物性与温度相关材料广义热弹性模型及渐近分析

计及材料物性与温度的相关性，基于Clausius不等式和L-S广义热弹性理论，通过对自由能公式的高阶展开，构建了具有变物性特征的广义耦合热弹性动力学模型。推导了各向同性材料表面受热冲击问题的线性化控制方程组，利用热冲击的瞬时特征，借助于Laplace正、逆变换技术及其极限性质，给出了变物性条件下一维热冲击问题的温度场、位移场和应力场的渐近表达式。通过算例，得到了热冲击作用下各物理场的分布规律以及材料物性与温度相关性对于热弹性响应的影响规律。结果表明：材料物性与温度相关性对于各物理场的阶跃位置、阶跃间隔以及阶跃峰值均产生影响，但值得注意的是，相比于位移场和应力场的显著影响，其对温度场的影响效果并不明显。

GENERALIZED THERMOELASTIC MODEL AND ASYMPTOTIC ANALYSIS FOR ELASTIC MEDIA WITH TEMPERATURE-DEPENDENT

Based on the Clausius inequality and L-S generalized thermoelasticity theory, the coupled model for the generalized thermoelasticity in an elastic media with temperature-dependent properties is established by the higher expansion of the free energy. The linear equations are reduced for the homogeneous and isotropic materials with the boundary subjected to thermal shock. In accordance with the transient behaviors of thermal shock, the asymptotic solutions of the temperature, displacement and stress for one dimensional problem are obtained via the Laplace transform and inverse transform and its limit theorem. Numerical simulation is conducted for a semi-infinite copper rod, the distribution of each physical field and the influence of the temperature-dependent properties on these thermoelastic response are obtained. The results show that the temperature-dependent properties have some influence on the locations, intervals and peak values of jumps, and it is notable that the influence on the temperature is very litter than that on the displacement and stress.