Constitutive equations in finite viscoplasticity of semicrystalline polymers.
type: Item
instance of: scholarly article
title: Constitutive equations in finite viscoplasticity of semicrystalline polymers.
zbMATH Open document ID: 1083.74008
DOI: 10.1016/S0020-7683(03)00414-1
author: D. Massart
published in: International Journal of Solids and Structures
publication date: 2004-05-27T00:00:00Z
review text: The paper deals with semicrystalline polymers at isothermal finite deformation, for which uniaxial tensile tests with different constant rates of deformation have been performed. In developing the model, the authors start from the multiplicative decomposition of the deformation gradient into its elastic and plastic (irreversible) parts, widely utilized in finite elasto-plasticity. Physical background of the intermediate (relaxed or isoclinic) configurations, with respect to which the material response is considered to be elastic, is related to the crystalline lattice of the material. In crystal plasticity theory, the rate of plastic deformation is generally prescribed by multislip in the appropriate slip systems. Here the authors identified the elastic parts to network stretch and slippage stretch, but in the model no slip systems, no yield condition or viscoplastic surface have been introduced. Moreover, the rate of plastic deformation, via formula (27), is considered to be proportional to a part of the deviator of Cauchy stress (but how can it be identified?), rotated with the elastic rotation. This feature is generally associated with the normality flow rule, when a quadratical yield condition is accepted. We leave away physical motivations in deriving the constitutive relations, and we draw out from the multitude of formulae presented in the paper, the two ones which can be considered to define the model: formula (37), which expresses the rate of left Cauchy-Green elastic tensor in terms of itself, of the velocity gradient, where the strain energy density and the scalar coefficient \(a(t)\) are considered to be given, and formula (35), the stress-strain relation which prescribes the deviatoric part of Cauchy stress in terms of the left Cauchy-Green tensors of the total deformation, as well as of the elastic deformation. Certain simplified versions, see formulae (42) and (43), provide the constitutive equations for the analysis of experimental data in three-dimen…
reviewed by: Sanda Cleja-Ţigoiu
Mathematics Subject Classification ID: 74C20
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 82D60
zbMATH DE Number: 2067528
zbMATH Keywords: Cauchy-Green elastic tensor
zbMATH Keywords: polyethylene
zbMATH Keywords: polypropylene
zbMATH Keywords: Cauchy stress tensor
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2067528