An inverse problem in estimating interfacial cracks in bimaterials by boundary element technique

An inverse elasticity problem by utilizing both the regularization method (RM) and the conjugate gradient method (CGM) is presented for estimating the interfacial cracks (including location and shape) of a bimaterial from the measurement of displacements at discrete locations internal to the domain and parallel to the interface. The present algorithm in determining the interfacial cracks is totally different from the conventional one. The comparisons of using the conjugate gradient method and commonly used regularization method are discussed systematically, moreover, the advantages and disadvantages in applying the large matrix (LM) and small matrix (SM) formulations are also examined. To the author's knowledge the present work is the first of its kind. Finally, the effects of the measurement errors on the inverse solutions are discussed. Results show that the present inverse algorithms are not sensitive to measurement errors. The CGM is recommended because it is straightforward, LM formulation is better than SM formulation without the consideration of computer time.