Crack analysis of nano-sized thermoelectric material structures.

• Analyses of thermoelectric nano-sized structures with cracks. • The size-effect phenomenon is considered by strain-gradients in constitutive equations. • The mixed FEM formulation is applied for numerical implementation. • The influence of the size effect on the crack-opening-displacements is investigated. General 2D boundary value problems with cracks in nano-sized structures of thermoelectric materials are analyzed by the finite element method (FEM). The size-effect phenomenon observed in nano-sized structures is considered by strain-gradients in the constitutive equation for the high-order stress tensor. The variational principle is applied for derivation of coupled thermo-electro-mechanical governing equations. The thermo-electrical fields are fully coupled and the mechanical fields are coupled with temperature only. The mixed FEM with the C0 continuous interpolation for displacements and strains is developed. A collocation approach for kinematic constraints between strains and displacements is applied. The influence of the size effect on variation of crack opening displacements is demonstrated by some numerical examples. [ABSTRACT FROM AUTHOR]