Effect of material non-homogeneity on the inhomogeneous shearing deformation of a Gent slab subjected to a temperature gradient

Ecevit Bilgili, Barry Bernstein, Hamid Arastoopour

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


It is well known that most rubber-like materials are non-homogeneous due to either imperfect manufacturing conditions or the action of severe thermo-oxidative environments in many practical applications. In this study, within the context of finite thermoelasticity, we theoretically analyze the inhomogeneous shearing deformation of a non-homogeneous rubber-like slab subjected to a thermal gradient across its thickness. The major objective of this study is to investigate the effect of the material non-homogeneity, which is the material-coordinate dependence of the material response functions, on the stress-strain fields for a given temperature gradient. First, we show the existence of a simple shearing deformation from which the generalized shear modulus and the generalized thermal conductivity of the slab could be obtained. Based on this information, the Gent material model is generalized to take the material non-homogeneity and the temperature dependence of the stress into account. To analyze the inhomogeneous shearing deformation of the non-homogeneous slab, deformation and temperature fields are postulated; then the decoupled temperature field is obtained analytically by solving the local energy balance equation. Finally, the static equilibrium equations are solved considering the linear temperature field. Our results show that the spatial pattern and the degree of the material non-homogeneity have profound effects on the stress-strain fields. The shear strain becomes nearly homogeneous and the stresses are relatively small for a certain spatial variation of the material non-homogeneity. This result suggests the possibility of designing a novel class of materials: functionally graded rubber-elastic materials (FGREMs).

Original languageEnglish (US)
Pages (from-to)1351-1368
Number of pages18
JournalInternational Journal of Non-Linear Mechanics
Issue number9
StatePublished - Nov 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • Finite thermoelasticity
  • Functionally graded
  • Inhomogeneous shearing
  • Material design
  • Non-homogeneous rubber


Dive into the research topics of 'Effect of material non-homogeneity on the inhomogeneous shearing deformation of a Gent slab subjected to a temperature gradient'. Together they form a unique fingerprint.

Cite this