Mathematical modelling of crack problems in bi-material structures containing imperfect interfaces using the weight function technique

摘要: The main aim of this thesis is to generalise weight function techniques tackle crack problems in bi-material linearly elastic and isotropic solids with imperfect interfaces. Our approach makes extensive use functions which are special solutions homogeneous boundary value that aid the evaluation constants asymptotic expressions describing behaviour physical fields near tips. We newly derived respective various aspects a number problems. first major application new analysis Bloch–Floquet waves; results include derivation low dimensional model including junction conditions fracture criterion form constant expansion second uses assist perturbation analysis. In particular, Betti’s formula applied an interface setting, introduces comparison previously studied perfect cases. derive by employing Wiener-Hopf technique strip containing semi-infinite interface. then present algorithm evaluate coefficients asymptotics wave propagation thin periodic array finite-length cracks situated along between two materials. introduce solve give relationships its solution’s at points tip full original problem. used estimate eigenfrequencies structure. will find via comparisons against finite element simulations gives excellent estimates most cases for frequencies waves propagating through strip; however, small discrepancy found standing eigenfrequencies. address suggesting improvement perform computations demonstrate greatly improved accuracy both ideal move on consider our problem concerns out-of-plane shear infinite domain geometry identity relate prescribed loadings faces. method presented allows tractions be point forces, as well continuous loadings. Having obtained function, we conduct determine how linear defects such elliptic inclusions influence forces tip. Computations performed unperturbed solution depends upon parameter imperfection, location may shield or amplify stresses