在麦克斯韦材料中应力σ、应变ε及其相对于时间 t 的变化率由以下形式的

偏微分方程描述：

$$\frac{\partial \sigma}{\partial t} = \frac{1}{\rho}\frac{\partial \tau}{\partial x} + \frac{\partial \sigma_{xx}}{\partial x} + \frac{\partial \sigma_{xy}}{\partial y} + \frac{\partial \sigma_{xz}}{\partial z}$$

$$\frac{\partial \epsilon}{\partial t} = \frac{1}{2\rho}\left(\frac{\partial \tau_{xx}}{\partial x} + \frac{\partial \tau_{yy}}{\partial y} + \frac{\partial \tau_{zz}}{\partial z}\right) + \frac{1}{2}\left(\frac{\partial \epsilon_{xx}}{\partial x} + \frac{\partial \epsilon_{yy}}{\partial y} + \frac{\partial \epsilon_{zz}}{\partial z}\right) + \frac{1}{2}\left(\frac{\partial \epsilon_{xy}}{\partial y} + \frac{\partial \epsilon_{yx}}{\partial x}\right) + \frac{1}{2}\left(\frac{\partial \epsilon_{xz}}{\partial z} + \frac{\partial \epsilon_{zx}}{\partial x}\right) + \frac{1}{2}\left(\frac{\partial \epsilon_{yz}}{\partial z} + \frac{\partial \epsilon_{zy}}{\partial y}\right)$$

其中，σ是应力张量，τ是剪切应力张量，ε是应变张量，ρ是材料密度，x、y、z是坐标轴。这两个方程描述了应力和应变随时间和空间的变化规律，是材料力学中的基本方程之一