Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modelling of metal forming processes

Roberts, Siân; Hall, F.R.; Bael, Albert Van; Hartley, P.; Pillinger, I.; Sturgess, C. E. N.; Houtte, Paul Van; Aernoudt, Etienne

doi:10.1016/0924-0136(92)90090-f

Cited by 29 publications

(16 citation statements)

References 2 publications

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“…Therefore, a very high accuracy can be easily achieved and the solution can serve as a simple benchmark test for numerical packages. A necessity of such tests has been pointed out in Roberts et al (1992).…”

Section: Introductionmentioning

confidence: 97%

The bending moment and springback in pure bending of anisotropic sheets

Alexandrov

Hwang

2009

International Journal of Solids and Structures

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a b s t r a c tFinite deformation rigid plastic and elastic-plastic analyses of plane strain pure bending of a plastically anisotropic sheet is presented. An efficient method for finding the exact solution is proposed by extending the previously developed method to the stage of unloading. Using this method the solutions are obtained in closed form or reduced to a numerical treatment of ordinary integrals, or an ordinary differential equation, or transcendental equations. An effect of plastic anisotropy and elastic properties on the bending moment is analyzed. The distribution of residual stresses is illustrated and an effect of material and process parameters on springback is investigated.

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Section: Introductionmentioning

confidence: 97%

The bending moment and springback in pure bending of anisotropic sheets

Alexandrov

Hwang

2009

International Journal of Solids and Structures

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“…The accuracy of numerical solutions can be tested in several ways. The usual strategy is to compare numerical results either with analytical solutions for given simplified initial and boundary conditions, experimental data, or with reference numerical solutions [ Krieg and Krieg , 1977; Ortiz and Popov , 1985; Simo and Hughes , 1998; Roberts et al , 1992; Wieners , 1999]. In linear elastic problems it is relatively straightforward to find exact solutions to which the finite element results may be compared.…”

Section: Introductionmentioning

confidence: 99%

An analytical benchmark with combined pressure and shear loading for elastoplastic numerical models

Yarushina

Dąbrowski

Podladchikov

2010

Geochem Geophys Geosyst

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[1] We discuss the benchmark strategy to check the accuracy of elastoplastic numerical solutions based on a fully two-dimensional analytical solution. Associated rate-independent non-hardening plasticity with von Mises or Tresca criteria is assumed throughout. Algorithms for integration of the rate equations, strategies for stress updating over a time step, and tangent operators are discussed. The accuracy of a simple incremental algorithm as a function of the time step is discussed.

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“…It is known that numerical codes should be verified before their use in applications [34][35][36]. The present solution is useful for this purpose since ordinary differential equations can be solved numerically with a very high accuracy with no difficulty.…”

Section: Discussionmentioning

confidence: 98%

Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks

2018

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Hill’s quadratic orthotropic yield criterion is used for revealing the effect of plastic anisotropy on the distribution of stresses and strains within rotating annular polar orthotropic disks of constant thickness under plane stress. The associated flow rule is adopted for connecting the stresses and strain rates. Assuming that unloading is purely elastic, the distribution of residual stresses and strains is determined as well. The solution for strain rates reduces to one nonlinear ordinary differential equation and two linear ordinary differential equations, even though the boundary value problem involves two independent variables. The aforementioned differential equations can be solved one by one. This significantly simplifies the numerical treatment of the general boundary value problem and increases the accuracy of its solution. In particular, comparison with a finite difference solution is made. It is shown that the finite difference solution is not accurate enough for some applications.

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Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modelling of metal forming processes

Cited by 29 publications

References 2 publications

The bending moment and springback in pure bending of anisotropic sheets

The bending moment and springback in pure bending of anisotropic sheets

An analytical benchmark with combined pressure and shear loading for elastoplastic numerical models

Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks

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