A new exact integration method for the Drucker–Prager elastoplastic model with linear isotropic hardening

Szabó, Loránd; Kossa, Attila

doi:10.1016/j.ijsolstr.2011.09.021

Cited by 28 publications

(10 citation statements)

References 18 publications

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“…The yield function restricting the effective stress state

{bold-italicσ}^{'} (boldx, t)

is assumed in the form of Drucker–Prager to take into account the dilatant/contractant behaviour of dense sands, respectively. The return mapping algorithm and the consistent tangent operator for the singular behaviour of the Drucker–Prager yield surface in the apex zone, using the concept of multisurface plasticity, are based on the contributions of .…”

Section: Constitutive Equationsmentioning

confidence: 99%

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

Cao

Sanavia

Schrefler

2016

Numerical Meth Engineering

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In this paper, the non-isothermal elasto-plastic behaviour of multiphase geomaterials in dynamics is investigated with a thermo-hydro-mechanical model of porous media. The supporting mathematical model is based on averaging procedures within the Hybrid Mixture Theory. A computationally efficient reduced formulation of the macroscopic balance equations which neglects the relative acceleration of the fluids and the convective terms is adopted. The modified effective stress state is limited by the Drucker-Prager yield surface. Small strains and dynamic loading conditions are assumed. The standard Galerkin procedure of the finite element method is applied to discretize the governing equations in space, while the generalized Newmark scheme is used for the time discretization. The final non-linear set of equations is solved by the Newton method with a monolithic approach.Coupled dynamic analyses of strain localization in globally undrained samples of dense and medium dense sands are presented as examples. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. {\color{red}A numerical study of the regularization properties of the finite element model is shown and discussed.} A non-isothermal case of incipient strain localization induced by temperature increase where evaporation takes place is also analysed

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“…The yield function restricting the effective stress state

{bold-italicσ}^{'} (boldx, t)

Section: Constitutive Equationsmentioning

confidence: 99%

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

Cao

Sanavia

Schrefler

2016

Numerical Meth Engineering

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“…The reader is referred to (de Souza Neto et al, 2008;Szabo & Kossa, 2012) for determination of the consistent tangent matrix associated with the Drucker-Prager yield criterion with isotropic hardening, and also to (Li & Tang, 2005) where the term (݀ߣ ۱ ) is the plastic corrector (return vector) to satisfy the yield criterion and ۱ ݀ (୰) is the trial elastic stress increment ݀ ୣ (୰) at r th iteration. As an alternative, the consistent tangent matrix can be also used together with an implicit elastic predictor/return-mapping algorithm for the DruckerPrager yield criterion (see, e.g., de Souza Neto et al, 2008 for details).…”

Section: Elasto-plastic Simulation Of Wedge Indentationmentioning

confidence: 99%

On couple-stress elasto-plastic constitutive frameworks for glassy polymers

Alisafaei

Han

Garg

2016

International Journal of Plasticity

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Various experimental studies have revealed length scale dependent deformation of different materials at micron and sub-micron length scales. In metals, such length scale dependent deformations are considered to be associated with geometrically necessary dislocations arising from an increase in strain gradients related to non-uniform plastic deformation. Recent experiments, however, have shown that the nature of length scale dependent deformation in polymers is quite different from metals as in polymers size effects have been observed in pure elastic as well as in elasto-plastic deformation. It is shown in this study that similar to metals, size effects in polymers can be associated with an increase in higher order displacement gradients with decreasing length scale. However, the experimental results discussed here reveals that, in contrast to metals, these higher order displacement gradients are mainly of elastic nature even when glassy polymers deform elasto-plastically. Taking the effects of these elastic higher order displacement gradients into account, a couple-stress theory is developed to predict size effect in glassy polymers with elasto-plastic deformation.

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“…In recent decades, numerous stress update algorithms have been proposed. ese algorithms can be mainly classified into three categories: explicit integration algorithms [1][2][3], return mapping algorithms [4][5][6], and exact stress integration algorithms [7,8]. Traditionally, the return mapping algorithm, also called the predictor-corrector scheme, is constructed in the six-dimensional stress space and is usually cumbersome since it requires that the second derivative of the plastic potential and nondifferentiable yield surface be smoothed.…”

Section: Introductionmentioning

confidence: 99%

A Return Mapping Algorithm for Nonlinear Yield Criteria with the Equivalent Mohr–Coulomb Strength Parameters

et al. 2020

Advances in Civil Engineering

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This paper proposes a modified return mapping algorithm for a series of nonlinear yield criteria. The algorithm is established in the principal stress space and ignores the effect of the intermediate principal stress. Three stress return schemes are derived in this paper: return to the yield surface, return to the curve, and return to the apex point. The conditions used for determining the correct stress return type are also constructed. After the proposed algorithm is programmed in the finite element software, we merely need the equivalent Mohr–Coulomb (M-C) strength parameters, the derivatives of their functions, and the tensile strength of these nonlinear yield criteria. In addition, the Hoek–Brown (H-B) yield criterion is taken as an example to validate the proposed method. The results show that the updated stresses and the final principal stresses obtained by the proposed method are in good agreement with those obtained by other methods. Furthermore, the proposed method is more suitable for the associated plastic-flow rule.

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A new exact integration method for the Drucker–Prager elastoplastic model with linear isotropic hardening

Cited by 28 publications

References 18 publications

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

On couple-stress elasto-plastic constitutive frameworks for glassy polymers

A Return Mapping Algorithm for Nonlinear Yield Criteria with the Equivalent Mohr–Coulomb Strength Parameters

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