On the stress integration in large strain elasto-plasticity

Montáns, Francisco J.; Bathe, Klaus‐Jürgen

doi:10.1016/b978-008044046-0/50122-6

Cited by 4 publications

(8 citation statements)

References 6 publications

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“…This effect was already noted in Reference [39], where also more results are reported using a spatial algorithm and a Finger tensor based algorithm. We note that this backstress rotation affects both the backstress and stress evolution during the plastic return, since the backstress rotation takes place over the trial value.…”

Section: Consequences Of Assumptionmentioning

confidence: 61%

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Computational issues in large strain elasto‐plasticity: an algorithm for mixed hardening and plastic spin

Montáns

Bathe

2005

Numerical Meth Engineering

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SUMMARYIn this paper an algorithm for large strain elasto-plasticity with isotropic hyperelasticity based on the multiplicative decomposition is formulated. The algorithm includes a (possible) constitutive equation for the plastic spin and mixed hardening in which the principal stress and principal backstress directions are not necessarily preserved. It is shown that if the principal trial stress directions are preserved during the plastic flow (as assumed in some algorithms) a plastic spin is inadvertently introduced for the kinematic/mixed hardening case. If the formulation is performed in the principal stress space, a rotation of the backstress is inadvertently introduced as well. The consistent linearization of the algorithm is also addressed in detail.

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Section: Consequences Of Assumptionmentioning

confidence: 61%

“…also considered in References [21,39] (a similar problem can be also found in Reference [22]). The material constants are the same as in the previous example.…”

Section: Simple Shearmentioning

confidence: 96%

Computational issues in large strain elasto‐plasticity: an algorithm for mixed hardening and plastic spin

Montáns

Bathe

2005

Numerical Meth Engineering

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“…Of course, a principal rotated configuration may be defined such that the following diagonal stress tensor is obtained [7] T = JR T τR = Diag T 1 ,T 2 ,T 3 (10) The previous comments are also applicable when this configuration is used, for which in a similar way, the quantities D P , ∂f /∂T,B are defined, but they are not necessarily diagonal.…”

Section: Constitutive Frameworkmentioning

confidence: 99%

“…A further analysis of the algorithms with tables of the actual procedures may be found in Ref. [10].…”

Section: Numerical Algorithmsmentioning

confidence: 99%

On the stress integration in large strain elasto-plasticity

Montáns

Bathe

2003

Computational Fluid and Solid Mechanics 2003

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We briefly compare three algorithms for large strain elastoplastic analysis in which the logarithmic strain tensor is used to measure the deformations. The first and second algorithms are based on using, respectively, the elastic stretch matrices in the right basis and left basis of the polar decomposition of the trial elastic deformation gradient, and the third algorithm uses the left basis and the Finger deformation tensor.

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“…We use the updated Lagrangian Hencky formulation, which is a solution approach based on the total elastic strain computed from the total deformation gradient and an evolution of the plastic deformation gradient. The stresses are calculated using the effective-stressfunction algorithm and consistent tangent matrices are used in the Newton-Raphson iterations [ 1,[15][16][17][18] 1.…”

Section: Mathematical Conditions On Finite Elementsmentioning

confidence: 99%

On the State of Finite Element Procedures for Forming Processes

Bathe¹

2004

AIP Conference Proceedings

149

154

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Abstract. The solution of forming processes requires reliable and efficient finite element methods to model the various complex physical phenomena encountered. The objective in this presentation is to focus on the current state of finite element methods with respect to reliability and efficiency in modeling forming processes. The finite element procedures pertain to the simulation of sheet metal forming, bulk forming, extrusion and drawing, rolling, welding, cutting processes, etc. It is emphasized that the appropriate finite element methods for a specific problem should be used, and that indeed procedures are available which are effective in many situations. The presentation briefly considers the state of modeling of solids, shell structures, contact conditions, friction, inelastic material response in large strains, thermomechanical coupling and fluid-solid interactions, as encountered in forming process simulations. The solutions of the governing finite element models are obtained using sparse direct or iterative solvers. The oral presentation will include the results of various example simulations.

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On the stress integration in large strain elasto-plasticity

Cited by 4 publications

References 6 publications

Computational issues in large strain elasto‐plasticity: an algorithm for mixed hardening and plastic spin

Computational issues in large strain elasto‐plasticity: an algorithm for mixed hardening and plastic spin

On the stress integration in large strain elasto-plasticity

On the State of Finite Element Procedures for Forming Processes

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