Internal symmetry groups for the Drucker–Prager material model of plasticity and numerical integrating methods

Liu, Chein‐Shan

doi:10.1016/j.ijsolstr.2004.02.035

Cited by 25 publications

(8 citation statements)

References 28 publications

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“…5(e) we show the consistency error defined by r t C À1 r + 2V t r À 2S y , which as can be seen is small, but is not zero exactly. In the paper by Liu (2004c), some consistent schemes are available for the Drucker-Prager model but by another approaches.…”

Section: Numerical Results For the Drucker-prager Yield Modelmentioning

confidence: 99%

“…Then, Liu (2004c) and Liu and Chang (2004) extended these studies to the Drucker-Prager model and convex plastic model. These authors explored the internal symmetry groups in the Minkowski space of the constitutive models of perfect elastoplasticity with or without considering large deformation, bilinear elastoplasticity, visco-elastoplasticity, isotropic work-hardening elastoplasticity, mixed-hardening elastoplasticity, the Drucker-Prager plasticity model as well as a rather general flow model with the yield function convex to ensure that the consistency condition is exactly satisfied at each time step once the computational schemes can take these symmetries into account.…”

Section: The Flow Model With Strain Energy As a Yield Criterionmentioning

confidence: 99%

“…The pseudo-Riemann manifold endowed with a metric tensor g dependent on the temporal component X 0 is known as the Robertson-Walker space in the special relativity theory; see Liu (2003aLiu ( , 2004c. Eq.…”

Section: Pseudo-riemann Manifoldmentioning

confidence: 99%

See 2 more Smart Citations

Non-canonical Minkowski and pseudo-Riemann frames of plasticity models with anisotropic quadratic yield criteria

Liu

Chang

2005

International Journal of Solids and Structures

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Section: Numerical Results For the Drucker-prager Yield Modelmentioning

confidence: 99%

Section: The Flow Model With Strain Energy As a Yield Criterionmentioning

confidence: 99%

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Non-canonical Minkowski and pseudo-Riemann frames of plasticity models with anisotropic quadratic yield criteria

Liu

Chang

2005

International Journal of Solids and Structures

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“…Hong and Liu [46][47][48] argued that the constitutive equations of the von-Mises plasticity with linear kinematic hardening could be represented by a system of linear differential equations. Liu [49][50][51] developed the method for the vonMises mixed-hardening and Drucker-Prager plasticity. Another integration process based on the exponential map techniques was developed by Auricchio and Beirao da Veiga [52] to solve the constitutive equations of the von-Mises plasticity model with a linear mixed-hardening mechanism.…”

Section: Introductionmentioning

confidence: 99%

“…These two schemes were first devised in Refs. [51,57] for the Drucker-Prager plasticity with no hardening. In this investigation, they are advanced for the nonassociative Drucker-Prager plasticity with nonlinear kinematic hardening, which are totally new and had never been carried out before.…”

Section: Introductionmentioning

confidence: 99%

Integrating the Pressure-Sensitive Nonassociative Plasticity by Exponential-Based Methods

Rezaiee‐Pajand

Sharifian

2013

Journal of Engineering Materials and Technology

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A nonassociative plasticity model of Drucker-Prager yield surface coupled with a generalized nonlinear kinematic hardening is considered. Conforming to the plasticity model, two exponential-based methods, called fully explicit and semi-implicit, are recommended for integrating its constitutive equations. These techniques are proposed for the first time to solve nonlinear hardening materials. The integrations are thoroughly investigated by utilizing stress and strain-updating tests along with a boundary value problem in diverse grounds of accuracy, convergence rate, and efficiency. The results indicate that the fully explicit scheme is more accurate and efficient than the Euler's, but the same convergence rate as the classical integrations is also perceived. Having a quadratic convergence, the semi-implicit is noticeably the most accurate and efficient procedure to use for this plasticity model among the algorithms in question. Since the plasticity model is in a great consistency with discontinuously reinforced aluminum (DRA) composites, the suggested formulations can be utilized pragmatically. The tangent moduli of the proposed and Euler's strategies are derived and examined, as well, due to their vital role in achieving the asymptotic quadratic convergence rate of the Newton-Raphson solution in nonlinear finite-element analyses.

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On the integration schemes for Drucker–Prager's elastoplastic models based on exponential maps

Rezaiee‐Pajand

Nasirai

2007

Numerical Meth Engineering

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SUMMARYRate plasticity equations for the case of Drucker-Prager's model in small strain regime are considered. By defining an augmented stress vector, the formulations convert the original problem into a quasi-linear differential equation system. Two new exponential mapping schemes for integrating model equations are proposed. In addition, two traditional schemes for solving the dynamical system in an explicit manner are discussed. The two semi-implicit schemes developed pose higher accuracy and better convergency. Error contours are provided for all four methods to display the accuracy of each scheme. In order to compare the results, these contours for the classical one-step backward Euler integration method are also displayed. Accuracy and efficiency along with the rate of convergency of the existing and the proposed methods are examined by numerical examples.

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Internal symmetry groups for the Drucker–Prager material model of plasticity and numerical integrating methods

Cited by 25 publications

References 28 publications

Non-canonical Minkowski and pseudo-Riemann frames of plasticity models with anisotropic quadratic yield criteria

Non-canonical Minkowski and pseudo-Riemann frames of plasticity models with anisotropic quadratic yield criteria

Integrating the Pressure-Sensitive Nonassociative Plasticity by Exponential-Based Methods

On the integration schemes for Drucker–Prager's elastoplastic models based on exponential maps

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