Design of simple low order finite elements for large strain analysis of nearly incompressible solids

Neto, E. A. de Souza; Perić, D.; Dutko, M.; Owen, D. R. J.

doi:10.1016/0020-7683(95)00259-6

Cited by 352 publications

(288 citation statements)

References 13 publications

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“…The problem was initially presented by Nagtegaal et al [23] for small strain plasticity to demonstrate the spurious response of standard finite elements and was subsequently reanalysed in a number of papers [28,31,33]. The plate had a Young's modulus of 206.9GPa, Poisson's ratio of 0.29 and was modelled using an elastic-perfectly plastic Prandtl-Reuss constitutive model with yield stress of ρ y = 0.45GPa.…”

Section: Notched Platementioning

confidence: 99%

NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

Coombs

Petit²,

Motlagh

2016

Computer Methods in Applied Mechanics and Engineering

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. (2016) 'NURBS plasticity : yield surface representation and implicit stress integration for isotropic inelasticity.', Computer methods in applied mechanics and engineering., 304 . pp. 342-358. Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn numerical analysis the failure of engineering materials is controlled through specifying yield envelopes (or surfaces) that bound the allowable stress in the material. However, each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case. These equations impact on the numerical implementation, specifically relating to stress integration, of the models and therefore a separate algorithm must be constructed for each model. This paper presents, for the first time, a way to construct yield surfaces using techniques from non-uniform rational basis spline (NURBS) surfaces, such that any isotropic convex yield envelope can be represented within the same framework. These surfaces are combined with an implicit backward-Euler-type stress integration algorithm to provide a flexible numerical framework for computational plasticity. The algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration. The performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models.

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Section: Notched Platementioning

confidence: 99%

NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

Coombs

Petit²,

Motlagh

2016

Computer Methods in Applied Mechanics and Engineering

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“…In fact, as referred by de Souza Neto et al [31] there is an inherent inability in the interpolation functions in the correct representation of isochoric displacement ÿelds.…”

Section: Incompressibility and Lockingmentioning

confidence: 99%

“…Kinematically, it is possible to locally decompose the deformation gradient in a distortional term and a dilatational term (as in Reference [31]). This type of decomposition can be specially useful when there is the intent of deÿning distinct interpolations for these two terms, as it is the case in this paper.…”

Section: Incompressibility and Lockingmentioning

confidence: 99%

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Quadrilateral elements for the solution of elasto‐plastic finite strain problems

Sá

Areias

Jorge

2001

Numerical Meth Engineering

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SUMMARYIn this paper two plane strain quadrilateral elements with two and four variables, are proposed. These elements are applied to the analysis of ÿnite strain elasto-plastic problems. The elements are based on the enhanced strain and B-bar methodologies and possess a stabilizing term. The pressure and dilatation ÿelds are assumed to be constant in each element's domain and the deformation gradient is enriched with additional variables, as in the enhanced strain methodology. The formulation is deduced from a four-ÿeld functional, based on the imposition of two constraints: annulment of the enhanced part of the deformation gradient and the relation between the assumed dilatation and the deformation gradient determinant. The discretized form of equilibrium is presented, and the analytical linearization is deduced, to ensure the asymptotically quadratic rate of convergence in the Newton-Raphson method. The proposed formulation for the enhanced terms is carried out in the isoparametric domain and does not need the usually adopted procedure of evaluating the Jacobian matrix in the centre of the element. The elements are very e ective for the particular class of problems analysed and do not present any locking or instability tendencies, as illustrated by various representative examples.

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“…Among others, the class of mixed variational methods developed by Simo et al (1985), the mixed u/p formulation proposed by Sussman and Bathe (1987), the geometrically non-linear Bbar methodology introduced by Hughes et al (1975) and Moran et al (1990), the family of enhanced mixed finite element methods which include nonlinear version of the method of incompatible modes (Taylor et al, 1976) are presented in Simo and Armero (1992) and have been extended in Simo et al (1993), and the F-bar method proposed by Neto et al (1996) are noteworthy.…”

Section: B1 Introductionmentioning

confidence: 99%

Standard and strain gradient crystal plasticity models: application to Titanium

Galán¹

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Design of simple low order finite elements for large strain analysis of nearly incompressible solids

Cited by 352 publications

References 13 publications

NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

Quadrilateral elements for the solution of elasto‐plastic finite strain problems

Standard and strain gradient crystal plasticity models: application to Titanium

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