Using assumed enhanced strain elements for large compressive deformation

Nagtegaal, J. C.; Fox, David

doi:10.1016/0020-7683(95)00250-2

Cited by 21 publications

(32 citation statements)

References 7 publications

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“…Referring to this deÿciency improvement was recently made by Nagtegaal and Fox. 22 They just enhanced the incremental displacement gradient and not the total displacement gradient, as in References 17,18 and 4. …”

Section: Resultsmentioning

confidence: 93%

Finite deformation coupled thermomechanical problems and ‘generalized standard materials’

Celigoj

1998

Int. J. Numer. Meth. Engng.

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Technological forming processes of thermo-elastoviscoplastic solids are numerically simulated via ÿnite elements based on an appropriate theoretical framework. Departing from the local balance laws of linear momentum and internal energy, the constitutive behaviour is introduced via the concept of 'generalized standard materials (gsm)', 1-3 where a thermodynamic potential and a dissipation potential are the only two scalar quantities needed. They are expressed in invariants of symmetric mixed-variant tensors, respectively. Then the dissipation term evolves from the thermodynamic potential in a very natural way as well as the evolution equations for the internal variables emanate from the dissipation potential. An Eulerian setting is used.The numerical solution (of the non-linear coupled thermomechanical problem) is carried out via 'displacement and assumed enhanced displacement-gradient'-based ÿnite ring-elements 4 in an 'isentropic' mechanical phase and via 'temperature'-based ÿnite ring-elements in an isogeometrical thermal phase and a global Newton-Raphson iterative method in both phases, respectively. The coupled consistent tangent moduli are carefully derived. Numerical results of the thermally triggered necking of a circular bar and of the impact of a copper rod on a rigid wall are given. ? 1998 John Wiley & Sons, Ltd.

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Section: Resultsmentioning

confidence: 93%

Finite deformation coupled thermomechanical problems and ‘generalized standard materials’

Celigoj

1998

Int. J. Numer. Meth. Engng.

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“…It is worth recalling that many interesting strategies have been developed in order to stabilize the methods at hand (cf., for instance, Klaas et al, 1999, Maniatty et al, 2002, Nagtegaal and Fox, 1996, Reese et al, 1999, Reese and Wriggers, 2000, Simo and Armero, 1992. However, a satisfactory analysis of finite element methods for finite strain problems is still missing.…”

Section: Introductionmentioning

confidence: 99%

Stability of Some Finite Element Methods for Finite Elasticity Problems

Auricchio

Veiga

Lovadina

et al. 2009

Mixed Finite Element Technologies

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We consider the finite elasticity problem for incompressible materials, proposing a simple bidimensional problem for which we provide indications on the solution stability. Furthermore, we study the stability of the discrete solution, obtained by means of some well-known finite elements, and we present several numerical experiments in order to evaluate and compare the performance of the different discrete schemes under investigation on the considered model problem.

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“…[23]). Much effort has been done in order to explain and, possibly, to cure the occurrence of such numerical spurious modes; here we quote, in a totally non-exhaustive way, References [1], [14], [20], [19]. What is interesting to note is that even the Pantuso-Bathe element, which is, to our knowledge, the only enhanced strain scheme satisfying the inf-sup condition in linear analysis, shows unrealistic instabilities in some large deformation situations (cf.…”

Section: Introductionmentioning

confidence: 99%