A unified multi-scale thermodynamical framework for coupling geomechanical and chemical simulations

Thermodynamics provides a unified framework to couple mechanics and chemistry, with practical numerical applications for realistic geodynamics problems. Our work is developed within the framework of classical thermodynamics, where we include the effect of chemical feedbacks by taking into account the fluxes exchanged by a Representative Volume Element with its surrounding. We follow earlier suggestions using full explicit coupling and find that they are numerically intractable for realistic geodynamics problems with a number of degrees of freedom potentially exceeding one hundred. As a method of reducing this number we employ a multi-scale approach where the given scale of interest allows a separation of direct and indirect feedbacks. Indirect feedbacks are not solved in the system of equations but are incorporated through pre-calculated thermodynamic databases. Direct feedbacks are calculated in the framework of thermodynamic equations and solved explicitly to define the dissipative structures emerging out of those feedbacks. Thus we propose a framework that can be used to extend in a computationally manageable manner the linear far-from-equilibrium theory from Prigogine and co-workers into the non-linear regime for thermo-chemo-mechanical problems.