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Cooperation with: I. Müller (Technische Universität (TU) Berlin), R. Lancellotta (Università di Torino, Italy), C. Lai (Studio Geotecnico Italiano, Milano)
Description: Aims and results of the project
The main task in this project is to establish a thermodynamic framework for multicomponent nonlinear thermomechanical models of porous materials. Due to the choice of the skeleton as the reference, the socalled Lagrangian description of motion [1] is used. Consequently, if we consider a porous medium whose channels are filled with a mixture of A fluid components, the model is constructed on a chosen reference configuration of the solid component, i.e. all fields are functions of a spatial variable , and time . In the work [5] we consider a thermomechanical model in which the governing fields are as follows:
Such a model was indicated in the work [2] (see as well [3, 4]), but the results were primarily related to the hierarchic structure of the socalled extended thermodynamics. In the present work we are primarily concerned with similarities and differences of the model with the classical Truesdell model of fluid mixtures. We show that the barycentric velocity of this classical theory must be replaced by the following relative Lagrangian velocity
With this relation in mind we obtain the following relation for the bulk PiolaKirchhoff stress tensor
This formula has a formal similarity to the classical Truesdell relations but it refers to the skeleton rather than to the center of gravity, and it is in the Lagrangian rather than Eulerian form.Similarly we obtain for the bulk internal energy
where is the CauchyGreen deformation tensor for the skeleton, and for the bulk heat flux These relations possess again a formal similarity to the Truesdell relations with the difference described above for the stress tensor.By means of these relations one can evaluate the second law of thermodynamics which is assumed to have the form proposed by I. Müller (TU Berlin) for mixtures of fluids. In the Lagrangian form it is as follows. The entropy inequality
where is the entropy density in the reference configuration, is the bulk entropy flux, and denotes the set of constitutive variables, must hold for all solutions of field equations. An evaluation of this law has been done for fully nonlinear poroelastic isotropic materials with ideal fluid components. We discuss in detail the twocomponent case which has been investigated already in the projects of the previous years.References:



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