Onsager’s reciprocal relationship applied to multiphysics poromechanics

Emergence of precursor instabilities in geo-processes: Insights from dense active matter

“…In our previous work, we interpreted Onsager's approach as an entropic reference frame for the definition of dissipative properties under local equilibrium conditions [10] . The notion of an entropic reference frame is new and there is still some debate about its objectivity.…”

“…A key problem which prompted criticism of the proliferation of Onsager's proposition as “Onsagerism” [33] lied in the lack of a consistent framework that rigorously identifies the appropriate thermodynamic forces and fluxes which is a non-trivial task and led to the proposition of a “rationale thermodynamic” approach. In an earlier communication [10] we have discussed the problem of properly acknowledging the role of internal elastic stresses in the microstructure inside a deformable medium such as in a non-associated modified Cam-Clay material. It has been clearly demonstrated that the use of the Cauchy stress as a thermodynamic force is inappropriate and a dissipative stress has to be used to define a dissipation potential function on which the thermodynamic flux (strain-rate) is co-axial [12] , thus satisfying Ziegler's orthogonality principle and still obeying local equilibrium condition.…”

“…In the following we will derive explicitly the non-local entropy production, by first simplifying the problem into a hydromechanically coupled problem. This implies that we use Ziegler's extended thermomechanics assumption [10] for the thermal problem and ignore the thermal diffusion process. In other words we use an adiabatic thermal assumption and reference all cross-coupling material coefficients to the reference temperature.…”

“…For non-associated cases the strain rate is not orthogonal to the proposed yield surface in the true effective stress space. This apparent contradiction to Ziegler's orthogonality principle can be alleviated when recasting the yield envelope in the dissipative stress space where orthogonality holds, [10] under the restrictive assumption of local equilibrium.…”

“…We have proposed an extension to relax isothermal conditions [10] for deformable porous materials. Without restricting its applications, the extension has been illustrated using the critical state line constitutive model with a modified Cam-Clay plasticity model [11] .…”