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Crack problems in nano-sized elastic structures under the Joule heating are analyzed by the finite element method (FEM). The variational principle is applied for derivation of coupled electrothermomechanical governing equations. The temperature field is described by classical Fourier′s law and it is not influenced by mechanical field. Transient heat conduction is considered since it is the slowest process among all other coupled fields here. Quasi-static conditions are considered for mechanical and electrical fields. Due to higher derivatives in governing equations the conventional FEM cannot be applied. Therefore, the mixed FEM with the C 0  continuous interpolation for displacements and strains is developed. The influence of the material characteristic length on variation of crack opening displacements in finite nano-sized structures under an electric current load is investigated.

Thermoelectric Joule heating in crack problems in nano-sized structures