Elastic Field Around A Nanosized Hole Embedded In An Elastic Half-space Under A Surface Loading

With the advancement of technology and productivity, the materials and nanocomposite with higher requirements are coming into us under the progress of society. At the nanoscale, because of the striking increase of the material’s surface-to-volume, surface atoms and interatomic are formed into huge potential energy difference. The remarkable surface efficiency can make nanomaterials’ mechanical properties differences from some of the macro-materials’ properties. In order to study the surface effect on the mechanical behavior of nanomaterials, Gurtin and Murdoch developed the surface mechanical elasticity which is based on the continuum mechanics. However, the defects such as cracks, holes or inclusions are usually produced in the process of the preparation of nanocomposites. In the frame of the surface elasticity theory, the elastic fields around the cavity within the elastic half plane are studied. The main studies and creative points are as follows:(1) Utilizing the complex function method, the effects of the cavity shape on the stress concentration around the cavity within elastic half-plane under uniform normal loading are discussed. Taking the conformal mapping and analytic continuation, the potential functions are expressed as the Fourier series with undetermined coefficients. By analyzing the special holes such as circles, ellipsoid, regular triangles and squares, the results show that the hoop stress decreases with the increase of the size of the hole. And the hoop stress concentration appears at the point of the biggest curvature.(2) Using the displacement potential function, the elastic fields surrounding the ellipsoidal hole within elastic half-space applied the axisymmetric loading are studied. Numerical results indicate that the elastic fields surrounding the hole strongly depend on surface residual tension and the size of the holes. In addition, the stresses caused by surface residual tension are different from those in the classical elasticity. The changes of stress and displacement induced by surface efficiency are remarkable, especially those at the two poles of the ellipsoid.