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REVIEW ARTICLES

Stress integration procedures for inelastic material models within the Finite Element Method

[+] Author and Article Information
Miloš Kojić

Faculty of Mechanical Engineering and Center for Scientific Research, Serbian Academy of Science and Arts, University of Kragujevac, 34000 Kragujevac, Serbia, Yugoslavia; kojic@knez.uis.kg.ac.yu

Appl. Mech. Rev 55(4), 389-414 (Jul 30, 2002) (26 pages) doi:10.1115/1.1482088 History: Online July 30, 2002
Copyright © 2002 by ASME
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References

Figures

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Graphical representation of the tangent stiffness-radial return method (von Mises perfect plasticity)
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Graphical representation of the secant stiffness method (von Mises perfect plasticity)
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Stress relaxation in the case of viscoplastic deformation of von Mises material
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A general scheme of return mapping in plasticity
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Schematic representation of generalized return mapping algorithms (associated plasticity): a) Generalized trapezoidal rule, b) generalized midpoint rule
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Residual stresses as functions of elongation and shear measures Ū and S̄, plastic material, ULJ analytical solution 107
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Stress solution for pure shear in case of isotropic and kinematic hardening; use of the spin W and a modified spin W * 110
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Representation of multiplicative decomposition of deformation gradient
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Perforated strip, perfect plasticity. Finite element mesh and elastic-plastic interface for Steps 3, 4, and 8 41
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Isoerror maps for the generalized trapezoidal and midpoint rule, perfectly plastic von Mises model, plane strain deformation 42
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Solution of thermoplastic deformation of plane strain element, perfect plasticity 82
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Solution of thermoplastic deformation of plane stress element, kinematic hardening 82
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Creep of beam subjected to bending 83
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Cauchy stresses in terms of shear strain γ (see Fig. 7) for simple shearing of von Mises material 168: a) Isotropic and kinematic hardening, b) Isotropic hardening, c) Kinematic hardening
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Large strain shear deformation of sand, MRS-Lade model for cohesionless granular material 174: a) Numerical setup of a Directional Shear Cell (DSC) test, b) Shear stress–shear deformation dependence, c) Volumetric strain–shear deformation dependence
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Necking of a circular bar 194: a) Final deformed configuration with field of effective plastic strain, b) Force-displacement dependence
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Impact of an aluminum bar on a rigid wall; deformed configurations at t=30 ms 165
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Buckling of a cruciform beam; effect of plastic deformation in the reduction of the critical load 165
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Necking of a thin sheet 98184187: a) Final configuration and field of effective plastic strain, b) Force-displacement of the specimen end dependence
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Deep drawing of a cylindrical cup 183: a) Initial geometry, b) Punch load versus punch displacement
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Elastic-plastic deformation of the soil specimen, Cam-clay model 160: a) Geometry of the specimen, b) Deformed mesh and field of volumetric plastic strain
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Perfect plasticity coupled to damage 58: a) Load versus average strain, b) Displacement patterns (top row) and accumulated plastic strain (bottom row)

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