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Archive of Applied Mechanics

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27-04-2021 | Original

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

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

Published in: Archive of Applied Mechanics | Issue 7/2021

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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.

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Title: The nonlinear thermo-hyperelasticity wave propagation analysis of near-incompressible functionally graded medium under mechanical and thermal loadings
Authors: Farshad Shakeriaski
Maryam Ghodrat
Juan Escobedo-Diaz
Masud Behnia
Publication date: 27-04-2021
Publisher: Springer Berlin Heidelberg
Published in: Archive of Applied Mechanics / Issue 7/2021
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI: https://doi.org/10.1007/s00419-021-01951-z

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