A complex finite element method to compute accurate weight functions

Analytically extending the finite element method to the complex domain provides a means to determine accurately the weight function of a crack in a two­dimensional object of any specific shape. When the imaginary part of a two­ dimensional finite element model's nodal coordinates represents a small opening­ mode increase of a modeled crack's length, the opening­mode weight function for that crack may be determined directly from the solution's complex displacements and complex strain energy calculation. The accuracy of this novel method is limited only by the fidelity of the finite element mesh used to model the object.