On the implementation of inelastic constitutive equations with special reference to large deformation problems

Nagtegaal, J. C.

doi:10.1016/0045-7825(82)90120-7

Cited by 217 publications

(70 citation statements)

References 3 publications

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“…Implicit methods have some significant advantages over, simpler, explicit methods in that they: allow for larger strain increments to be applied, rigorously enforce the consistency conditions (see Section 2.1) and allow the derivation of the algorithmic consistent tangent [22,32] that facilitates optimum convergence of the boundary value simulation.…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…This observation is ÿrst made by Nagtegaal 29 and Simo and Taylor 15 leading to the notion of the consistent elastoplastic tangent modulus. The di erence between the consistent and continuum tangent moduli concerns the third term in (76) above, which is due to the change of normal to the yield surface over a time step.…”

Section: Consistent Tangent Operator For Plasticitymentioning

confidence: 67%

Classical plasticity and viscoplasticity models reformulated: theoretical basis and numerical implementation

Ibrahimbegović

Gharzeddine

Chorfi

1998

Int. J. Numer. Meth. Engng.

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The well-known phenomenological model of small strain rate-independent plasticity is reformulated in this paper. The main di erence from the classical expositions concerns the absence of the plastic strain from the list of state variables. We show that with the proposed choice of state variables, including the total and the elastic strains and strain-like variables which control hardening, we recover all the ingredients of the classical model from a minimum number of hypotheses: instantaneous elastic response and the principle of maximum plastic dissipation. We also show that using a regularized, penalty-like form of the principle of maximum plastic dissipation, we can recover the classical viscoplasticity model.As opposed to the previous schemes used for the ÿnite element implementation of this model (e.g. B-bar method), we propose an approach in which the basic set of equations need not be modiÿed. The operator split method is used to simplify the details of the numerical implementation concerning both the computation of state variables and the incompatible mode based ÿnite element approximations. The latter proves to be indispensable for accommodating the near-incompressible deformation patterns arising in the classical plasticity. An extensive set of numerical simulations is used to illustrate the proposed formulation. ? 1998 John Wiley & Sons, Ltd.

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“…In nearly incompressible conditions, the mesh is expected to lock [17]. To avoid locking, F r is deÿned such that a predetermined number of volumetric degrees of freedom is obtained.…”

Section: The Assumed Strain Methodsmentioning

confidence: 99%

An object-oriented programming approach to the Lagrangian FEM analysis of large inelastic deformations and metal-forming processes

Zabaras

Srikanth

1999

Int. J. Numer. Meth. Engng.

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SUMMARYThe general deformation problem with material and geometric non-linearities is typically divided into a number of subproblems including the kinematic, the constitutive, and the contact=friction subproblems. These problems are introduced for algorithmic purposes; however, each of them represents distinct physical aspects of the deformation process. For each of these subproblems, several well-established mathematical and numerical models based on the ÿnite element method have been proposed for their solution.Recent developments in software engineering and in the ÿeld of object-oriented C++ programming have made it possible to model physical processes and mechanisms more expressively than ever before. In particular, the various subproblems and computational models in a large inelastic deformation analysis can be implemented using appropriate hierarchies of classes that accurately represent their underlying physical, mathematical and=or geometric structures.This paper addresses such issues and demonstrates that an approach to deformation processing using classes, inheritance and virtual functions allows a very fast and robust implementation and testing of various physical processes and computational algorithms. Here, speciÿc ideas are provided for the development of an objectoriented C++ programming approach to the FEM analysis of large inelastic deformations. It is shown that the maintainability, generality, expandability, and code re-usability of such FEM codes are highly improved. Finally, the e ciency and accuracy of an object-oriented programming approach to the analysis of large inelastic deformations are investigated using a number of benchmark metal-forming examples.

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On the implementation of inelastic constitutive equations with special reference to large deformation problems

Cited by 217 publications

References 3 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

Classical plasticity and viscoplasticity models reformulated: theoretical basis and numerical implementation

An object-oriented programming approach to the Lagrangian FEM analysis of large inelastic deformations and metal-forming processes

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