# 材料和结构 Materials and Structures FEEG2005W1-01

$$\frac{\partial \eta}{\partial t}=-M_{\eta} \frac{\delta F}{\delta \eta}$$
where $\mathrm{M}_{\eta}$ is a kinetic coefficient. The temperature field satisfies the equation of heat conduction with a source term 
$$\frac{\partial T}{\partial t}=\nabla \cdot(D \nabla T)+\frac{q}{c} \frac{d \eta}{d t}$$
where $\mathrm{D}$ is the thermal diffusivity, $\mathrm{q}$ is the latent heat, and $\mathrm{c}$ is the heat capacity.
$\dot{U}{Z}=\frac{\partial \dot{U}{R}}{\partial Z}=\frac{\partial \dot{U}{\theta}}{\partial Z}=0$ at $Z=0$ and $Z=L$, where $L$ is the length of the CNT. The homogeneous governing equations (9) and boundary conditions (10) constitute an Eigenvalue problem for the displacement increment $\dot{U}$. The Eigenvalue is the axial strain $E{z Z}$. In other words, Eqs. (9) and (10) have only the trivial solution $\dot{U}=0$ until the axial strain $E_{z z}$ reaches a critical value $\left(E_{\text {ZZ }}\right)_{\text {critical }}$ for bifurcation.