Stress resultant plasticity for shells revisited

In this work, we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the Ilyushin–Shapiro two-surface yield function with isotropic and kinematic hardening. The main focus is on implicit projection algorithms for computation of updated val...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 247-248; pp. 146 - 165
Main Authors: Dujc, Jaka, Brank, Boštjan
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.11.2012
Elsevier
Subjects:
4-node finite element
Algorithms
Computer simulation
Elastoplasticity
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Geometrically exact model
Implicit integration algorithms
Inelasticity (thermoplasticity, viscoplasticity...)
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Physics
Resultants
Sciences and techniques of general use
Shell
Shells
Solid mechanics
Stress resultant plasticity
Stresses
Structural and continuum mechanics
Two-surface yield function
Stress resultant plasticity
Shell
Two-surface yield function
Implicit integration algorithms
4-node finite element
Geometrically exact model
Performance evaluation
Numerical integration
Yield criterion
Computational complexity
Modeling
Finite element method
Inelasticity
Internal stress
Kinematic hardening
Elastoplasticity
Isotropic hardening
Plasticity
Internal variable material
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:In this work, we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the Ilyushin–Shapiro two-surface yield function with isotropic and kinematic hardening. The main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity. Four different algorithms are derived and compared. Three of them yield practically identical final results, yet they differ considerably in computational efficiency and implementation complexity, since they solve different sets of equations and they use different procedures that choose active yield surfaces. One algorithm does not provide acceptable accuracy. It turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently. Several numerical examples are presented to illustrate the Ilyushin–Shapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2012.07.012