A rigid line inclusion in an elastic film with surface elasticity

Abstract

The paper makes an elastic analysis of an elastic film containing a rigid line inclusion. Surface effects are taken into account, since the film is extraordinarily thin. The inclusion is assumed to penetrate the film along the film’s thickness. When remote loading is applied, the associated problem of an infinite isotropic homogeneous film with a rigid inclusion is solved by superposition. For elastic fields disturbed by the inclusion, the Fourier integral transform is applied to derive the problem to a singular integral equation with Cauchy kernel of the first kind. Full elastic field in the whole plane is obtained for uniform tension and shear loadings. Furthermore, exact analytic expressions for the elastic field induced by a semi-infinite rigid line inclusion are directly determined. Stress singularity coefficients are evaluated and displayed graphically. Results show that stress singularity coefficients depend on all material properties including bulk and surface properties. When neglecting surface stress and surface elasticity, the obtained stress singularity coefficients reduce to the well-known classical counterparts.