In the framework of continuum thermodynamics, the present paper presents the thermo-hyperelastic models for both the surface and the bulk of nanostructured materials, in which the residual stresses are taken into account. Due to the existence of residual stresses, different configuration descriptions of the surface (or the bulk) thermo-hyperelastic constitutive equations are not the same even in the cases of infinitesimal deformation. As an example, the effective thermal expansion coefficient of spherical nanoparticles is analyzed.
This paper aims at investigating the size-dependent self-buckling and bending behaviors of nano plates through incorporating surface elasticity into the elasticity with residual stress fields.In the absence of external loading,positive surface tension induces a compressive residual stress field in the bulk of the nano plate and there may be self-equilibrium states corresponding to the plate self-buckling.The self-instability of nano plates is investigated and the critical self-instability size of simply supported rectangular nano plates is determined.In addition,the residual stress field in the bulk of the nano plate is usually neglected in the existing literatures,where the elastic response of the bulk is often described by the classical Hooke's law.The present paper considered the effect of the residual stress in the bulk induced by surface tension and adopted the elasticity with residual stress fields to study the bending behaviors of nano plates without buckling.The present results show that the surface effects only modify the coefficients in corresponding equations of the classical Kirchhoff plate theory.
