This article deals with the thermo-viscoelastic interaction in a two-dimensional homogeneous, isotropic, infinite space subjected to an instantaneous heat source. The problem is considered in the domain of dual-phase-lag (DPL) model of generalized thermo-viscoelasticity with memory-dependent derivative (MDD). The joint Laplace–Fourier transform is used as mathematical tool to obtain vector matrix differential equation and it is then solved by utilizing eigenvalue approach. Numerical estimation of displacements, stresses, and temperature are figured for a certain material by utilizing Bellman method and Gaussian quadrature formula. At last, the impact of space variable, time, kernel function, time-delay, and phase-lag parameters on the thermophysical quantities is analyzed graphically.

本文讨论二维均匀、各向同性、无限空间中受瞬时热源影响的热粘弹性相互作用。该问题在具有记忆相关导数 (MDD) 的广义热粘弹性双相滞后 (DPL) 模型域中考虑。联合拉普拉斯-傅立叶变换作为数学工具得到向量矩阵微分方程，然后利用特征值方法求解。利用贝尔曼方法和高斯求积公式，对某种材料的位移、应力和温度进行数值估计。最后，图形分析了空间变量、时间、核函数、时滞和相位滞后参数对热物理量的影响。