A Dugdale-Barenblatt model for a strip with a semi-infinite crack embedded in decagonal quasicrystals

The present study is to determine the solution of a strip with a semi-infinite crack embedded in decagonal quasicrystals,which transforms a physically and mathematically daunting problem.Then cohesive forces are incorporated into a plastic strip in the elastic body for nonlinear deformation.By superposing the two linear elastic fields,one is evaluated with internal loadings and the other with cohesive forces,the problem is treated in Dugdale-Barenblatt manner.A simple but yet rigorous version of the complex analysis theory is employed here,which involves a conformal mapping technique.The analytical approach leads to the establishment of a few equations,which allows the exact calculation of the size of cohesive force zone and the most important physical quantity in crack theory：stress intensity factor.The analytical results of the present study may be used as the basis of fracture theory of decagonal quasicrystals.