An augmented Lagrangian element-free (ALEF) approach for crack discontinuities Original Research Article

A new meshless formulation for numerical analysis in fracture mechanics is presented. The formulation is based on the construction of shape functions by a moving least-squares approximation (MLSA). The peculiarity of the present approach lies in the definition of an augmented Lagrangian total potential energy functional. With this technique, called augmented Lagrangian element-free (ALEF), some drawbacks on imposing boundary and interfaces conditions are worked out. A large number of Lagrangian multipliers can be introduced without increasing the number of primary variables and inducing the strict convexity of the total potential energy functional. A new model for simulating fracture discontinuity based on the imposition of interface conditions on the edges of a virtual crack is defined, which permits to avoid some crack simulation difficulties inherent in the element-free Galerkin method. Some numerical examples are reported to evaluate the accuracy of the formulation.