Tangent modulus tensor in plasticity under finite strain

    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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