Constitutive modeling of porous viscoelastic materials

F. Xu, Petros Athanasios Sofronis, N. Aravas, S. Meyer

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The effect of porosity on the constitutive response of an isotropic linearly viscoelastic solid that obeys a constitutive law of the standard differential form is investigated under small strain deformation conditions. The correspondence principle of linear viscoelasticity is used to solve the viscoelastic boundary value problem at a unit cell containing a spherical void and loaded axisymmetrically by macroscopic stresses. The results are used to devise a constitutive potential for the description of the porous material for any arbitrary combination of hydrostatic and deviatoric loadings, and the associated 3-D constitutive relationship is determined in the Laplace transform domain. Inversion to the time domain yields the constitutive law of the porous material as a function of porosity in the standard form of convolution integrals. The presence of porosity establishes relaxation time scales for the porous body that differ from the relaxation time of the pure matrix material and brings about a viscous character to the overall hydrostatic response. The numerical implementation of the model in a general purpose finite element code is outlined. The model is used to predict the response of a porous solid propellant material in uniaxial tension and cyclic loading at room temperature.

Original languageEnglish
Pages (from-to)936-955
Number of pages20
JournalEuropean Journal of Mechanics, A/Solids
Volume26
Issue number6
DOIs
Publication statusPublished - Nov 1 2007
Externally publishedYes

Fingerprint

Porous materials
Porosity
porous materials
hydrostatics
porosity
Relaxation time
relaxation time
solid propellants
Solid propellants
matrix materials
viscoelasticity
Laplace transforms
Viscoelasticity
Convolution
convolution integrals
boundary value problems
Boundary value problems
voids
inversions
room temperature

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Cite this

Constitutive modeling of porous viscoelastic materials. / Xu, F.; Sofronis, Petros Athanasios; Aravas, N.; Meyer, S.

In: European Journal of Mechanics, A/Solids, Vol. 26, No. 6, 01.11.2007, p. 936-955.

Research output: Contribution to journalArticle

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