Integration algorithm forJ2 elastoplasticity under arbitrary mixed stress-strain control

Ritto‐Corrêa, Manuel; Camotim, Dinar

doi:10.1002/1097-0207(20010220)50:5<1213::aid-nme74>3.0.co;2-a

Cited by 8 publications

(5 citation statements)

References 9 publications

(21 reference statements)

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“…A note is made concerning the Newton iteration (66): the trust region method (minpack) is used, as discussed in our recent work [4]. Together with the iterative calculation of m 33 we have extended the method of RittoCorrêa and Camotim [41] to finite strains. The calculation of the consistent modulus is provided in Appendix 4.…”

Section: Only Constitutive Functions Are T (B) and φ(T ) = φ[T (B)] mentioning

confidence: 99%

“…These were introduced by Key and Krieg [28] and were subsequently disseminated by Simo and co-workers [44]. However, some applications require combined strain and stress control (fundamental arguments for combined control were established by Ritto-Corrêa and Camotim [41]). This is the case of shells when the contravariant normal stress s 33 is known.…”

Section: Introductionmentioning

confidence: 99%

“…The procedure of [41] can be adopted if strains are infinitesimal. However, for finite strains, deformations of the shell faces (or beam ends) occur.…”

Section: Introductionmentioning

confidence: 99%

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Finite strain plasticity, the stress condition and a complete shell model

Areias

Ritto‐Corrêa

Martins³

2009

Comput Mech

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The null stress (s 33 = 0) and incompressibility (J = 1) conditions in finite strain elasto-plastic shell analysis are studied in closed-form and implemented with a variant of the combined control by Ritto-Corrêa and Camotim. Coupling between constitutive laws and shell kinematics results from the satisfaction of either of the conditions; nonlocality results from the coupling. We prove that the conditions are, in general, incompatible. A new thickness-deformable is studied in terms of kinematics and strong-ellipticity. The affected continuum laws are derived and, in the discrete form, it is shown that thickness degrees-of-freedom and enhanced strains are avoided: a mixed displacement-shear strain shell element is used. Both hyperelastic and elasto-plastic constitutive laws are tested. Elasto-plasticity follows Lee's decomposition and direct smoothing of the complementarity condition. A smooth root finder is employed to solve the resulting algebraic problem. Besides closed-form examples, numerical examples consisting of classical and newly proposed benchmarks are solved.

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Section: Only Constitutive Functions Are T (B) and φ(T ) = φ[T (B)] mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite strain plasticity, the stress condition and a complete shell model

Areias

Ritto‐Corrêa

Martins³

2009

Comput Mech

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“…At the end of each iteration, elastoplastic stresses are updated using the backward-Euler return with the =0 constraint. The quadratic convergence of the iterative procedure is ensured by using the consistent tangent constitutive operator (see, e.g., [21,27]). In a bifurcation (linear stability) analysis, the element geometric matrix is obtained from the second term of Eq.…”

Section: The Mitc-4 Shell Finite Elementmentioning

confidence: 99%

On the Modeling of Thin-Walled Member Assemblies Combining Shell and GBT-Based Beam Finite Elements: the Linear and Bifurcation Case

Manta¹,

Gonçalves²,

Camotim³

2021

14th WCCM-ECCOMAS Congress

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In this paper, a general and efficient approach to model thin-walled members and frames with complex geometries (including tapered segments and holes). The approach combines shell and GBT-based (beam) finite elements, using each of them where it is most efficient: (i) shell elements in the plastic and geometrically complex zones, and (ii) GBT elements in the prismatic and elastic zones. To illustrate the capabilities and potential of the proposed approach, a set of numerical examples are presented, concerning linear, bifurcation (linear stability) and first-order plastic zone analyses. The examples analysed involve (i) members with tapered segments, (ii) members with holes and (iii) tapered beam-column assemblies. For validation and comparison purposes, full shell finite element solutions are provided and it is demonstrated that the proposed approach yields very accurate solutions in all cases, while involving much less DOFs.

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“…The interpretation of the plane stress condition in the more general setting of plasticity under mixed stress-strain control is discussed by Klisinski et al (1992) and the relevant implementation is addressed by Ritto-Corrêa and Camotim (2001) where, although limited to the J 2 case, the family of algorithms for the entire range of mixed control situations is derived. Finally, for the plane stress J 2 model a closed-form solution is also available; it has been provided by Simo and Govindjee (1988) for the case of linear kinematic hardening and later extended by Alfano et al (1999) to encompass linear isotropic hardening and Perzyna-like viscoplasticity.…”

Section: Introductionmentioning

confidence: 99%

Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part I: Theoretical formulation

Valoroso

Rosati

2009

International Journal of Solids and Structures

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A derivation of the projected algorithm for general isotropic three-invariant plasticity models\ud under plane stress conditions is presented. It is obtained by consistently specializing the\ud 3D formulation to the 2D subspace defined by the plane stress condition. Closed-form\ud intrinsic algorithm linearization and a novel expression of the consistent tangent tensor\ud are provided; these are also shown to directly emanate from the analogous quantities pertaining\ud to the fully 3D case. A detailed discussion of the proposed implementation along\ud with a representative set of numerical examples is provided in the second part of this paper\ud [Valoroso, N., Rosati, L., 2008. Consistent derivation of the constitutive algorithm for plane\ud stress isotropic plasticity. Part II: Computational issues. International Journal of Solids and\ud Structures, 46, 92–124.

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Integration algorithm forJ2 elastoplasticity under arbitrary mixed stress-strain control

Cited by 8 publications

References 9 publications

Finite strain plasticity, the stress condition and a complete shell model

Finite strain plasticity, the stress condition and a complete shell model

On the Modeling of Thin-Walled Member Assemblies Combining Shell and GBT-Based Beam Finite Elements: the Linear and Bifurcation Case

Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part I: Theoretical formulation

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