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.

本文提出了一种非傅里叶热超弹性模型，以研究在各种热和机械边界条件下，近不可压缩的功能梯度介质（FGM）中的热和应力波传播现象。考虑到机械项和热项的耦合效应，选择应变能函数来修改FGM的超弹性方程。通过切换张量不变式，可以开发方程式来估计橡胶的近不可压缩模型。橡胶的特征在于在纵向方向上的逐渐变化。因此，橡胶的材料性能主要取决于通过指数函数的坐标。非线性控制方程式是使用有限应变理论从大位移方法中得出的。为了找到非线性的时变热超弹性方程的可接受解，采用了Newmark的时间积分过程和非线性Hermitian有限元算法。示意性地描述了最终系统对不同边界条件（例如输入表面牵引力，热通量和可变材料特性）的响应，并计算了它们对波传播的影响。结果表明，功能梯度超弹性介质的振动幅度小于具有恒定特性的介质的振动幅度。结果还表明，波传播通过介质的速度比FGM快。此外，应用改进的热传导傅里叶定律，讨论了增强的热传导模型对热-超弹性响应的影响。采用了纽马克的时间积分过程和非线性厄米有限元算法。示意性地描述了最终系统对不同边界条件（例如输入表面牵引力，热通量和可变材料特性）的响应，并计算了它们对波传播的影响。结果表明，功能梯度超弹性介质的振动幅度小于具有恒定特性的介质的振动幅度。结果还表明，波传播通过介质的速度比FGM快。此外，应用改进的热传导傅里叶定律，讨论了增强的热传导模型对热-超弹性响应的影响。采用了纽马克的时间积分过程和非线性厄米有限元算法。示意性地描述了最终系统对不同边界条件（例如输入表面牵引力，热通量和可变材料特性）的响应，并计算了它们对波传播的影响。结果表明，功能梯度超弹性介质的振动幅度小于具有恒定特性的介质的振动幅度。结果还表明，波传播通过介质的速度比FGM快。此外，应用改进的热传导傅里叶定律，讨论了增强的热传导模型对热-超弹性响应的影响。示意性地描述了最终系统对不同边界条件（例如输入表面牵引力，热通量和可变材料特性）的响应，并计算了它们对波传播的影响。结果表明，功能梯度超弹性介质的振动幅度小于具有恒定特性的介质的振动幅度。结果还表明，波传播通过介质的速度比FGM快。此外，应用改进的热传导傅里叶定律，讨论了增强的热传导模型对热-超弹性响应的影响。示意性地描述了最终系统对不同边界条件（例如输入表面牵引力，热通量和可变材料特性）的响应，并计算了它们对波传播的影响。结果表明，功能梯度超弹性介质的振动幅度小于具有恒定特性的介质的振动幅度。结果还表明，波传播通过介质的速度比FGM快。此外，应用改进的热传导傅里叶定律，讨论了增强的热传导模型对热-超弹性响应的影响。结果表明，功能梯度超弹性介质的振动幅度小于具有恒定特性的介质的振动幅度。结果还表明，波传播通过介质的速度比FGM快。此外，应用改进的热传导傅里叶定律，讨论了增强的热传导模型对热-超弹性响应的影响。结果表明，功能梯度超弹性介质的振动幅度小于具有恒定特性的介质的振动幅度。结果还表明，波传播通过介质的速度比FGM快。此外，应用改进的热传导傅里叶定律，讨论了增强的热传导模型对热-超弹性响应的影响。