Time-domain modeling of linear viscoelasticity using augmenting thermodynamic fields

George A. Lesieutre, E. Bianchini

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

A time-domain model of linear viscoelasticity is developed in terms of augmenting thermodynamic fields (ATF) that are coupled with the mechanical displacement field. Previous related efforts addressed time-domain finite element modeling of frequency-dependent material damping, but were effectively limited to one-dimensional stress states. The current work is based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic. General coupled constitutive equations for the total and anelastic stresses are developed in terms of the total and anelastic strains, and specialized to the case of isotropic materials. The partial differential equations governing the temporal evolution of the total and anelastic displacement fields are developed in a parallel fashion, involving the divergence of appropriate stress tensors. Boundary conditions are also discussed: the anelastic displacement field is effectively an internal field, as it cannot be directly affected by applied loads, but only through coupling to the total displacement. In order to illustrate the use of the method, ATF model parameters for a commonly-used high damping polymer are developed from available complex modulus data.

Original languageEnglish (US)
Pages (from-to)2101-2109
Number of pages9
JournalCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
Issue numberpt 4
StatePublished - 1993

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Viscoelasticity
Thermodynamics
Damping
Constitutive equations
Partial differential equations
Tensors
Polymers
Boundary conditions
Decomposition

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

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abstract = "A time-domain model of linear viscoelasticity is developed in terms of augmenting thermodynamic fields (ATF) that are coupled with the mechanical displacement field. Previous related efforts addressed time-domain finite element modeling of frequency-dependent material damping, but were effectively limited to one-dimensional stress states. The current work is based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic. General coupled constitutive equations for the total and anelastic stresses are developed in terms of the total and anelastic strains, and specialized to the case of isotropic materials. The partial differential equations governing the temporal evolution of the total and anelastic displacement fields are developed in a parallel fashion, involving the divergence of appropriate stress tensors. Boundary conditions are also discussed: the anelastic displacement field is effectively an internal field, as it cannot be directly affected by applied loads, but only through coupling to the total displacement. In order to illustrate the use of the method, ATF model parameters for a commonly-used high damping polymer are developed from available complex modulus data.",
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N2 - A time-domain model of linear viscoelasticity is developed in terms of augmenting thermodynamic fields (ATF) that are coupled with the mechanical displacement field. Previous related efforts addressed time-domain finite element modeling of frequency-dependent material damping, but were effectively limited to one-dimensional stress states. The current work is based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic. General coupled constitutive equations for the total and anelastic stresses are developed in terms of the total and anelastic strains, and specialized to the case of isotropic materials. The partial differential equations governing the temporal evolution of the total and anelastic displacement fields are developed in a parallel fashion, involving the divergence of appropriate stress tensors. Boundary conditions are also discussed: the anelastic displacement field is effectively an internal field, as it cannot be directly affected by applied loads, but only through coupling to the total displacement. In order to illustrate the use of the method, ATF model parameters for a commonly-used high damping polymer are developed from available complex modulus data.

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