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Efficient variational constitutive updates by means of a novel parameterization of the flow rule
Author(s) -
Bleier Nikolaus,
Mosler Jörn
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3280
Subject(s) - hessian matrix , constitutive equation , mathematics , flow (mathematics) , mathematical optimization , scheme (mathematics) , computer science , state variable , point (geometry) , algorithm , finite element method , mathematical analysis , geometry , physics , thermodynamics
SUMMARY Analogously to the classical return‐mapping algorithm, so‐called variational constitutive updates are numerical methods allowing to compute the unknown state variables such as the plastic strains and the stresses for material models showing an irreversible mechanical response. In sharp contrast to standard approaches in computational inelasticity, the state variables follow naturally and jointly from energy minimization in case of variational constitutive updates. This leads to significant advantages from a numerical, mathematical as well as from a physical point of view. However, while the classical return‐mapping algorithm has been being developed for several decades, and thus, it has already reached a certain maturity, variational constitutive updates have drawn attention only relatively recently. This is particularly manifested in the numerical performance of such algorithms. Within the present paper, the numerical efficiency of variational constitutive updates is critically analyzed. It will be shown that a naive approximation of the flow rule causes a singular Hessian within the respective Newton–Raphson scheme. However, by developing a novel parameterization of the flow rule, an efficient algorithm is derived. Its performance is carefully compared to that of the classical return‐mapping scheme. This comparison clearly shows that the novel variationally consistent implementation is, at least, as efficient as the classical return‐mapping algorithm. Copyright © 2011 John Wiley & Sons, Ltd.