Computational Methods for Elastoplasticity: An Overview of Conventional and Less-Conventional Approaches

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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“…The difficulties associated with a reliable implementation of integration schemas have limited the employment of complex model [30][31][32].…”

Section: Importance Of Integration Methods For the Constitutive Modelmentioning

confidence: 99%

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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“…Note that the residual of the transverse normal stress is incorporated into the internal force vectors. Considering the importance of the mechanical formulations, these numerical algorithms have been employed in practical situation 18‐20 . Thus, the mechanical approach using the path independent scheme is extended to the field of the sensitivity analysis 21‐23 .…”

Section: Introductionmentioning

confidence: 99%

Simultaneously iterative procedure based on block Newton method for elastoplastic problems

Yamamoto

Yamada

Matsui

2021

Numerical Meth Engineering

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In this article, the authors formulate elastoplastic problems as a coupled problem of the equilibrium equation and the yield condition at each material point, and develop a numerical procedure based on the block Newton method to solve the overall structure using the finite element discretization. For the integration of stress, the backward difference scheme is employed. In the conventional return mapping algorithm, the algorithmic tangent moduli are derived analytically so that it is consistent with local iterative calculation to determine internal variables. On the other hand, in the proposed block Newton method, the tangent moduli can be obtained algebraically by eliminating the internal variables, and the internal variables are also updated algebraically without local iterative calculation. The residual of the yield condition is incorporated into the linearized equilibrium equation. The proposed approach enables the errors of the equilibrium equation and the yield condition to decrease simultaneously. Some numerical examples show the validity and effectiveness of the proposed approach by comparing the results of the proposed approach with those of the conventional return mapping algorithm.

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“…Fincato and Tsutsumi 30 treated the extended subloading surface model by the closest‐point projection method and proposed a return mapping algorithm for the subloading surface model of plasticity and damage 31 . Scalet and Auricchio 32 reviewed the conventional and nonconventional integration approaches to the constitutive equations and discussed computational issues in the solution of the equations.…”

Section: Introductionmentioning

confidence: 99%

A novel accurate and computationally efficient integration approach to viscoplastic constitutive model

Kumar

Patel

2020

Numerical Meth Engineering

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A novel, accurate, and computationally efficient integration approach is developed to integrate small strain viscoplastic constitutive equations involving nonlinear coupled first-order ordinary differential equations. The developed integration scheme is achieved by a combination of the implicit backward Euler difference approximation and the implicit asymptotic integration. For the uniaxial loading case, the developed integration scheme produces accurate results irrespective of time steps. For the multiaxial loading case, the accuracy and computational efficiency of the developed integration scheme are better than those of either the implicit backward Euler difference approximation or the implicit asymptotic integration. The simplicity of the developed integration scheme is equivalent to that of the implicit backward Euler difference approximation since it also reduces the solution of integrated constitutive equations to the solution of a single nonlinear equation. The algorithm tangent constitutive matrix derived for the developed integration scheme is consistent with the integration algorithm and preserves the quadratic convergence of the Newton-Raphson method for global iterations.

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Computational Methods for Elastoplasticity: An Overview of Conventional and Less-Conventional Approaches

Cited by 29 publications

References 202 publications

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

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

Simultaneously iterative procedure based on block Newton method for elastoplastic problems

A novel accurate and computationally efficient integration approach to viscoplastic constitutive model

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