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Geophysical models of heat and fluid flow in damageable poro-elastic continua

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Abstract

A rather general model for fluid and heat transport in poro-elastic continua undergoing possibly also plastic-like deformation and damage is developed with the goal to cover various specific models of rock rheology used in geophysics of Earth’s crust. Nonconvex free energy at small elastic strains, gradient theories (in particular the concept of second-grade nonsimple continua), and Biot poro-elastic model are employed, together with possible large displacement due to large plastic-like strains evolving during long time periods. Also the additive splitting is justified in stratified situations which are of interest in modelling of lithospheric crust faults. Thermodynamically based formulation includes entropy balance (in particular the Clausius–Duhem inequality) and an explicit global energy balance. It is further outlined that the energy balance can be used to ensure, under suitable data qualification, existence of a weak solution and stability and convergence of suitable approximation schemes at least in some particular situations.

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  1. Institute of Thermomechanics, Czech Academy of Sciences, Dolejškova 5, 182 00, Praha 8, Czech Republic

    Tomáš Roubíček

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Roubíček, T. Geophysical models of heat and fluid flow in damageable poro-elastic continua. Continuum Mech. Thermodyn. 29, 625–646 (2017). https://doi.org/10.1007/s00161-016-0547-5

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