Recent advances in the alternating method for elastic and inelastic fracture analyses Original Research Article

The numerical-analytical alternating method (wherein finite elements or boundary elements are used for numerical analysis of an uncracked structure) is a very efficient and accurate method for fracture analysis. It saves both time in the computational analysis and human effort in preparing analysis models. In this paper we summarize the recent developments in this method, including: (1) the alternating method and its convergence for mixed boundary value problems, with the presence of both traction and displacement boundary conditions; (2) a non-iterative method to construct solutions for multiple arbitrarily located embedded cracks using the solution for a single embedded crack in an infinite body; (3) the analysis of elastic-plastic fracture mechanics problems; (4) the analysis of crack-growth in plane fracture situations; and (5) an efficient and accurate algorithm for the evaluation of elastoplastic stress state in a cracked structure, based on the generalized mid-point radial return for 3D constitutive laws and the stress subspace method for the plane stress analysis, and a study of link-up of multiple cracks in a wide-spread fatigue damage situation in an aircraft panel. Some numerical examples are also given.