An accurate numerical algorithm for stress integration with finite rotations

Flanagan, David; Taylor, L.M.

doi:10.1016/0045-7825(87)90065-x

Cited by 155 publications

(54 citation statements)

References 11 publications

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“…In any case it should be understood that the rate of deformation and the rotation that is used to un-rotate it may not be consistent. This is a minor detail that has been largely overlooked in the literature (see [11]). …”

Section: The Matparams Structurementioning

confidence: 99%

Library of Advanced Materials for Engineering : LAME.

Hammerand¹,

Scherzinger²

2007

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Constitutive modeling is an important aspect of computational solid mechanics. Sandia National Laboratories has always had a considerable effort in the development of constitutive models for complex material behavior. However, for this development to be of use the models need to be implemented in our solid mechanics application codes. In support of this important role, the Library of Advanced Materials for Engineering (LAME) has been developed in Engineering Sciences. The library allows for simple implementation of constitutive models by model developers and access to these models by application codes. The library is written in C++ and has a very simple object oriented programming structure. This report summarizes the current status of LAME. 4 ACKNOWLEDGMENTSThe authors would like to acknowledge the help of a number of people at Sandia National Laboratories. The Adagio and Presto code development teams, including Arne Gullerud, Kendall Pierson, Jason Hales and Nathan Crane have been especially helpful in the development of LAME and the interface between Strumento and LAME. A large portion of the original implementation of LAME was written by William Gilmartin. The SNTools team, especially Mark Hamilton and Kevin Brown, have helped with code management issues. A number of constitutive model developers, including Bob Chambers, Mike Neilsen and Shane Schumacher, have given very useful feedback on the design of LAME. Finally, analysts that have been willing to use LAME, Jeff Gruda, Matthew Neidigk and Frank Dempsey, have also helped guide its design.5

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Section: The Matparams Structurementioning

confidence: 99%

Library of Advanced Materials for Engineering : LAME.

Hammerand¹,

Scherzinger²

2007

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“…Position vectors for material points at time t are denoted x (configuration B in Fig. 1, after Flanagan and Taylor [8]). The displacements of material points are thus given by u = x-X.…”

Section: Kinematics Strain-stress Measures and Their Ratesmentioning

confidence: 99%

“…The spatial gradient of this material derivative with respect to the current configuration is given by Using the RU decomposition of F, the spatial gradient L may be also written in the form (6) in which the following relations are used :if = RV +RV (7) and (8) The first term in egn (6) is the rate of rigid-body rotation at a material point and is denoted Q. The spin rate Wand Q are identical when the principal axes of D coincide with the principal axes of the current stretch V. Simple extension and pure rotation satisfy this condition.…”

Section: Kinematics Strain-stress Measures and Their Ratesmentioning

confidence: 99%

“…The computational effort required for the polar decomposition should be insignificant relative to the element stiffness computation and the equation solving effort. For their explicit code, Flanagan and Taylor [8] developed an algorithm for the integration of R = QR that maintains orthogonality of R for the very small displacement increments characteristic of explicit solutions. Numerical tests readily show their procedure fails for large displacement increments experienced with implicit global solutions.…”

Section: Polar Decompositionmentioning

confidence: 99%

“…This constitutive model predicts monotonically increasing stresses in simple shear for incremental, linear-elasticity. Using this concept of an unrotated reference frame for constitutive modeling, Flanagan and Thylor [8] developed the PRONTO 2-D and 3-D [32] codes for transient dynamic analysis with explicit time integration. An impressive collection of material behaviors and contact algorithms are included in these codes.…”

Section: Introductionmentioning

confidence: 99%

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A large strain plasticity model for implicit finite element analyses

Healy

Dodds

1992

Computational Mechanics

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Annual:11-1-89 to 12-31-90 14.The theoretical basis and numerical implementation of a plasticity model suitable for finite strains and rotations are described. The constitutive equations governing J2 flow the0!y' are formulated using strainsstresses and their rates defined on the unrotated frame of reference. Unhke models based on the classical J aumann (or corotational) stress rate, the present model predicts physically acceptable responses for homogeneous deformations of exceedingly large magnitude. The associated numerical algorithms accommodate the large strain increments that arise in finite-element formulations employing an implicit solution of the global equilibrium equations. The resulting computational framework divorces the finite rotation effects on . Consequently, all of the numerical refinements developed previously for small-strain plasticity (radial return with subincrementation, plane stress modifications, kinematic hardening, consistent tangent operators) are utilized without modificatIOn. Details of the numerical algorithms are provided including the necessary transformation matrices and additional techniques re9.uired for finite deformations in plane stress. Several numerical examples are presented to illustrate the realIstic responses predicted by the model and the robustness of the numerical procedures. ABSTRACTThe theoretical basis and numerical implementation of a plasticity model suitable for finite strains and rotations are described. The constitutive equations governing J2 flow theory are formulated using strains-stresses and their rates defined on the unrotated frame of reference. Unlike models based on the classical Jaumann (or corotational) stress rate, the present model predicts physically acceptable responses for homogeneous deformations of exceedingly large magnitude. The associated numerical algorithms accommodate the large strain increments that arise in finite-element formulations employing an implicit solution of the global equilibrium equations. The resulting computational framework divorces the finite rotation effects on strain-stress rates from integration of the rates to update the material response over a load (time) step. Consequently, all of the numerical refinements developed previously for small-strain plasticity (radial return with subincrementation, plane stress modifications, kinematic hardening, consistent tangent operators) are utilized without modification. Details of the numerical algorithms are provided including the necessary transformation matrices and additional techniques required for finite deformations in plane stress. Several numerical examples are presented to illustrate the realistic responses predicted by the model and the robustness of the numerical procedures.-ii - ACKNOWLEDGMENTS

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An Algorithm for Integrating the Spin on Convected Bases

Nefussi

Dahan

1996

Int. J. Numer. Meth. Engng.

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SUMMARYA new algorithm is proposed for integrating the spin in the frame of large deformation analysis. The method is based on the integration of a matrix relation, obtained from an adapted decomposition of the deformation gradient, and directly written in convected co-ordinates. The input of this algorithm is either the Gram matrix at any time (if a kinematical method is used, for instance) or more generally, the incremental deformation gradient, and the output is the required rotation matrix on convected bases. The result takes a very simple form in the important case of classical shells.

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An accurate numerical algorithm for stress integration with finite rotations

Cited by 155 publications

References 11 publications

Library of Advanced Materials for Engineering : LAME.

Library of Advanced Materials for Engineering : LAME.

A large strain plasticity model for implicit finite element analyses

An Algorithm for Integrating the Spin on Convected Bases

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