The solid phase stress tensor in porous media mechanics and the Hill-Mandel condition. (English) Zbl 1170.74324

Gray, William G.; Schrefler, Bernhard A.; Pesavento, Francesco

J. Mech. Phys. Solids 57, No. 3, 539-554 (2009).

Summary: An assessment of the stress tensors used currently for the modeling of partially saturated porous media is made which includes concepts like total stress, solid phase stress, and solid pressure. Thermodynamically constrained averaging theory is used to derive the solid phase stress tensor. It is shown that in the upscaling procedure the Hill conditions are satisfied, which is not trivial. The stress tensor is then compared to traditional stress measures. The physical meaning of two forms of solid pressure and of the Biot coefficient is clarified. Finally, a Bishop-Skempton like form of the stress tensor is obtained and a form of the total stress tensor that does not make use of the effective stress concept.

MSC:

74F10

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Keywords:

porous media; Hill-Mandel condition; elasticity; bishop parameters; skempton stress

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