Anti-plane problem of hollow nano inclusion composites

The effective anti-plane shear modulus was studied for the composites containing hollow nano inclusion. Based on the theory of Gurtin-Murdoch surface/interface theory and the generalized self-consistent method, the rigorous whole-field solution is obtained for the void-inclusion-matrix-equivalent medium model. The closed-form solution of the effective anti-plane shear modulus of the hollow nano inclusion composites is presented. Many significant solutions can be regarded as special or degenerated cases. The numerical results reveal that the effective anti-plane shear modulus is influenced remarkably when the size of the hollow nano inclusion is on the order of nanometer. With the increase of the size of the hollow nano inclusion, the surface/interface effect abates gradually. For the same volume fraction and outer radius of the hollow nano inclusion, the thinner the wall thickness is, the greater of the surface/interface effect is. The surface/interface effect of the hollow nano composites is much larger than that of the solid nano composites for the same outer radius of the inclusion. The effective anti-plane shear modulus of the hollow nano composites depends strongly on the surface/interface property and the stiffness of the inclusion. A very hard inclusion shields the surface/interface effect.