In present paper, a linear thermoelastic theory for porous materials is established by extending the existing theory, in which the strain relaxation and the thermal relaxation are included. Based on the thermodynamic laws, the constitutive relations are derived, and then the corresponding constitutive equations are obtained by specifying the generalized free energy. Further, by combining the existing theory, the non-Fourier's heat conduction law and the obtained constitutive equations, the linear thermoelastic theory for porous materials is formulated. To apply the established theory, the transient response of a half-space with voids is considered. The half-space with voids is subjected to a thermal shock and a mechanical shock simultaneously on its bounding surface. The problem is solved by means of Laplace transform and its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress as well as the volume fraction field are obtained and illustrated graphically. In calculation, the effects of the thermal relaxation factor, the strain relaxation factor and the magnitude of the mechanical shock on the considered variables are examined and discussed in detail.

在本文中，通过扩展现有的理论建立了多孔材料的线性热弹性理论，其中包括应变松弛和热松弛。根据热力学定律，推导本构关系，然后通过指定广义自由能得到相应的本构方程。此外，通过结合现有理论，非傅立叶热传导定律和所获得的本构方程，建立了多孔材料的线性热弹性理论。为了应用已建立的理论，考虑了具有空隙的半空间的瞬态响应。具有空隙的半空间在其边界表面上同时受到热冲击和机械冲击。该问题通过拉普拉斯变换及其数值反演得以解决。获得并显示了无量纲温度，位移，应力以及体积分数场的分布。在计算中，检查并详细讨论了热松弛因子，应变松弛因子和机械冲击的大小对所考虑变量的影响。