Gradient Theory for Crack Analysis in Thermoelectric Materials.

In this paper the strain gradients in constitutive equation of stresses are considered as coupled to the thermos-electric-mechanical problem with cracks. The principle of virtual work is applied to derive the finite element equation for a general 2d boundary value problem. Due to the higher order of derivatives in gradient theory it is needed to use C¹- continuous elements to guarantee the continuity of the derivates at the element boundaries. It is not an easy task to develop C¹ continuous elements. Therefore, the mixed FEM formulation is developed here. The C⁰ continuous interpolation is independently applied for both the displacements and displacement gradients. The kinematic constraints between strains and displacements are satisfied at some cleverly chosen internal points inside elements. [ABSTRACT FROM AUTHOR]