A finite element formulation of gradient-based plasticity for porous media with C1 interpolation of internal variables |
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| Institution: | 1. Applied Mechanical Dept., Universidad Nacional del Nordeste, Las Heras 727, Resistencia, Chaco, Argentina;2. CONICET and Faculty for Exact Sciences & Technology, Universidad Nacional de Tucumán, Maipu 780, 4000 Tucumán, Argentina;1. Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann Str. 9, 45127 Essen, Germany;2. Alexandru Ioan Cuza University of Ia?i, Department of Mathematics, Blvd. Carol I, no. 11, 700506 Ia?i, Romania;3. Octav Mayer Institute of Mathematics of the Romanian Academy, Ia?i Branch, 700505 Ia?i, Romania;1. Computational Physics Group, AWE Aldermaston, Reading, Berkshire, RG7 4PR, UK;2. Methods and Algorithms, XCP-4, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;1. Institute of Continuum Mechanics and Material Mechanics, Hamburg University of Technology, Hamburg, Germany;2. Institute of Materials Research, Helmholtz-Zentrum Geesthacht, Geesthacht, Germany |
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| Abstract: | In this paper a new finite element formulation for numerical analysis of diffused and localized failure behavior of saturated and partially saturated gradient poroplastic materials is proposed. The new finite element includes interpolation functions of first order (C1) for the internal variables field while classical C0 interpolation functions for the kinematic fields and pore pressure. This finite element formulation is compatible with a thermodynamically consistent gradient poroplastic theory previously proposed by the authors. In this material theory the internal variables are the only ones of non-local character. To verify the numerical efficiency of the proposed finite element formulation, the non-local gradient poroplastic constitutive theory is combined with the modified Cam Clay model for partially saturated continua. Thereby, the volumetric strain of the solid skeleton and the plastic porosity are the internal variables of the constitutive theory. The numerical results in this paper demonstrate the capabilities of the proposed finite element formulation to capture diffuse and localized failure modes of boundary value problems of porous media, depending on the acting confining pressure and on the material saturation degree. |
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