On effective properties of materials at the nano- and microscales considering surface effects

Abstract

In the last years, the rapid increase in the technical capability to control and design materials at the nanoscale has pushed toward an intensive exploitation of new possibilities concerning optical, chemical, thermoelectrical and electronic applications. As a result, new materials have been developed to obtain specific physical properties and performances. In this general picture, it was natural that the attention toward mechanical characterization of the new structures was left, in a sense, behind. Anyway, once the theoretically designed objects proceed toward concrete manufacturing and applications, an accurate and general description of their mechanical properties becomes more and more scientifically relevant. The aim of the paper is therefore to discuss new methods and techniques for modeling the behavior of nanostructured materials considering surface/interface properties, which are responsible for the main differences between nano-and macroscale, and to determine their actual material properties at the macroscale. Our approach is intended to study the mechanical properties of materials taking into account surface properties including possible complex inner microstructure of surface coatings. We use the Gurtin-Murdoch model of surface elasticity. We consider the inner regular and irregular surface thin coatings (i.e., ordered or disordered nanofibers arrays) and present few examples of averaged 2D properties of them. Since the actual 2D properties depend not only on the mechanical properties of fibers or other elements of a coating, but also on the interaction forces between them, the analysis also includes information on the geometry of the microstructure of the coating, on mechanical properties of elements and on interaction forces. Further we use the obtained 2D properties to derive the effective properties of solids and structures at the macroscale, such as the bending stiffness or Young's modulus.

Lattice with vacancies: elastic fields and effective properties in frameworks of discrete and continuum models

“…This expression is substituted into equilibrium Equations (8). The resulting equations are solved with respect to u n,m using DFT.…”

“…Although the continuum mechanics modelling is expected to be appropriate for the effective properties [4], it may become inadequate at microscale, in particular, near vacancies, where the discreteness plays important role [5,6]. For example, Krivtsov and Morozov [7] have shown that the effect of discreteness is significant even in the absence of surface tension [8]. Examination of these issues is the main motivation for the present work.…”

Mathematical study of boundary-value problems within the framework of Steigmann–Ogden model of surface elasticity

“…A more complex form of (4) is discussed in [13]. For infinitesimal deformations of an isotropic material, the surface strain energy density is given by the formulas [39,40] …”

Torsional vibration of single-walled carbon nanotubes using doublet mechanics

“…Dell'Isola et al [4] reported on the status of modeling and analyses of materials exhibiting a rich and varied macroscopic response conferred by complex microstructures. Eremeyev discussed new methods and techniques for modeling the behavior of nanostructured materials considering surface properties to determine their actual material properties at the macroscale using the Gurtin-Murdoch model of surface elasticity [37]. Dell'Isola et al [38] considered a discrete spring model for extensible beams and proposed a heuristic homogenization technique to formulate a continuum fully nonlinear beam model.…”