Accurate integration scheme for von‐Mises plasticity with mixed‐hardening based on exponential maps

Rezaiee‐Pajand, Mohammad; Nasirai, Cyrus

doi:10.1108/02644400710774806

Cited by 23 publications

(5 citation statements)

References 9 publications

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“…In the herein presented algorithm, the semi-analytical approach is presented, in which all second derivatives are gathered in a single term of the above-mentioned explicit expression for the ATS. Only this term is calculated numerically, and no repetition of the integration procedure is needed. Efficiency : Convergence of a particular model in implicit schemes is mostly dependent on the skills of a researcher in reformulating the model equations; hence, the introduction of a new model also usually leads to the task of discovering the innovative numerical formulation of the introduced model to assure satisfactory convergence (Rezaiee-Pajand and Nasirai, 2007). The proposed algorithm was implemented via UMAT code and confronted with ABAQUS default algorithms.…”

Section: Discussionmentioning

confidence: 99%

“…Efficiency : Convergence of a particular model in implicit schemes is mostly dependent on the skills of a researcher in reformulating the model equations; hence, the introduction of a new model also usually leads to the task of discovering the innovative numerical formulation of the introduced model to assure satisfactory convergence (Rezaiee-Pajand and Nasirai, 2007). The proposed algorithm was implemented via UMAT code and confronted with ABAQUS default algorithms.…”

Section: Discussionmentioning

confidence: 99%

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A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation

Halilovic̆

Starman

Vrh

et al. 2017

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Purpose The purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit integration algorithm for rate-independent elasto-plastic constitutive models. Design/methodology/approach The proposed automatic substepping algorithm is founded on an explicit integration scheme. The estimation of the maximal subincrement size is based on the stability analysis. Findings In contrast to other explicit substepping schemes, the algorithm is self-correcting by definition and generates no cumulative drift. Although the integration proceeds with maximal possible subincrements, high level of accuracy is attained. Algorithmic tangent stiffness is calculated in explicit form and optionally no analytical second-order derivatives are needed. Research limitations/implications The algorithm is convenient for elasto-plastic constitutive models, described with an algebraic constraint and a set of differential equations. This covers a large family of materials in the field of metal plasticity, damage mechanics, etc. However, it cannot be directly used for a general material model, because the presented algorithm is convenient for solving a set of equations of a particular type. Practical implications The estimation of the maximal stable subincrement size is computationally cheap. All expressions in the algorithm are in explicit form, thus the implementation is simple and straightforward. The overall performance of the approach (i.e. accuracy, time consumption) is fully comparable with a default (built-in) ABAQUS/Standard algorithm. Originality/value The estimated maximal subincrement size enables the algorithm to be stable by definition. Subincrements are much larger than those in conventional substepping algorithms. No error control, error correction or local iterations are required even in the case of large increments.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation

Halilovic̆

Starman

Vrh

et al. 2017

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“…Later on, the exponential mapping integration was improved by Artioli et al (2005, 2006) to be consistent with the yield surface and present a second-order accuracy rate for von-Mises plasticity model with combined linear hardening. Subsequently, Rezaiee-Pajand and Nasirai (2007, 2008) formulated a semi-implicit technique constructed upon exponential scheme with second-order accuracy rate. They also developed two exponential map integrations for Drucker–Prager plasticity.…”

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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“…Artioli et al [7] enhanced this method to obtain a fully consistent algorithm. Finally, further improvements were made to this scheme and consistent methods with a second-order accuracy were developed [8,9]. Liu [10] investigated the internal symmetry of a constitutive model of Drucker-Prager's type and converted this model into a dynamical systemẊ = AX using two separate approaches.…”

Section: Introductionmentioning

confidence: 99%

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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Accurate integration scheme for von‐Mises plasticity with mixed‐hardening based on exponential maps

Cited by 23 publications

References 9 publications

A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation

A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation

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

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

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