Accurate and approximate integrations of Drucker–Prager plasticity with linear isotropic and kinematic hardening

Rezaiee‐Pajand, Mohammad; Sharifian, Mehrzad; Sharifian, Mehrdad

doi:10.1016/j.euromechsol.2010.12.001

Cited by 27 publications

(11 citation statements)

References 31 publications

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“…For the Drucker-Prager plasticity, the algorithm was first devised by Liu [51] with no hardening and then developed for linear mixed hardening by the authors [36]. In this section, the scheme is advanced for the nonassociative plasticity of the same yield criterion but with generalized nonlinear kinematic hardening.…”

Section: Fully Explicit Updating Stressmentioning

confidence: 99%

“…Choosing a variable as a representative of this term helps the equations be much more comprehensible. The mentioned term is given below (36) ,=1…”

Section: (30)mentioning

confidence: 99%

“…Considering the von-Mises plasticity model with a class of multicomponent nonlinear kinematic hardening, Rezaiee-Pajand et al [58,59] developed the exponential-based formulations and extended them to nonlinear mixed-hardening models. Recently, two new exponential-based approximate formulations for associative Drucker-Prager plasticity model were developed by Rezaiee-Pajand et al [36] assuming linear hardening. They also derived an accurate solution for the constitutive equations.…”

Section: Introductionmentioning

confidence: 99%

“…Integrating these equations, stresses are updated and an important part of the nonlinear finiteelement analysis is fulfilled. Although the analytical exact integrating methods [30][31][32][33][34][35][36][37] have been developed for a few plasticity models and are rarely used for their restrictions, still the general approach is utilizing the numerical integrations due to their universality, flexibility and tolerance toward all kinds of materials and plasticity models. The problem is, though, these approximate procedures usually involve many iterations and calculations, and their accuracy and performance are in a direct relationship with the final outcomes of the nonlinear analyses.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Fully Explicit Updating Stressmentioning

confidence: 99%

“…Choosing a variable as a representative of this term helps the equations be much more comprehensible. The mentioned term is given below (36) ,=1…”

Section: (30)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Rezaiee‐Pajand

Sharifian

2013

Journal of Engineering Materials and Technology

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“…Rezaiee-Pajand et al (2010) proposed an exponential-based scheme in integrating the constitutive equations along with multi-component nonlinear kinematic hardening. Finally, Rezaiee-Pajand et al (2011) derived an accurate solution and two exponential-based integrations for Drucker-Prager plasticity with linear mixed hardening.…”

Section: Introductionmentioning

confidence: 99%

Integration of nonlinear mixed hardening models

Rezaiee‐Pajand

Nasirai

Sharifian

2011

Multidiscipline Modeling in Materials and Structures

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Purpose -The purpose of this paper is to present a new effective integration method for cyclic plasticity models. Design/methodology/approach -By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm. Findings -The numerical tests show the robustness and high efficiency of the proposed integration scheme.Research limitations/implications -The von-Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening. Practical implications -Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses. Originality/value -The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential-based integration method is more efficient than the classical strategies.

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Explicit integration methods for constitutive equations of a mean-stress dependent elastoviscoplastic model: impact on structural finite element analyses

Abdulhameed

Roguet

Brusselle-Dupend

et al. 2019

Engineering with Computers

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The strong dependent behavior of semi-crystalline polymers can lead to the use of simplified material laws in Finite Element structural calculations for reasons of robustness to the detriment of the quantitative response of the models. This work focuses on numerical integration methods as a solution to overcome the possible convergence and robustness limitations of mean-stress dependent elastoviscoplastic material laws, typical of the semi-crystalline polymers mechanical behavior.What is proposed here is a rational application of three explicit integration methods (fourth and second order Rung-Kutta method, a hybrid schema between Runge-Kutta and Euler method) in engineering structural calculations, which provide a reliable solution for constitutive models of semi-crystalline polymer. These methods are examined for structure creep test and tensile test, in comparison with experimental data. The investigations have been done in terms of the stability toward convergence, the accuracy of results, the plastic consistency, and CPU time efficiency. This work, proposes an easy implementation of integration methods in any computational Finite Element code. It also provides a flexible modular implementation which is applicable to any different constitutive equations. An integration step sub-division technique is recommended. It is a powerful technique to improve the convergence of solution and accuracy of result by damping oscillation around stress Gauss point integration solution. The results obtained illustrate the effect of numerical integration schemas on structural analysis and provide an insight to select suitable method.

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Accurate and approximate integrations of Drucker–Prager plasticity with linear isotropic and kinematic hardening

Cited by 27 publications

References 31 publications

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

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

Integration of nonlinear mixed hardening models

Explicit integration methods for constitutive equations of a mean-stress dependent elastoviscoplastic model: impact on structural finite element analyses

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