I am interested in exploring the implications of non-equilibrium thermodynamics on practical theories such as phase-field modeling, with applications to porous media like geomaterials. Phase-field theory is well fitted for modeling interfacial problems and although usually applied for mixing phases, it can be adapted to modeling geomaterials at the grain scale. For that I use the underlying mathematical framework of thermodynamics based on contact geometry, providing a consistent and systematic way of rederiving various models. This procedure extends the usual phase-field equations by allowing both the normal variations of the interface and the usually missing curvature variations to be fully dissipative. The new curvature variations term introduces a secondary complementary leverage, an inhibition effect balancing the already existing initiation effect. This proves prevalent for modeling high-curvature interfacial structures like geomaterials. Such modeling simply using elasticity at the grain scale can be upscaled as a damage law. A further application is unsaturated media and the addition of the water and air phases. Similarly, the Young-Laplace law can be extended with a dynamic curvature variation term. An interesting application will be desiccation cracks in collaboration with the rest of the group as part of the DOE project on nuclear waste disposals.
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