Coupled 1-D stress and thermal waves in temperature dependent nonlinear elastic and viscoelastic media*

Harry H. Hilton, Mohamed H. Elalfy, Hazem S. Eldahshan, Mohamed Khairy

Research output: Contribution to journalArticlepeer-review


A general analysis is formulated for the closed loop coupled thermal and displacement viscoelastic 1-D wave problem. The proper inclusion of the highly temperature sensitive viscoelastic material properties renders the problem nonlinear, even though the displacements and material properties are considered to obey linear relations. In the present article. the previous analysis is enlarged and reformulated by (a) the inclusion of nonlinear elastic and viscoelastic constitutive relations as formulated in Hilton, (b) the addition of thermal waves to the displacement waves, and by (c) temperature dependent material density and viscoelastic moduli and compliances. The wave problem studied here is of significant importance in modeling, material characterization, determination of instantaneous moduli, nonlinear analytical solution protocols and the nonlinear interaction of temperature, material properties, and wave motions. Analytical and numerical solution protocols are presented and evaluated.

Original languageEnglish (US)
Pages (from-to)122-151
Number of pages30
JournalJournal of Thermal Stresses
Issue number1
StatePublished - Jan 2 2019


  • Coupled 1-D waves
  • longitudinal displacement and thermal waves
  • material temperature sensitivity
  • nonlinear coupled variable coefficient integral PDEs
  • nonlinear elasticity and viscoelasticity
  • nonlinear moduli

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics


Dive into the research topics of 'Coupled 1-D stress and thermal waves in temperature dependent nonlinear elastic and viscoelastic media*'. Together they form a unique fingerprint.

Cite this