In the present study, in order to provide some flexible and more appropriate tools which can better describe cases of the dynamics with memory effects or of nonlocal phenomena, a novel mathematical model of elasto-thermodiffusion introduced in the context of Taylor's series expansion involving memory-dependent derivative of the function for the dual-phase-lag heat conduction law is proposed. The governing equations of this new model are applied to a one-dimensional half-space, which is taken to be traction free and is subjected to different time-dependent thermal loadings (thermal shock, periodically varying thermal loading and ramp-type heating) and chemical shocks. Laplace transform technique is employed to find out the analytical solutions and the inversion of Laplace transform is carried out using a method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed due to thermodiffusion. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative also.

在本研究中，为了提供一些更灵活、更合适的工具来更好地描述具有记忆效应或非局部现象的动力学情况，在涉及记忆的泰勒级数展开的背景下引入了一种新的弹性热扩散数学模型——提出了双相滞后热传导定律函数的相关导数。该新模型的控制方程应用于一维半空间，该半空间被视为无牵引力并受到不同时间相关的热载荷（热冲击、周期性变化的热载荷和斜坡型加热）和化学冲击。采用拉普拉斯变换技术求解析解，并采用基于傅立叶级数展开技术的方法进行拉普拉斯变换的反演。根据与数值结果对应的图形表示，由于热扩散而构建了关于新理论的结论。由于内存依赖导数的存在，也证明了出色的预测能力。