Formulation and implementation of the eigenstrain method employing higher order elements

The: analysis of three-dimensional crack problems using the eigenstrain method yields a set of hyper-singular integral equations. A key step in the numerical solution of these equations lies in the accurate evaluation of the hyper-singular terms which exist only in the finite part sense. Based on recent studies by the authors (Dai et al., 1993, J. Mech. Phys. Solids 41, 1003) which employ an analytical treatment of those integrals, a numerical method employing higher order non-confoting elements within the eigenstrain technique is presented here. The object is to enhance computational accuracy and efficiency. The numerical procedure is discussed in some detail, with the emphasis on evaluation of I:he associated singular integrals. The performance of the method is assessed by reevaluating some well-known crack problems and comparing the results with theory where appropriate, as well as presenting some new data