In this article, thermoelastic interaction in a two-temperature generalized thermoelastic unbounded isotropic medium having spherical cavity has been studied in the context of memory-dependent derivative (MDD). The governing coupled equations for the problem associated with kernel function and time delays are considered in the perspective of two-temperature (2 T) three-phase-lag thermoelasticity theory. The bounding surface of the spherical cavity is subjected to mechanical and thermal loading. Using Laplace transform, the problem is transformed from the space–time domain and then solved by the state–space approach method. Suitable numerical technique is used to find the inversion of Laplace transforms. Comparisons are made graphically, between the 2 T three-phase-lag model and 2 T Lord Shulman model with MDD. Also, the effects of time-delay parameter and the kernel function on the distributions of the strain component, thermodynamic temperature, conductive temperature, displacement components, radial and hoop stresses are examined and illustrated graphically. The results show that due to the influence of the three-phase-lag-effect, memory effect, two-temperature parameter, the kernel function and time-delay, all the distributions are affected extensively.

在本文中，已经在具有记忆依赖的导数（MDD）的背景下研究了具有球腔的两温广义热弹性无界各向同性介质中的热弹性相互作用。从两温（2 T）三相滞后热弹性理论的角度考虑了与核函数和时间延迟相关的问题的控制耦合方程。球形腔的边界表面受到机械和热负荷。使用拉普拉斯变换，从时空域转换问题，然后通过状态空间方法解决。使用适当的数值技术来查找拉普拉斯变换的反演。在2 T三相滞后模型和带有MDD的2 T Lord Shulman模型之间进行图形比较。还，考察了时延参数和核函数对应变分量，热力学温度，传导温度，位移分量，径向和环向应力分布的影响，并以图形方式进行了说明。结果表明，受三相滞后效应，记忆效应，两温参数，核函数和时间延迟的影响，所有分布均受到较大影响。