Transverse Shear Effect Within The Surface Layer Of Solid

The surface of the object has different properties from the interior.The larger the ratio of the surface area and volume of the object is,the more significant the surface effect is.At the macro scale,the surface effect can be ignored,but at the micro scale,the surface effect becomes significant.Many micro nano structures and soft materials need to consider the surface effect.The study of surface effect originated from the study of liquid surface tension,and then expanded to the field of solid.So far,many solid surface constitutive models were born,but the transverse shear effect was not considered while solid can bear the transverse shear but liquid not.In this paper,several classical solid surface constitutive models and a new solid surface constitutive model with transverse shear effect proposed by Huang are introduced.The variational principle considering transverse shear effect of solid surface is emphatically established,and the transverse shear model and Gurtin-Murdoch model are applied to the rotating ellipsoid respectively.Then we compare residual deformation and elastic response under hydrostatic pressure of the rotating ellipsoid under the two models.It is concluded that the transverse shear effect will greatly affect the residual deformation and hydrostatic response,which provides a sufficient theoretical basis for the experimental verification of the transverse shear effect on the solid surface.In addition,the transverse shear effect will cause greater Mises stress.If the transverse shear effect is large,the damage failure criterion of micro nano scale materials should be modified.In addition,this paper also compares the hydrostatic elastic response of the rotating ellipsoid under the transverse shear model and the Steigmann-Ogden model.Both of them consider the characteristics of the solid different from the liquid.Under the same load,the deformation of the surface layer described by the latter is smaller than the former.Finally,the influence of the surface roughness of the ellipsoid on the calculation results is analyzed.The results show that the influence of the surface roughness on the calculation results can be greatly reduced by reducing the change of the surface roughness.