Poromechanics of saturated media based on the logarithmic finite strain |
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| Affiliation: | 1. CSIRO Earth Science and Resource Engineering, 26 Dick Perry Ave., Kensington, WA 6151, Australia;2. School of Civil and Resource Engineering, University of Western Australia, Australia;3. Western Australian Geothermal Centre of Excellence, School of Earth and Environment, University of Western Australia, Australia;1. Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305-4060, USA;2. Institute for Theoretical Physics Amsterdam, University of Amsterdam, 1098 XH Amsterdam, the Netherlands;3. Department of Physics, University of Wisconsin, Madison, WI 53706, USA;1. Research Professor, School of Architecture and Architectural Engineering, Hanyang University, 55 Hanyangdaehak-ro, Sangnok-gu, 426-791 Kyeonggi-do, Republic of Korea;2. Professor, Department of Mechanical & Aerospace Engineering, State University of New York at Buffalo, NY 14260, USA |
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| Abstract: | In this paper, we introduce the mathematical formulation and numerical implementation of a coupled thermo-hydro-mechanical model for saturated poromaterials undergoing logarithmic finite deformation and corotational rates. The model combines (i) the thermodynamics of standard materials, (ii) the frame indifferent hyperelastoplasticty, (iii) the orthogonality condition of maximum dissipation, as well as (iv) the principles of conservations of mass, energy and momenta. This formulation involves new developments based on the logarithmic strain measures and corotational rates which overcome the aberrant oscillations classically encountered in large simple shear. It also takes into accounts recent findings on the thermodynamics of dissipative materials which consist of deriving the yielding conditions and flow rules from suitable free energy and dissipation functions. This framework resulted in the implementation of a new finite element algorithm based on Galerkin’s method. The numerical procedures used in this paper involve the spectral decomposition of the logarithmic strain measures, the gradient split techniques as well as the return mapping method. The formulation is validated using the classical problems of Terzaghi and strip loading consolidation. |
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