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

Authors:
P. Areias;D. Dias-Da-Costa;E. B. Pires;J. Infante Barbosa
Affiliations:
Departamento de Física, Universidade de Évora, Colégio Luís António Verney, Evora, Portugal 7002-554 and ICIST, Lisbon, Portugal;INESC Coimbra, Department of Civil Engineering, University of Coimbra, Coimbra, Portugal 3030-788;Departamento de Engenharia Civil e Arquitectura, Instituto Superior Técnico, Lisbon, Portugal 1049-001;Departamento de Física, Universidade de Évora, Colégio Luís António Verney, Evora, Portugal 7002-554
Venue:
Computational Mechanics
Year:
2012

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Abstract

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.