Extension of the temperature-related Cauchy–Born rule: Material stability analysis and thermo-mechanical coupling

In this paper, we first study the material stability of nanostructured materials via the continuum linearized stability analysis technique with the temperature-related Cauchy–Born (TCB) rule. As a temperature-related homogenization technique, the TCB rule considers the free energy instead of the potential so that temperature effects on material stability can be investigated. In addition, we develop a thermo-mechanical coupling model through implementing the thermal diffusion equation into nanoscale continuum approximation. Crack propagation at a nanoplate is studied as an example. Since the nanoscale phenomenon of bond breaking is involved when crack propagates, temperature increasing around the crack tip due to the released potential is considered in our thermo-mechanical coupling model.