An efficient exponential based integration for von Mises plasticity combined with Lemaitre damage model

Purpose The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics. Design/methodology/approach By benefiting the properties of the well-known explicit and implicit integrations, a new mixed method is derived. In fact, the advantages of the mentioned techniques are used to achieve an efficient integration. Findings The numerical studies demonstrate the high precision and robustness of the suggested algorithm. Research limitations The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations. Practical implications Updating stress and plastic internal variables are of utmost importance in elastoplastic analyses of structures. The accuracy and efficiency of stress-updating methods significantly affect the final outcomes of nonlinear analyses. Originality/value The idea which is used to derive the hybrid method leads to an efficient integration method for updating the constitutive equations of the damage mechanics.

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A Modified Phase-Field Damage Model for Metal Plasticity at Finite Strains: Numerical Development and Experimental Validation

Metals ◽

10.3390/met11010047 ◽

2020 ◽

Vol 11 (1) ◽

pp. 47

Author(s):

Jelena Živković ◽

Vladimir Dunić ◽

Vladimir Milovanović ◽

Ana Pavlović ◽

Miroslav Živković

Keyword(s):

Phase Field ◽

Damage Evolution ◽

Deformation Gradient ◽

Damage Model ◽

Steel Structures ◽

Plasticity Model ◽

Metal Plasticity ◽

Damage And Fracture ◽

Von Mises ◽

Von Mises Plasticity

Steel structures are designed to operate in an elastic domain, but sometimes plastic strains induce damage and fracture. Besides experimental investigation, a phase-field damage model (PFDM) emerged as a cutting-edge simulation technique for predicting damage evolution. In this paper, a von Mises metal plasticity model is modified and a coupling with PFDM is improved to simulate ductile behavior of metallic materials with or without constant stress plateau after yielding occurs. The proposed improvements are: (1) new coupling variable activated after the critical equivalent plastic strain is reached; (2) two-stage yield function consisting of perfect plasticity and extended Simo-type hardening functions. The uniaxial tension tests are conducted for verification purposes and identifying the material parameters. The staggered iterative scheme, multiplicative decomposition of the deformation gradient, and logarithmic natural strain measure are employed for the implementation into finite element method (FEM) software. The coupling is verified by the ‘one element’ example. The excellent qualitative and quantitative overlapping of the force-displacement response of experimental and simulation results is recorded. The practical significances of the proposed PFDM are a better insight into the simulation of damage evolution in steel structures, and an easy extension of existing the von Mises plasticity model coupled to damage phase-field.

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On the Characteristic Surfaces of the von Mises Plasticity Equations

Indiana University Mathematics Journal ◽

10.1512/iumj.1952.1.51009 ◽

1952 ◽

Vol 1 (3) ◽

pp. 343-357

Author(s):

T. Thomas

Keyword(s):

Mises Plasticity ◽

Von Mises ◽

Von Mises Plasticity

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A novel ‘optimal’ exponential-based integration algorithm for von-Mises plasticity with linear hardening: Theoretical analysis on yield consistency, accuracy, convergence and numerical investigations

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.1637 ◽

2006 ◽

Vol 67 (4) ◽

pp. 449-498 ◽

Cited By ~ 32

Author(s):

E. Artioli ◽

F. Auricchio ◽

L. Beirão da Veiga

Keyword(s):

Theoretical Analysis ◽

Integration Algorithm ◽

Linear Hardening ◽

Numerical Investigations ◽

Mises Plasticity ◽

Von Mises ◽

Von Mises Plasticity

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A General Orthotropic von Mises Plasticity Material Model With Mixed Hardening: Model Definition and Implicit Stress Integration Procedure

Journal of Applied Mechanics ◽

10.1115/1.2788875 ◽

1996 ◽

Vol 63 (2) ◽

pp. 376-382 ◽

Cited By ~ 12

Author(s):

M. Kojic´ ◽

N. Grujovic´ ◽

R. Slavkovic´ ◽

M. Zˇivkovic´

Keyword(s):

Equivalent Stress ◽

Parameter Method ◽

Plasticity Model ◽

Integration Procedure ◽

Mixed Hardening ◽

Tangent Moduli ◽

Stress Integration ◽

Mises Plasticity ◽

Von Mises ◽

Von Mises Plasticity

A general orthotropic von Mises plasticity model, with an extension of the Hill’s yield criterion to include mixed hardening, is introduced in the paper. Material constants and equivalent stress-equivalent plastic strain curves are defined in a way to suggest their experimental determination. The model represents a special case of a general anisotropic metal plasticity model proposed by the authors. An implicit stress integration procedure, representing an application of the governing parameter method (GPM) introduced by the first author, is presented. The GPM is briefly described, and the computational procedure, together with calculation of the consistent tangent moduli, are given in some detail for a general three-dimensional deformation, with direction of application to plane stress/shell conditions. Numerical examples illustrate applicability of the model and effectiveness of the computational algorithm.

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