A Partition of Unity Boundary Element Method for Fracture and Fatigue Analysis

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The aim of this proposal is to produce a novel computational modelling algorithm for the analysis of engineering components containing cracks. A number of recent, high profile accidents clearly demonstrate that when fracture failures occur due to cracking, they often do so suddenly, catastrophically and without warning. The process of cracks growing to a critical size under cyclical loading is termed fatigue. The work proposes a new method of simulating both fracture mechanics and fatigue crack growth.Simulations in fracture and fatigue are based around the determination of the stresses and displacements in the material in the vicinity of the crack. There are well established computational methods of finding this type of solution, but in the presence of cracks the traditional approaches based on conventional 'finite element' and 'boundary element' methods can become cumbersome and inefficient. In recent years, a number of variants of these techniques have been proposed to overcome some of these difficulties.The proposed work involves the combination of two such strategies: the 'Dual Boundary Element Method' (DBEM) and the 'Partition of Unity Method' (PUM). The DBEM overcomes the need for a very refined computational model, though there are some drawbacks making the method more difficult to implement. The PUM is expected to allow for further reductions in the required model refinement.The PUM is based on the inclusion in our approximate model of a set of functions derived from the theoretical behaviour of the materials locally at the crack tip. This has been successfully used with the finite element method for fracture mechanics. However, our own group in Durham has achieved great success with the PUM in a boundary element algorithm for wave propagation simulation. Here we have found up to 8 orders of magnitude reduction in errors over conventional boundary elements and allows for a considerable reduction in the size of the problem.Since the PUM seems well suited to a boundary element implementation, and boundary elements are well known for their suitability for crack problems, we anticipate this project to have a good probability of success, and could have a significant impact on fracture and fatigue simulations in mechanical and aerospace engineering.