Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants

M. H.B.M. Shariff; R. Bustamante; J. Merodio

doi:10.1016/j.mechrescom.2017.06.010

Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants

M. H.B.M. Shariff, R. Bustamante, J. Merodio

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear.

Original language	British English
Pages (from-to)	60-64
Number of pages	5
Journal	Mechanics Research Communications
Volume	84
DOIs	https://doi.org/10.1016/j.mechrescom.2017.06.010
State	Published - Sep 2017

Keywords

Deformation indicators
Fiber reinforcement
Nonlinear viscoelasticity
Rate of deformation indicators
Spectral physical invariants

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10.1016/j.mechrescom.2017.06.010

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title = "Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants",

abstract = "In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear.",

keywords = "Deformation indicators, Fiber reinforcement, Nonlinear viscoelasticity, Rate of deformation indicators, Spectral physical invariants",

author = "Shariff, {M. H.B.M.} and R. Bustamante and J. Merodio",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Ltd",

year = "2017",

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doi = "10.1016/j.mechrescom.2017.06.010",

language = "British English",

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T1 - Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants

AU - Shariff, M. H.B.M.

AU - Bustamante, R.

AU - Merodio, J.

PY - 2017/9

Y1 - 2017/9

N2 - In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear.

AB - In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear.

KW - Deformation indicators

KW - Fiber reinforcement

KW - Nonlinear viscoelasticity

KW - Rate of deformation indicators

KW - Spectral physical invariants

UR - http://www.scopus.com/inward/record.url?scp=85021148559&partnerID=8YFLogxK

U2 - 10.1016/j.mechrescom.2017.06.010

DO - 10.1016/j.mechrescom.2017.06.010

M3 - Article

AN - SCOPUS:85021148559

SN - 0093-6413

VL - 84

SP - 60

EP - 64

JO - Mechanics Research Communications

JF - Mechanics Research Communications

ER -

Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants

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Keywords

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