Numerical modelling of heat generation during shear band formation in rock

This article gives a computational continuum mechanics answer to a question of
how much heat is generated, in terms of temperature rise, during controlled shear band formation in a rock like material. This problem is treated as adiabatic heating due to mechanical dissipation at the material point level. Assuming that only the compressive strength of the rock is temperature dependent, the coupled system of the constitutive equations and the adiabatic heat equation can be solved as a second order polynomial equation for the viscoplastic multiplier at an integration point. A Mohr-Coulomb viscoplastic model with linear softening is employed for rock material description. Numerical simulations of a 2D strip under uniaxial compression at strain rates up to 10 1/s show that the temperature rise in a rock like material with a compressive strength of 100 MPa is less than two degrees.