Abstract

In this study, a nonlinear numerical method is presented to solve the governing equations of generalized thermoelasticity in a large deformation domain of an elastic medium subjected to thermal shock. The main focus of the study is on the modified Green–Lindsay thermoelasticity theory, solving strain and temperature rate-dependent model using finite strain theory. To warrant the continuity of the finding responses at the boundary after the applied shock, higher order elements are adopted. An analytical solution is provided to validate the numerical findings and an acceptable agreement between the two presented solutions is obtained. The findings revealed that stress and thermal waves have distinct interactions and a harmonic temperature variation may lead to a systematic uniform stress distribution. Besides, a notable difference in the results predicted by the modified Green–Lindsay model and classic theory is observed. It is also found that the modified Green–Lindsay theory is more efficient in determining the wave propagation phenomenon. Furthermore, the findings established that thermal shock induces tensile stresses in the structure immediately after the shock, and the perceived phenomenon mainly depends on the defined boundary conditions. The results show that the strain rate can have a significant influence on the displacement and stress wave propagation in a structure subjected to thermal shock and these impacts may be more considerable with mechanical loading.

中文翻译：

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修改后的格林-林赛热弹性波在热冲击下在弹性材料中的传播

摘要

在这项研究中，提出了一种非线性数值方法来求解受热冲击的弹性介质大变形域中广义热弹性的控制方程。该研究的主要重点是改进的格林-林赛热弹性理论，使用有限应变理论求解应变和温度速率相关的模型。为了保证施加冲击后边界处发现响应的连续性，采用了高阶元素。提供了一种分析解决方案以验证数值结果，并在两个提出的解决方案之间获得了可接受的协议。研究结果表明，应力波和热波具有明显的相互作用，谐波温度变化可能导致系统的均匀应力分布。除了，修改后的格林-林赛模型和经典理论所预测的结果之间存在显着差异。还发现，改进的格林-林赛理论在确定波传播现象方面更为有效。此外，发现确定热冲击在冲击后立即在结构中引起张应力，并且感知到的现象主要取决于定义的边界条件。结果表明，应变率可能会对受热冲击的结构中的位移和应力波传播产生重大影响，而在机械负载下，这些影响可能会更大。还发现，改进的格林-林赛理论在确定波传播现象方面更为有效。此外，发现确定热冲击在冲击后立即在结构中引起张应力，并且感知到的现象主要取决于定义的边界条件。结果表明，应变率可能会对受热冲击的结构中的位移和应力波传播产生重大影响，而在机械负载下，这些影响可能会更大。还发现，改进的格林-林赛理论在确定波传播现象方面更为有效。此外，发现确定热冲击在冲击后立即在结构中引起张应力，并且感知到的现象主要取决于定义的边界条件。结果表明，应变率可能会对受热冲击的结构中的位移和应力波传播产生重大影响，而在机械负载下，这些影响可能会更大。