The Research On Stress Fields Around A Spheroidal Nano-Inclusion/Nano-Cavity With Surface/Interface Effects

When the size of solid material approach to nanometers, its mechanical behaviorsdisplay remarkable size-dependent phenomena due to their high surface-to-volume ratios,and the effect of surface or interface stress has been considered as one of major factors tothe mechanical behaviors. Since there is no intrinsic length scale involved in theconstitutive laws of the classical elastic theory, it is unable to predict the size-dependentbehavior of nanosized structures and devices. In the aforementioned studies, however, theeffect of surface/interface stress is not taken into account and plays a significant role onthe size-dependent behavior of nanosized elements or devices. Comparison with atomsimulation indicates surface elasticity is an effective method to research size-dependentmechanical behaviors of defect solid with nanosized cavities or inclusions.Four kinds of methods to solve the cavity or inclusion problems include: theEshelby’s equivalent inclusion method, the integral equation method, the complex variablefunction method and the displacement potentials method. Generally, the displacementpotentials method has Boussinesq-Sadowsky displacement potentials and the Papkovich-Neuber displacement potentials method.In frame of surface elasticity, by applying Papkovich-Neuber displacement potentialfunction method, we obtain stress fields around cavity or inclusion as following cases.(1) A semi-infinite elastic medium with a spheroidal nano-cavity problem applied anuniformly biaxial tension paralleling to the plane boundary at infinity.(2) A semi-infinite elastic medium embedded a spheroidal nano-inclusion subjectedto biaxial tension paralleling to the plane boundary at infinity.(3) An isotropic, hemogenous, infinite elastic circular cylinder medium contains aspheroidal nano-cavity under remote torsion.(4) An isotropic, hemogenous, infinite elastic circular cylinder medium embedded aspheroidal nano-inclusion under remote torsion.The results show that the elastic fields around a cavity or an inclusion depend not only on the bulk properties and the shape of cavity or inclusion, but also on thesurface/interface properties and the size of cavity or inclusion. Especially, thesize-dependent phenamena of the nanosized cavity or inclusion is remarkable innanoscale.