A mechanical model for dissolution–precipitation creep based on the minimum principle of the dissipation potential

In contrast to previous approaches that consider dissolution–precipitation creep as a multi-stage process and only simulate its governing subprocess, the present model treats this phenomenon as a single continuous process. The applied strategy uses the minimum principle of the dissipation potential according to which a Lagrangian consisting of elastic power and dissipation is minimized. Here, the elastic part has a standard form while the assumption for dissipation stipulates the driving forces to be proportional to two kinds of velocities: the material-transport velocity and the boundary-motion velocity. A Lagrange term is included to impose mass conservation. Two ways of solution are proposed. The strong form of the problem is solved analytically for a simple case. The weak form of the problem is used for a finite-element implementation and for simulating more complex cases.