


[Contents]  [Index] 
Collaborator: K. Wilmanski
Description:
The modeling of thermoporoelastic materials which has been the subject of research for eight years has been completed in 2004. In particular, the following problems were solved
 The general form of the energy balance equation for thermoporoelastic materials: It has been shown, for instance, that the socalled simple mixture model yields in the Lagrangian description the following form of relation between the entropy flux and the heat flux , [3], [4],
where T is the absolute temperature, denotes the Helmholtz free energy of the fluid, is the deformation gradient of the skeleton, and , are velocities of components. This has also been proved in the case of a generalized model with a nonlinear dependence on the diffusion velocity .
 It has been shown that the classical linear Biot model with added mass effects follows as a nonobjective approximation of a nonlinear model in which the following definition of the objective relative acceleration has been introduced, [4], [5],
where is a material parameter. In the same work, it has been shown that the added mass effect cannot be related to tortuosity in spite of frequent claims in the literature.
 As the result of the micromacro analysis [6], the balance equation for porosity has been corrected for an equilibrium contribution
where n_{E} denotes the equilibrium porosity, and n_{E},, are constitutive quantities, the latter being the relaxation time of porosity. In particular, in the linear Biot model ( ), this equation yields the relation for porosity [6]
where is the material constant. This relation checks with results of micromacro transitions.
The model described above has been investigated in application to the description of linear and nonlinear waves. It has been shown ([4], [7], [1]) that linear acoustic waves correspond qualitatively with waves following from Biot's model. Quantitative discrepancies may be as large as 30 % and in some cases (e.g., attenuation), they indicate that the new model is physically better justified and in some cases (e.g., dependence of speeds on coupling of stresses), they are better within Biot's model. The new model yields also important results for surface waves (e.g., [2]). The analysis of nonlinear waves has been performed for the model in which material parameters are dependent on porosity, [8], [9]. It has been shown that for some physically justified cases, the P1 wave may yield the creation of strong discontinuities which have been attributed to the liquefaction. This conclusion is confirmed by comparison with theoretical results of Osinow within a onecomponent hypoplastic model and with experiments on Karlsruhe sands.
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