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首页> 外文期刊>Journal of thermal stresses >An asymptotic approach to one-dimensional model of nonlinear thermoelasticity at low temperatures and small strains*
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An asymptotic approach to one-dimensional model of nonlinear thermoelasticity at low temperatures and small strains*

机译：低温和小应变的非线性热弹性一维模型的渐近方法*

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摘要

A one-dimensional nonlinear homogeneous isotropic thermoelastic model with an elastic heat flow at low temperatures and small strains is analyzed using the method of weakly nonlinear asymptotics. For such a model, both the free energy and the heat flux vector depend not only on the absolute temperature and strain tensor but also on an elastic heat flow that satisfies an evolution equation. The governing equations are reduced to a matrix partial differential equations, and the associated Cauchy problem with a weakly perturbed initial condition is solved. The solution is given in the form of a power series with respect to a small parameter, the coecients of which are functions of a slow variable that satisfy a system of nonlinear second-order ordinary differential transport equations. A family of closed-form solutions to the transport equations is obtained. For a particular Cauchy problem in which the initial data are generated by a closed-form solution to the transport equations, the asymptotic solution in the form of a sum of four traveling thermoelastic waves admitting blow-up amplitudes is presented.
机译：利用弱非线性渐近方法分析了一维非线性弹性热流在低温和小应变情况下的一维非线性均质热弹性模型。对于这种模型，自由能和热通量向量不仅取决于绝对温度和应变张量，而且还取决于满足演化方程的弹性热流。将控制方程简化为矩阵偏微分方程，并解决了初始条件弱的伴随柯西问题。该解决方案以关于小参数的幂级数形式给出，其系数为慢变量的函数，该慢变量满足非线性二阶常微分输运方程组。获得了运输方程的一类封闭形式的解。对于一个特定的柯西问题，在该问题中，初始数据是通过输运方程的闭式解生成的，提出了以四个传播爆破振幅的热弹性行波之和形式的渐近解。

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