mises we show the significance of considering the micro-structure of crystals in modeling the overall elasto-plastic deformation of crystal aggregates.