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An analysis of strong discontinuities in a saturated poro-plastic solid. (English) Zbl 0971.74029
From the summary: We present an analysis of strong discontinuities in fully saturated porous media in the infinitesimal range. In particular, from a local constitutive level we describe the incorporation of the local effects of surfaces of discontinuity in the displacement field, and thus the singular distributions of associated strains, into the large-scale problem characterizing the quasi-static equilibrium of the solid. The characterization of the flow of the fluid through the porous space is accomplished by means of a localized (singular) distribution of the fluid content, that is, involving a regular fluid mass distribution per unit volume and a fluid mass per unit area of the discontinuity surfaces in the small scale of the material. The proposed framework also involves the coupled equation of conservation of fluid mass and seepage through the porous solid via Darcy’s law, and considers a continuous pressure field with discontinuous gradients. Enhanced finite element methods are developed, which accommodate different localized fields at the element level. Numerical simulations are presented illustrating the performance of the numerical methods.

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76S05 Flows in porous media; filtration; seepage
Full Text: DOI
[1] Rudnicki, Journal of the Mechanics and Physics of Solids 23 pp 371– (1995)
[2] Rice, Journal of Geophysical Research 80 pp 1536– (1995)
[3] Loret, Journal of Engineering Mechanics 117 pp 907– (1993)
[4] Pietruszczak, Journal of Engineering Mechanics 121 pp 1292– (1995)
[5] Schrefler, Archives of Mechanics 47 pp 577– (1995)
[6] Vardoulakis, GĂ©otechnique 46 pp 441– (1996)
[7] Runesson, International Journal of Solids and Structures 33 pp 1501– (1996) · Zbl 0921.73018
[8] Simo, Journal of Computational Mechanics 12 pp 277– (1993) · Zbl 0783.73024
[9] Armero, International Journal of Solids and Structures 33 pp 2863– (1996) · Zbl 0924.73084
[10] Oliver, International Journal for Numerical Methods in Engineering 39 pp 3575– (1996) · Zbl 0888.73018
[11] Larsson, Journal of Engineering Mechanics 122 pp 402– (1996)
[12] Steinmann, International Journal of Solids and Structures 34 pp 969– (1997) · Zbl 0947.74508
[13] On the characterization of localized solutions in inelastic solids: an analysis of wave propagation in a softening bar. SEMM/UCB Report no. 97/18, 1997, Computer Methods in Applied Mechanics and Engineering, to appear.
[14] Armero, Mechanics of Cohesive-Frictional Materials 4 pp 101– (1999) · Zbl 0968.74062
[15] Biot, Journal of Applied Physics 12 pp 155– (1941) · JFM 67.0837.01
[16] Mechanics of Porous Continua. Wiley: Chichester, 1995.
[17] Larsson, International Journal of Solids and Structures 33 pp 3081– (1996) · Zbl 0919.73279
[18] Zhang, Mechanics of Cohesive-Frictional Materials (1999)
[19] Recent advances in the analysis and numerical simulation of strain localization in inelastic solids. In Proceedings of COMPLAS IV, (eds). CIMNE: Barcelona, 1995.
[20] Green’s Functions and Boundary Value Problems. Wiley: New York, 1979.
[21] Armero, Computer Methods in Applied Mechanics and Engineering 171 pp 205– (1999) · Zbl 0968.74062
[22] The nonlinear field theories of mechanics. In Handbuch der Physik Bd. III/3, (ed.). Springer: Berlin, 1965.
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