Thermoelectrical effects in fractured media are encountered in many situations of practical interest; and the numerical treatment of this physical phenomenon has run into difficulties due to the temperature and voltage discontinuity.
In this presentation, a general computational procedure, which is based on the eXtended finite element method (XFEM), is proposed to efficiently deal with transient and nonlinear problems, and to estimate field distributions in cracked medium.
The finite element approximation is enriched in order to take into account the crack discontinuities due to the jump and the asymptotic near-tip function, using the partition of unity method. And the discretization results in a nonlinear system that is solved using the Newton-Raphson algorithm.
Different numerical examples show the high accuracy and the robustness of the proposed computational procedure in efficiently capturing the temperature and voltage jumps across the crack.