Surface and interface stress effects on the interaction of nano-inclusions and nano-cracks in an infinite domain under anti-plane shear

• BEM has been used to study the interaction between nano-inclusions and nano-cracks.
• The displacement boundary integral equation is used to discretize the interfaces.
• The stress boundary integral equation is used to mesh the nano-crack surfaces.

This paper studies the stress fields around nano-inclusions and nano-cracks as well as the interaction between nano-inclusions and nano-cracks, which are embedded in the infinite elastic isotropic domain subjected to the remote anti-plane shear. Since inclusions and cracks are under the nanometer level, the interface/surface effect between the nano-inhomogeneities (nano-inclusions and nano-cracks) and the matrix should be considered. In numerical implementation, the Gurtin–Murdoch model is adopted to simulate the inclusion-matrix interface and the crack surface conditions, respectively. In the case only containing nano-inclusions, the displacement boundary integral equation is needed in which the quadratic isoparametric elements are used to discrete the inclusion-matrix interface. In the case containing nano-inclusions and nano-cracks, the stress boundary integral equation is also needed in which the discontinuous quadratic parametric elements, i.e. the physical shape functions are different from geometrical shape functions, are adopted to mesh the nano-crack surfaces. Some examples are given and compared with the existing solutions.