Elastic Theory of Nanomaterials Based on Surface-Energy Density

Abstract

Recent investigations into surface-energy density of nanomaterials lead to a ripe chance to propose, within the framework of continuum mechanics, a new theory for nanomaterials based on surface-energy density. In contrast to the previous theories, the linearly elastic constitutive relationship that is usually adopted to describe the surface layer of nanomaterials is not invoked and the surface elastic constants are no longer needed in the new theory. Instead, a surface-induced traction to characterize the surface effect in nanomaterials is derived, which depends only on the Eulerian surface-energy density. By considering sample-size effects, residual surface strain, and external loading, an explicit expression for the Lagrangian surface-energy density is achieved and the relationship between the Eulerian surface-energy density and the Lagrangian surface-energy density yields a conclusion that only two material constants-the bulk surface-energy density and the surface-relaxation parameter-are needed in the new elastic theory. The new theory is further used to characterize the elastic properties of several fcc metallic nanofilms under biaxial tension, and the theoretical results agree very well with existing numerical results. Due to the nonlinear surface effect, nanomaterials may exhibit a nonlinearly elastic property though the inside of nanomaterials or the corresponding bulk one is linearly elastic. Moreover, it is found that externally applied loading should be responsible for the softening of the elastic modulus of a nanofilm. In contrast to the surface elastic constants required by existing theories, the bulk surface-energy density and the surface-relaxation parameter are much easy to obtain, which makes the new theory more convenient for practical applications.

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

“…Such a new theory has been adopted to predict successfully the mechanical behavior of nanofilms subjected to a bi-axial tension, size effect of the surface energy density of nanoparticles and the static bending behavior of nanowires. [43][44][45] All the theoretical predictions agree well with the experimental and numerical results. [3][4][5]7,[46][47][48][49] In the present paper, the resonant vibration of both fixed-fixed nanowires and cantilevered ones is investigated with the new developed elastic theory for nanomaterials and theoretical predictions are further compared with the existing numerical results.…”

“…The Lagrangian surface energy density / 0 in the reference configuration can be divided into a structural part / stru 0 related to the surface strain energy and a chemical part / chem 0 originating from the surface dangling-bond energy, 43,52,53 …”

“…43 Consider a nano-solid with an idealized crystal structure in an initial (or reference) configuration. A Lagrangian coordinate system is imbedded in the crystal surface and attached to surface atoms, 50 with principal axes 1 and 2 parallel to the two basic vectors of the surface unit cell as shown in Figure 1.…”

“…Recently, an elastic theory for nanomaterials was developed, 43 in which only the surface energy density of a bulk solid and the surface relaxation parameter in nanoscale are needed to characterize the surface effect in nanomaterials without introducing surface elastic constants. Such a new theory has been adopted to predict successfully the mechanical behavior of nanofilms subjected to a bi-axial tension, size effect of the surface energy density of nanoparticles and the static bending behavior of nanowires.…”

Interface effect of nanoscaled adhesive interlayer on force transfer in biological microjoint

“…13 An alternative interface energy density-based elastic theory can formulate the misfit at interface to avoid introduction of interface elastic constants. 14,15 Considering the geometry of microjoint, shear lag theory combined with Gurtin-Murdoch model can be used to quantify how the coherent interface effect of nanoscaled adhesive interlayer influences the force transfer in microjoint. This letter aims to elucidate the planar force transfer mechanism of the nanoscale interlayers in microjoint.…”