http://dx.doi.org/10.1007/bf01312655

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Title

Tangent modulus tensor in plasticity under finite strain

Authors

Authors

D. W. Nicholson;B. Lin

Comments

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Abbreviated Journal Title

Acta Mech.

Keywords

ELEMENT; Mechanics

Abstract

The tangent modulus tensor, denoted as D, plays a central role in finite element simulation of nonlinear applications such as metalforming. Using Kronecker product notation, compact expressions for D have been derived in Refs. [1]-[3] for hyperelastic materials with reference to the Lagrangian configuration. In the current investigation, the corresponding expression is derived for materials experiencing finite strain due to plastic flow, starling from yield and now relations referred to the current configuration. Issues posed by the decomposition into elastic and plastic strains and by the objective stress flu!: are addressed. Associated and non-associated models are accommodated, as is "plastic incompressibility". A constitutive inequality with uniqueness implications is formulated which extends the condition for "stability in the small" to finite strain. Modifications of D are presented which accommodate kinematic hardening. As an illustration, D is presented for finite torsion of a shaft, comprised of a steel described by a von Mises yield function with isotropic hardening.

Journal Title

Acta Mechanica

Volume

134

Issue/Number

3-4

Publication Date

1-1-1999

Document Type

Article

Language

English

First Page

199

Last Page

215

WOS Identifier

WOS:000079134000005

ISSN

0001-5970

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