RUI: A New Method to Obtain Highly Accurate Three Dimensional Analysis of Crack Propagation and Stress on Composite Materials

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Oh The investigator develops numerical methods for solving three-dimensional crack propagation problems. In order to obtain any practical solutions for crack propagation, the Finite Element Method (FEM) requires use of either graded discretizations (very small elements near the crack front, larger elements elsewhere) or special singular basis functions. The graded discretizations make the computation very expensive, while singular basis functions destroy the nice band structure of the FEM. Thus, the standard FEM is impractical for accurate numerical simulation of 3-D crack propagation. The accuracy of the FE solution depends on the regularity of the true solution. The investigator studies a new method, called Method of Auxiliary Mapping (MAM), to deal with three-dimensional singularities: vertex, edge, and edge-vertex. To remove the ineffectiveness of the FEM in the presence of singularities, MAM transforms a region where the stress functions are singular to a region where the transformed stress functions are of higher regularity. The investigator also studies three auxiliary mappings for these purposes. The annual cost of fracture-related damage in the United States (human injury and loss of life aside) has been estimated at more than $10 billion. Metal fatigue has been cited as the probable cause of several recent airline accidents, and the airworthiness of aging fleets is a national concern. Material failures are a major concern for other large engineering structures (ships, bridges, nuclear power plants, hydroelectric dams, and so on). Thus, for effective inspection and preventive maintenance programs, an accurate fracture analysis is demanded. However, because of the complicated geometry and nonlinearities that characterize fracture mechanics, the use of analytical techniques is very limited and in most cases not practical. Numerical methods seem to be the only feasible approach for such analysis. On the basis of very successful results o f the stress analysis for plane elasticity problems, the investigator studies a new method that should yield highly accurate numerical simulation of three-dimensional fracture analysis.