On the Equivalent of Mixed Element Formulations and the Concept of Reduced Integration in Large Deformation Problems

Reese, Stefanie

doi:10.1515/ijnsns.2002.3.1.1

Cited by 52 publications

(45 citation statements)

References 77 publications

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“…This pathology has been identified by a number of authors, with a sound analysis being carried out initially by Wriggers and Reese [100] and, subsequently, in references [64,79,[80][81][82], to name but a few. The common point in all these works is the focusing on plane-strain and full three-dimensional problems.…”

Section: Thick-wall Sphere Problem With Geometric Nonlinearitymentioning

confidence: 99%

An enhanced strain 3D element for large deformation elastoplastic thin-shell applications

Valente

Sousa

Jorge

2004

Computational Mechanics

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In this work a previously proposed solid-shell finite element, entirely based on the Enhanced Assumed Strain (EAS) formulation, is extended in order to account for large deformation elastoplastic thin-shell problems. An optimal number of 12 enhanced (internal) variables is employed, leading to a computationally efficient performance when compared to other 3D or solid-shell enhanced elements. This low number of enhanced variables is sufficient to (directly) eliminate either volumetric and transverse shear lockings, the first one arising, for instance, in the fully plastic range, whilst the last appears for small thickness' values. The enhanced formulation comprises an additive split of the Green-Lagrange material strain tensor, turning the inclusion of nonlinear kinematics a straightforward task. Finally, some shell-type numerical benchmarks are carried out with the present formulation, and good results are obtained, compared to well-established formulations in the literature. Keywords Solid-shell elements, Enhanced strains, Volumetric and transverse shear lockings, Geometric and material nonlinearities, Thin shells 1 Introduction Finite element analysis of shell structures goes back in time until the onset of the so-called degenerated approach in works of Ahmad et al. [1] and Zienkiewicz et al. [101], as well as in early papers of Ramm [78], and afterwards with Hughes and Liu [55] and Hughes and Carnoy [57], among others. Soon it was verified that brick elements were prone to the appearance of volumetric and transverseshear locking effects. The first one is characteristic of common metal plasticity models, where plastic deformation is taken to be isochoric or, in other words, incompressible [19]. The second one comes from the analysis of thin shells, were the limit between ''thick'' and ''thin'' geometries is somewhat difficult to establish, with the occurrence of locking not only strictly relying on thickness/length ratios, as demonstrated by Chapelle, Bathe and co-workers [11,12,29,30,31].In order to circumvent these parasitic phenomena, selective reduced integration (or, equivalently, u/p formulation, mean-dilatation technique and B-bar methods) -for volumetric locking -and the ''mixed interpolation of tensorial components''/assumed strain method -for transverse shear locking -had arisen as possible and successful techniques. In the literature see, for instance, references [4,45,53,54,61,68,69,74,85,86,96] for the grounds of computational treatment of incompressibility, in elastic and elastoplastic finite element cases, and also [9,38,56,67] for earlier works dealing with transverse shear locking.In the specific case of shell elements, original planestress assumptions were enough to avoid or postpone incompressibility issues in the nonlinear material range [5,47,55,78,88], although at the expense of a rotation tensor inclusion. As more generality was needed, higher order theories including thickness change via extensible director fields and/or ''layerwise'' approaches were developed, including (or not) rotatio...

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Section: Thick-wall Sphere Problem With Geometric Nonlinearitymentioning

confidence: 99%

An enhanced strain 3D element for large deformation elastoplastic thin-shell applications

Valente

Sousa

Jorge

2004

Computational Mechanics

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“…Flanagan and Belytschko were early contributors [1] to the reduced-integration technique with requisite hourglass stabilization. Other recent successful treatments with these approaches include [2,3]. Mixed variational and projection methods have a major contributor in Simo et al [4].…”

Section: Introductionmentioning

confidence: 99%

Assumed‐deformation gradient finite elements with nodal integration for nearly incompressible large deformation analysis

Broccardo¹,

Micheloni²,

Krysl³

2009

Numerical Meth Engineering

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SUMMARYAn assumed-strain finite element technique for non-linear finite deformation is presented. The weightedresidual method enforces weakly the balance equation with the natural boundary condition and also the kinematic equation that links the elementwise and the assumed-deformation gradient. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual. A variety of finite element shapes fits the derived framework: four-node tetrahedra, eight-, 27-, and 64-node hexahedra are presented here. Since the assumed-deformation gradients are expressed entirely in terms of the nodal displacements, the degrees of freedom are only the primitive variables (displacements at the nodes). The formulation allows for general anisotropic materials and no volumetric/deviatoric split is required. The consistent tangent operator is inexpensive and symmetric. Furthermore, the material update and the tangent moduli computation are carried out exactly as for classical displacement-based models; the only deviation is the consistent use of the assumed-deformation gradient in place of the displacement-derived deformation gradient. Examples illustrate the performance with respect to the ability of the present technique to resist volumetric locking. A constraint count can partially explain the insensitivity of the resulting finite element models to locking in the incompressible limit.

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“…Some examples are the works of Puso [27], Reese [28,29], Reese et al [31] and Legay and Combescure [45], with the common characteristic of using a fixed number of Gauss points in the thickness direction.…”

Section: Introductionmentioning

confidence: 99%

A new one‐point quadrature enhanced assumed strain (EAS) solid‐shell element with multiple integration points along thickness—part II: nonlinear applications

Sousa

Cardoso

Valente

et al. 2006

Numerical Meth Engineering

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SUMMARYIn this work the recently proposed Reduced Enhanced Solid-Shell (RESS) finite element, based on the enhanced assumed strain (EAS) method and a one-point quadrature integration scheme, is extended in order to account for large deformation elastoplastic thin-shell problems. One of the main features of this finite element consists in its minimal number of enhancing parameters (one), sufficient to circumvent the well-known Poisson and volumetric locking phenomena, leading to a computationally efficient performance when compared to other 3D or solid-shell enhanced strain elements. Furthermore, the employed numerical integration accounts for an arbitrary number of integration points through the thickness direction within a single layer of elements. The EAS formulation comprises an additive split of the Green-Lagrange material strain tensor, making the inclusion of nonlinear kinematics a straightforward task. A corotational coordinate system is used to integrate the constitutive law and to ensure incremental objectivity. A physical stabilization procedure is implemented in order to correct the element's rank deficiencies. A variety of shell-type numerical benchmarks including plasticity, large deformations and contact are carried out, and good results are obtained when compared to well-established formulations in the literature.

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On the Equivalent of Mixed Element Formulations and the Concept of Reduced Integration in Large Deformation Problems

Cited by 52 publications

References 77 publications

An enhanced strain 3D element for large deformation elastoplastic thin-shell applications

An enhanced strain 3D element for large deformation elastoplastic thin-shell applications

Assumed‐deformation gradient finite elements with nodal integration for nearly incompressible large deformation analysis

A new one‐point quadrature enhanced assumed strain (EAS) solid‐shell element with multiple integration points along thickness—part II: nonlinear applications

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