A new semi-implicit formulation for multiple-surface flow rules in multiplicative plasticity

We derive the equations of the multiplicative decomposition in the context of finite strain plasticity with elastic isotropy and arbitrary (isotropic and anisotropic) flow rules. We include multiple surface yield criteria and mixed control of stress components, a requirement for special stress state...

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Bibliographic Details
Published in:Computational mechanics Vol. 49; no. 5; pp. 545 - 564
Main Authors: Areias, P., Dias-da-Costa, D., Pires, E. B., Barbosa, J. Infante
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.05.2012
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Anisotropy
Classical and Continuum Physics
Computational Science and Engineering
Ductile fracture
Elastic anisotropy
Engineering
Isotropy
Mapping
Mathematical analysis
Original Paper
Plane stress
Plastic properties
Single crystals
Strain
Theoretical and Applied Mechanics
Two dimensional analysis
Yield criteria
Finite strain plasticity
Multiple yield surfaces
Ductile fractures
Multiplicative decomposition
ISSN:0178-7675, 1432-0924
Online Access:Get full text
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Summary:We derive the equations of the multiplicative decomposition in the context of finite strain plasticity with elastic isotropy and arbitrary (isotropic and anisotropic) flow rules. We include multiple surface yield criteria and mixed control of stress components, a requirement for special stress states such as plane stress or uniaxial stress. Ductile damage and fracture are also considered. The approach is also appropriate for symmetric single-crystal flow rules. A direct integration of the rate equations is performed as well as smoothing of the complementarity conditions with the Chen-Mangasarian function. The resulting problem is smooth and always converges quadratically, typically requiring fewer steps than return-mapping algorithms. Exceptional robustness is observed. Illustrative examples are shown in 2D, shells and 3D analyses confirming the combination as very effective for the class of problems considered.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-011-0659-5