Multiple Circular Nano-inhomogeneities And/or Nano-pores In One Of Two Joined Isotropic Elastic Half-planes

摘要

The paper considers the problem of multiple interacting circular nano-inhomogeneities or/and nano-pores located in one of two joined, dissimilar isotropic elastic half-planes. The analysis is based on the solutions of the elastostatic problems for (ⅰ) the bulk material of two bonded, dissimilar elastic half-planes and (ⅱ) the bulk material of a circular disc. These solutions are coupled with the Gurtin and Murdoch model of material surfaces [Curtin ME, Murdoch AI. A continuum theory of elastic material surfaces. Arch Ration Mech Anal 1975:57:291-323; Gurtin ME, Murdoch AI. Surface stress in solids. Int J Solids Struct 1978:14:431 -40.]. Each elastostatic problem is solved with the use of complex Somigliana traction identity [Mogilevskaya SG, Linkov AM. Complex fundamental solutions and complex variables boundary element method in elasticity. Comput Mech 1998:22:88-92]. The complex boundary displacements and tractions at each circular boundary are approximated by a truncated complex Fourier series, and the unknown Fourier coefficients are found from a system of linear algebraic equations obtained by using a Taylor series expansion. The resulting semi-analytical method allows one to calculate the elastic fields everywhere in the half-planes and inside the nano-inhomogeneities. Numerical examples demonstrate that (ⅰ) the method is effective in solving the problems with multiple nano-inhomogeneities, and (ⅱ) the elastic response of a composite system is profoundly influenced by the sizes of the nano-featurcs.