Abstract
Abstract. We propose a multiscale approach for coupling multi-physics processes across the scales. The physics is based on discrete phenomena, triggered by local thermo-hydro-mechano-chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4×4 THMC diffusion matrix are shown to lead to multiple diffusional P and S wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time–space relations entirely defined by the coefficients of the coupled THMC reaction–cross-diffusion equations. A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead to an energy cascade connecting large and small scales and cause solid-state turbulence.
Highlights
The theory presented in this paper grew out of the conference series dedicated to understanding coupled thermo-hydromechanical-chemical (THMC) in Geosystems (GEOPROC)
In order to recover the dissipative wave equations, we present in the following the standard constitutive assumptions for any generic thermodynamic fluid or solid mechanical system and describe how the physics of THMC feedbacks can be implemented to resolve the phenomenon of propagating dissipative waves in these systems
This paper has introduced three important innovations for modelling THMC instabilities: (i) a multiscale extension of the theory of thermodynamics of irreversible processes to include dynamic events by using a mesomacro-scale model; (ii) a generalization of the theory of cross-diffusion waves from chemical systems to generalized THMC thermodynamic-force flux pairs; (iii) a transfer of knowledge from classical quantum mechanics to characterize any system at a larger scale in order to deal with the discreteness of multiscale material behaviour
Summary
The theory presented in this paper grew out of the conference series dedicated to understanding coupled thermo-hydromechanical-chemical (THMC) in Geosystems (GEOPROC). Integration of mechanical, hydrodynamical, thermal, and chemical processes covers, a much wider field from the pore to plate-tectonic scale for a wide range of natural and engineering problems in geological systems discussed in focus topics at earlier GEOPROC conferences. Likewise closed, coupled, far-from-equilibrium THMC systems that feature irreversible behaviours can be modelled by a thermomechanics approach (Collins and Houlsby, 1997), called a thermodynamics with internal variables approach (Maugin and Muschik, 1999) or a hyperplastic approach (Houlsby and Puzrin, 2007) This theory is, only applicable to faults that have reached a thermal steady state as implied by a standing-wave solution of acceleration waves. Before discussing cross-scale coupling of thermodynamic forces and fluxes in Sect. 3.3, it is useful to briefly review insights into the formation of discrete dissipative structures
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