In order to describe the complex interaction in the heat and moisture transfer process, a coupled time‐fractional hygrothermal theory is developed to describe the anomalous phenomenon of coupled heat and moisture diffusion. The hygrothermoelastic behaviors in a plate with an edge crack are investigated. The surfaces of the plate are both subjected to hygrothermal shocks. The Laplace transform and the finite Fourier transform are applied to seek an analytical solution of temperature change, moisture distribution, and stress response that are expressed in terms of the Mittag‐Leffler function. With this solution, the stress intensity factors at the crack tip are numerically calculated through the weight function method. The coupling effects of the heat and moisture on the stress intensity factors are illustrated graphically for sub‐diffusion, normal diffusion, and super‐diffusion respectively. The results show that the coupling hygrothermal effects are significant and different when compared with the uncoupled model.

中文翻译：

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边缘裂纹弹性板中湿热弹性场的瞬态响应

为了描述热量和水分传递过程中的复杂相互作用，发展了时间-分数湿热耦合理论来描述热量和水分扩散耦合的异常现象。研究了具有边缘裂纹的板的湿热弹性行为。板的表面都受到湿热冲击。应用拉普拉斯变换和有限傅里叶变换来寻找温度变化，水分分布和应力响应的解析解，这些解析解以米塔格-莱夫勒函数表示。利用该解决方案，通过权函数法对裂纹尖端处的应力强度因子进行了数值计算。热量和水分对应力强度因子的耦合作用以图形方式说明了亚扩散，正扩散和超扩散。结果表明，与非耦合模型相比，耦合湿热效应显着不同。