TY - JOUR

T1 - Comparison of different isotropic elastoplastic models at finite strains used in numerical analysis

AU - Idesman, Alexander V.

N1 - Funding Information:
We gratefully acknowledge the support of Texas Tech University.

PY - 2003/10/10

Y1 - 2003/10/10

N2 - Several thermodynamically consistent isotropic elastoplastic models at finite strains, that are based on the multiplicative decomposition of the total deformation gradient, are analyzed and compared. It occurs that some of them, that are often used in numerical calculations and cited in literature, are completely equivalent and give the same results, despite quite different structures of the final equations. However, not all models for isotropic elastoplasticity at finite strains that are based on the multiplicative decomposition of the total deformation gradient, and the same elastic and plastic constitutive equations are equivalent because of different equations for the plastic rotation tensor. Comparison of some models showed their dependency on equations for the plastic spin. Such equations are often accepted as assumptions that help to construct an effective numerical algorithm. It is shown that the assumption of a zero modified plastic spin for a thermoelastoplastic model, with the thermal deformation gradient, leads to a new, very effective finite element procedure that is similar to the case of small strains. The derivation and details of such a numerical algorithm are given. A two-dimensional thermoelastoplastic problem at finite strains is solved.

AB - Several thermodynamically consistent isotropic elastoplastic models at finite strains, that are based on the multiplicative decomposition of the total deformation gradient, are analyzed and compared. It occurs that some of them, that are often used in numerical calculations and cited in literature, are completely equivalent and give the same results, despite quite different structures of the final equations. However, not all models for isotropic elastoplasticity at finite strains that are based on the multiplicative decomposition of the total deformation gradient, and the same elastic and plastic constitutive equations are equivalent because of different equations for the plastic rotation tensor. Comparison of some models showed their dependency on equations for the plastic spin. Such equations are often accepted as assumptions that help to construct an effective numerical algorithm. It is shown that the assumption of a zero modified plastic spin for a thermoelastoplastic model, with the thermal deformation gradient, leads to a new, very effective finite element procedure that is similar to the case of small strains. The derivation and details of such a numerical algorithm are given. A two-dimensional thermoelastoplastic problem at finite strains is solved.

KW - Elastoplastic models

KW - Finite element method

KW - Finite strains

UR - http://www.scopus.com/inward/record.url?scp=0141457784&partnerID=8YFLogxK

U2 - 10.1016/S0045-7825(03)00444-4

DO - 10.1016/S0045-7825(03)00444-4

M3 - Article

AN - SCOPUS:0141457784

SN - 0045-7825

VL - 192

SP - 4659

EP - 4674

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 41-42

ER -