Title

Tangent Modulus Tensor In Plasticity Under Finite Strain

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, starting from yield and flow relations referred to the current configuration. Issues posed by the decomposition into elastic and plastic strains and by the objective stress flux 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.

Publication Date

1-1-1999

Publication Title

Acta Mechanica

Volume

134

Issue

3

Number of Pages

199-215

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF01312655

Socpus ID

0032665586 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0032665586

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