Analysis Of Two-dimensional Multi-field Fracture Problem With Iterative-BEM

In multi-field environment,the opening of the crack in smart materials depends on the applied loading,while the physical fields in the crack cavity will change the boundary conditions on the crack surfaces,which in turn will influence the crack opening,thus it is a typical geometric nonlinear problem.In the thesis,we proposed an iterative-BEM method to solve the typical nonlinear problem.Considering that the crack is long and narrow,we treated the crack as an independent domain and developed the corresponding sub-region BEM.With the aid of the commercial software Mathematica,we also conducted numerical simulation on some typical crack problems.The main contributions of the thesis are as follows:(1)We analyzed the central crack problem in a thermoelastic medium under exact crack boundary condition.Considering the temperature field in the crack cavity,we treated the crack cavity as an independent sub-domain,and constructed the corresponding boundary integral equations for the crack cavity and the outer boundary,respectively.Utilizing the boundary conditions and an iterative process,we obtained the distribution of the temperature in the crack cavity and the stress field as well as temperature field near the crack tip.In addition,we discussed the extended stress intensity factors for the exact and other simplified crack boundary conditions,respectively.(2)We analyzed the central crack problem in a magnetoelectroelastic medium under exact crack boundary condition.Considering the electric and temperature fields,we treated the crack cavity as an independent sub-domain,and constructed the corresponding boundary integral equations for the crack cavity and the outer boundary,respectively.Utilizing the boundary conditions and an iterative process,we obtained the distribution of the electric and temperature fields in the crack cavity and the stress,electric and temperature fields near the crack tip.In addition,we discussed the extended stress intensity factors for the exact and other simplified crack boundary conditions,respectively.(3)Based on the nonlinear constitutive equation of piezoelectric semiconductors,we combined the "Piezoelectric-Conductor" iterative concept with BEM,and established the boundary integral equations for the piezoelectric governing equations with volume charge,and the conductor governing equation with volume electric current,respectively.An iterative procedure was used to analyze the plane problem and hole problem in piezoelectric semiconductors.Besides,the effects of the applied loading on the extended displacement and stress fields,and the phenomenon of extended stress concentration near the hole,are discussed.