An iterative BEM for the dynamic analysis of interface crack contact problems

A boundary integral equation method in the frequency domain for cracks under transient loading

“…where x ∈ , ω k = 2π k/T , j = 1, 2 and contact area would be unknown beforehand and must be determined as a part of the solution, see, for example, [39,42,43], where the nonlinear effects due to the crack closure were analysed for cracks under time-harmonic loading in homogeneous and heterogeneous elastic materials. Considering this crack face interaction effect for the case of transient impact loading will be the next natural stage of the research.…”

“…In the present study, the external transient dynamic load is approximated by the Fourier exponential series, that provided an opportunity to use the methodology and results obtained by the authors previously in the frequency domain [39,41,42]. The approximations of the triangular stress pulse…”

“…1 and 2 for different numbers of the Fourier coefficients used. Then, following the references [39,41,42], all components of the solution should be expanded into the Fourier series:…”

“…To solve the problem of a crack located on the bimaterial interface under time harmonic loading, the BIEM was used. An iterative algorithm which makes it possible to take the crack closure into account was developed in [39]. The algorithm was used to solve the problem of an interface crack with allowance for crack face contact interaction under time harmonic normal tension-compression load.…”

“…The contact interaction between opposite crack faces has a very complex nature, and a great majority of researchers neglected the crack closure effects due to the difficulties with the problem solution. The crack closure effect for interfacial cracks subjected to dynamic loading was considered in [38][39][40][41]. To solve the problem of a crack located on the bimaterial interface under time harmonic loading, the BIEM was used.…”