Computational plasticity of mixed hardening pressure-dependency constitutive equations

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

doi:10.1007/s00707-013-0998-8

Cited by 11 publications

(3 citation statements)

References 41 publications

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“…Associated with the well-known radial return mapping in stress integration presented by Wilkins [58], many research subjects such as consistent tangent operator, iso-error map, and integration stability were studied [59][60][61]. Recently introduced exponential map based stress integration schemes showed their robustness [62][63][64][65]. However, these studies were hardly utilized to overcome the non-convergent issues in YPP applications.…”

Section: Stress Integration Algorithmsmentioning

confidence: 99%

Computational Studies for the Yield-Point Phenomenon of Metals

Kim

2020

Multiscale Sci. Eng.

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The yield-point phenomenon (YPP) is an accustomed topic in sheet metal forming fields. Over hundred and fifty years since the first observation of the YPP, many research efforts have been continued to understand and describe it. Recent spotlights for the YPP studies are focusing on high-degree numerical methods with the support of increasing computing performance. Here, we review the representative computational studies on YPP to share the latest progress and remaining challenges to obtain better mechanical insights into it. After the duality of the YPP is addressed in terms of avoiding and utilizing it, the constitutive material models for the YPP as well as bake hardening models are discussed for a continuum level FE simulations, and the features of the discussed YPP models are compared. Microscopic and multiscale schemes are also briefly handled. It is expected that more advanced computational work can be initiated from this review.

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Section: Stress Integration Algorithmsmentioning

confidence: 99%

Computational Studies for the Yield-Point Phenomenon of Metals

Kim

2020

Multiscale Sci. Eng.

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“…Afterward, the average error for these methods is calculated by equation (28) for Δ t = 0.05s. Finally, the efficiency of the methods can be obtained by the subsequent equation (Rezaiee-Pajand et al (2014a, 2014b): …”

Section: Numerical Examinationsmentioning

confidence: 99%

“…Moreover, the exponential map method was advanced by Rezaiee-Pajand et al (2010, 2011, 2014a, 2014b for cyclic plasticity models comprising von-Mises yield function along with nonlinear kinematic hardening laws of Chaboche (1986), Ohno and Wang (1993) and Abdel-Karim and Ohno (2000). Considering the pressure-sensitive material's elastoplastic behavior, the Drucker-Prager yield surface along with the mixed hardening was take into account to propose the angels based integrations by Rezaiee-Pajand and Sharifian (2012) and Rezaiee-Pajand et al (2014a, 2014b. In addition, for the aforementioned yield conditions, an efficient first-order integration was suggested by Sharifian et al (2018aSharifian et al ( , 2018b.…”

Section: Introductionmentioning

confidence: 99%

A hybrid method to update stress for perfect von-Mises plasticity coupled with Lemaitre damage mechanics

Tavoosi

Sharifian

2019

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Purpose The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics. Design/methodology/approach By benefiting the properties of the well-known explicit and implicit integrations, a new mixed method is derived. In fact, the advantages of the mentioned techniques are used to achieve an efficient integration. Findings The numerical studies demonstrate the high precision and robustness of the suggested algorithm. Research limitations The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations. Practical implications Updating stress and plastic internal variables are of utmost importance in elastoplastic analyses of structures. The accuracy and efficiency of stress-updating methods significantly affect the final outcomes of nonlinear analyses. Originality/value The idea which is used to derive the hybrid method leads to an efficient integration method for updating the constitutive equations of the damage mechanics.

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A sequentially updated projection method for integrating the rate form of plasticity

Dharmasiri,

Maddegedara,

Fujita

et al. 2024

Comput Mech

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We propose a novel fully implicit algorithm named the Implicit Sequential Projection Method (ISPM) for integrating the rate form of plasticity. ISPM is inspired by the implicit construction of the Closest Point Projection Method (CPPM) and the Cutting Plane Method’s (CPM) treatment of state variables as functions of the plastic multiplier. Though all the state variables are treated as functions of the plastic multiplier, the evaluation of the derivatives of the state variables with respect to the plastic multiplier at the unknown solution makes ISPM a fully implicit algorithm similar to CPPM. ISPM iteratively updates the solution by projecting the state at the end of prior iteration to the yield surface, producing its characteristic sequential projection of the solution, hence the name. Furthermore, ISPM provides a straightforward to derive consistent tangent operator (CTO) with global convergence on par with CPPM. The mathematical formulation, main attributes, and geometric details of the return mapping are discussed in relation to CPPM and CPM, with an emphasis on showing the distinctness of the algorithm. Further, we establish the relationship between ISPM and CPPM. The versatility and accuracy of ISPM and its CTO are explored through a series of numerical tests conducted with three plasticity models. Tests that focus on material-level iterations show that the stress remapping of ISPM is as accurate as CPPM’s. Further, the mixed stress–strain loading history test conducted with non-linear elastic Drucker–Prager plastic material shows that ISPM can provide a runtime advantage over CPPM for some complex plasticity models involving all three stress invariants.

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Computational plasticity of mixed hardening pressure-dependency constitutive equations

Cited by 11 publications

References 41 publications

Computational Studies for the Yield-Point Phenomenon of Metals

Computational Studies for the Yield-Point Phenomenon of Metals

A hybrid method to update stress for perfect von-Mises plasticity coupled with Lemaitre damage mechanics

A sequentially updated projection method for integrating the rate form of plasticity

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