In the framework of hyperelasticity, we treat the configuration of a terminated crack at the interface of an incompressible full plane composite. Considering the traction-free boundary conditions, three particular cases are discussed when a cylinder is subjected to an anti-plane shear transformation. Taking all these conditions into account, an asymptotic analysis is performed to identify the sufficient orders contributing to the singular form of the Cauchy stress static fields. Adding to that, an inquiry about the presence of logarithmic singularities was achieved using the approach of Dempsey and Sinclair.
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