Crack analysis of solids with gradient thermo-piezoelectricity

The flexoelectric effect and higher-order heat conduction equation are considered for the fracture mechanics analysis of piezoelectric nano-sized structures under a thermal load. The variational principle is applied to the governing equations of generalized uncoupled thermoelasticity to obtain the formulation for the finite element method (FEM). In the numerical implementation of the FEM, the physical fields are approximated by conforming elements with C-1-continuity. Since uncoupled thermoelasticity is considered, the heat conduction problem is analyzed independently of the mechanical fields in the first step. The influence on the crack behaviour of the characteristic time parameter that occurs in generalized heat conduction is investigated in some numerical examples.