The nonlinear thermo-hyperelasticity wave propagation analysis of near-incompressible functionally graded medium under mechanical and thermal loadings

Farshad Shakeriaski, Maryam Ghodrat, Juan Escobedo-Diaz, Masud Behnia

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This article presents a non-Fourier thermo-hyperelastic model to investigate thermal and stress wave propagation phenomenon in a near-incompressible functionally graded medium (FGM) for various thermal and mechanical boundary conditions. A strain energy function is chosen to modify FGM’s hyperelastic equations considering the coupling effects of mechanical and thermal terms. By switching the strain tensor's invariants, equations are developed to estimate a near-incompressible model for rubber. The rubber is characterized by a gradual variation in the longitudinal direction. Therefore, the material properties of rubber mainly depend on coordinates in through an exponential function. The nonlinear governing equations are derived from the large displacement approach using Finite Strain Theory. To find an acceptable solution of nonlinear time-dependent thermo-hyperelastic equations, Newmark's time integration process and a nonlinear Hermitian finite element algorithm are employed. The final system’s responses to different boundary conditions such as input surface traction, heat flux and variable material properties are described schematically, and their influence on the wave propagation is calculated. It is shown that the amplitude of oscillation in a functionally graded hyperelastic medium is less than that of a medium with constant properties. The results also show that the wave travels through the medium faster than the FGM. Moreover, the modified Fourier law of heat conduction is applied and the impact of enhanced heat conduction model on the thermo-hyperelastic responses is discussed.
Original languageEnglish
Pages (from-to)3075-3094
Number of pages20
JournalArchive of Applied Mechanics
Volume91
Issue number7
Early online date27 Apr 2021
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Finite strain theory
  • Near-incompressible functionally graded medium
  • Strain energy
  • Thermo-hyperelasticity analysis

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