A Combined Boundary Integral Method for Crack Problems in Multilayered Elastic Media under the Plane Strain Condition

Doctor of Philosophy, Graduate Program in Mechanical Engineering
University of California, Riverside, December 2013
Professor Guanshui Xu, Chairperson

The   crack   problems   in   multilayered   elastic   media   are   of considerable   interest   in   many  engineering   applications,   particularly   in   hydraulic   fracturing   treatments   for   increasing hydrocarbon  production.  Various  computational  methods  have  been  developed  for  the  analysis of  crack  problems,  and  boundary  integral  methods  stand  out  for  their  broad  applicability  and accuracy.  Among  various  boundary  integral  methods  the  standard  boundary  integral  method, such as the direct method, can be used for general elastic analysis of multilayered media, while the  displacement  discontinuity  method  based  on  fundamental  dislocation  solution  is  more suitable  for  the  analysis  of  crack  problems.  The  displacement  discontinuity  method,  however, cannot be applied directly to the general crack problems in multilayered media due to the lack of fundamental dislocation  solutions.  In  this  dissertation  study,  we  therefore  address  this  issue  by developing a new approach that combines the displacement discontinuity method and the direct method.  The  combined  method  shares  both  the  efficiency  of  the  displacement  discontinuity method  and  the  applicability  of  the  direct  method.  In  this  combined  method,  the  displacement discontinuity method is implemented to construct the fracture matrix in each    layer, while the direct method is used to characterize the effects of the interfaces. As a consequence, all variables on  the  interfaces  can  be  eliminated  through  continuity  conditions,  leading  to  the  final  equation which only consists of variables on crack surfaces. The concept of the crack tip element is also adopted and extended for better treatment of the crack tip singularity. The example studies have demonstrated  that  the  combined  method  has  comparable  accuracy  but  far  more  efficiency  for practical applications as compared to the traditional direct method.