Development of elasto-plastic material models in a natural coordinate system

Duxbury, Paul; Li, Xikui

doi:10.1016/0045-7825(95)00950-7

Cited by 25 publications

(11 citation statements)

References 3 publications

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“…p are initial cohesion, strain hardening parameter and the equivalent plastic strain [12] deÿned for pressure dependent elasto-plastic materials, respectively. In the present example c 0 = 10 kPa, h c p = 1 kPa, the internal frictional angle = 15…”

Section: Numerical Resultsmentioning

confidence: 99%

A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non‐linear solids and saturated porous media

Dongmei

Lewis

2003

Numerical Meth Engineering

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SUMMARYA time-discontinuous Galerkin ÿnite element method (DGFEM) for dynamics and wave propagation in non-linear solids and saturated porous media is presented. The main distinct characteristic of the proposed DGFEM is that the speciÿc P3-P1 interpolation approximation, which uses piecewise cubic (Hermite's polynomial) and linear interpolations for both displacements and velocities, in the time domain is particularly proposed. Consequently, continuity of the displacement vector at each discrete time instant is exactly ensured, whereas discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously saved, particularly in the materially non-linear problems, as compared with that required for the existing DGFEM. Both the implicit and explicit algorithms are developed to solve the derived formulations for linear and materially non-linear problems. Numerical results illustrate good performance of the present method in eliminating spurious numerical oscillations and in providing much more accurate solutions over the traditional Galerkin ÿnite element method using the Newmark algorithm in the time domain.

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Section: Numerical Resultsmentioning

confidence: 99%

A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non‐linear solids and saturated porous media

Dongmei

Lewis

2003

Numerical Meth Engineering

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“…where h p , h s , h T , h c are the hardening/softening parameters for cohesion due to the effects of plastic strains, the suction, the temperature and the chemical component concentration, respectively, the equivalent incremental plastic strain ¯ p is defined as [24,35] …”

Section: The Csl Criterionmentioning

confidence: 99%

Mixed finite element method for coupled thermo-hydro-mechanical process in poro-elasto-plastic media at large strains

Liu

Lewis

2005

Int. J. Numer. Meth. Engng

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SUMMARYA mixed finite element for coupled thermo-hydro-mechanical (THM) analysis in unsaturated porous media is proposed. Displacements, strains, the net stresses for the solid phase; pressures, pressure gradients, Darcy velocities for pore water and pore air phases; temperature, temperature gradients, the total heat flux are interpolated as independent variables. The weak form of the governing equations of coupled THM problems in porous media within the element is given on the basis of the Hu-Washizu three-filed variational principle. The proposed mixed finite element formulation is derived. The non-linear version of the element formulation is further derived with particular consideration of the THM constitutive model for unsaturated porous media based on the CAP model. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elasto-plastic tangent modulus matrix and the element tangent stiffness matrix are developed. For geometrical non-linearity, the co-rotational formulation approach is utilized. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization and the softening behaviours caused by thermal and chemical effects.

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“…According to the definition of the equivalent plastic strain for isotropic, pressure-dependent materials with strain hardening/ softening [27], the coefficient h can be expressed by [29] …”

Section: The Non-linear Constitutive Equations For the Solid Skeletonmentioning

confidence: 99%

“…It is also one of the basic components to constitute some sophisticated constitutive models with multiplicate yield surfaces such as the Cap model for saturated/unsaturated clay. The nonassociated Drucker-Prager criterion can be plotted as a straight line in s m À q plane defined by [26,27] …”

Section: The Non-linear Constitutive Equations For the Solid Skeletonmentioning

confidence: 99%

Instability of wave propagation in saturated poroelastoplastic media

Zhang

2002

Num Anal Meth Geomechanics

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SUMMARYIn the present work, stationary discontinuities and fluttery instabilities of wave propagation in saturated poro-elastoplastic media are analysed in the frame of Biot theory. The generalized Biot formulations are particularly employed for simulating non-linear coupled hydro-mechanical behaviour of the media. Inertial coupling effect between the solid and the fluid phases of the media is also taken into account. The nonassociated Drucker-Prager criterion to describe non-linear constitutive behaviour of pressure dependent elasto-plasticity for the solid skeleton of the media is particularly considered. With omission of compressibility of solid grains and the pore fluid, the critical conditions of stationary discontinuities and flutter instabilities occurring in wave propagation are given in explicit forms. It is shown that when the stationary discontinuity is triggered at the surface of discontinuity there still may exist real wave speeds. The wave speeds across the stationary discontinuity surface entirely cease to be real only in non-associated plasticity, certain ranges of value of Poisson's ratio and when compression stress normal to the surface of discontinuity dominates the stress state at the surface. It is also indicated that the fluttery instabilities, under which some wave speeds cease to be real even in strain hardening stage, may occur prior to stationary discontinuities only for non-associated plasticity under certain conditions. These conditions are: (1) both the porosity and the Poisson's ratio possess relatively low values and (2) the deviatoric part of the effective stress normal to the surface of discontinuity is compressive. A region in the porosity-Poisson's ratio plot, in which fluttery instabilities are possible to occur, is given.

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Development of elasto-plastic material models in a natural coordinate system

Cited by 25 publications

References 3 publications

A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non‐linear solids and saturated porous media

A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non‐linear solids and saturated porous media

Mixed finite element method for coupled thermo-hydro-mechanical process in poro-elasto-plastic media at large strains

Instability of wave propagation in saturated poroelastoplastic media

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