A. Ian Murdoch

Bio: A. Ian Murdoch is an academic researcher from University of Cincinnati. The author has contributed to research in topics: Surface stress & Field (physics). The author has an hindex of 3, co-authored 4 publications receiving 1188 citations.

Symmetry considerations for materials of second grade

Abstract: The symmetry group associated with a material point of second grade is characterized, thereby eludicating the interplay between first-and second-order strain measures in determining its response to deformation.

On spatially-averaged electrokinetics of point charges and Maxwell's equations

Abstract: Maxwell-like field relations which describe spatially-averaged kinematic behaviour of electrons and atomic nuclei (modelled as point charges) are obtained at any prescribed scale using weighting function methodology. Upon appeal to the experimental laws of Coulomb and Biot-Savart, and to dimensional considerations, these relations yield the macroscopic Maxwell equations as they pertain to electrostatics and magnetostatics. Generalisation to classical macroscopic electrodynamics is effected by taking account of signal transmission delay and selection of appropriate retardation potentials. Unlike previous derivations, no appeal is made to the microscopic field relations of Lorentz.

Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films

Abstract: Atoms at a free surface experience a different local environment than do atoms in the bulk of a material. As a result, the energy associated with these atoms will, in general, be different from that of the atoms in the bulk. The excess energy associated with surface atoms is called surface free energy. In traditional continuum mechanics, such surface free energy is typically neglected because it is associated with only a few layers of atoms near the surface and the ratio of the volume occupied by the surface atoms and the total volume of material of interest is extremely small. However, for nano-size particles, wires and films, the surface to volume ratio becomes significant, and so does the effect of surface free energy. In this paper, a framework is developed to incorporate the surface free energy into the continuum theory of mechanics. Based on this approach, it is demonstrated that the overall elastic behavior of structural elements (such as particles, wires, films) is size-dependent. Although such size-dependency is negligible for conventional structural elements, it becomes significant when at least one of the dimensions of the element shrinks to nanometers. Numerical examples are given in the paper to illustrate quantitatively the effects of surface free energy on the elastic properties of nano-size particles, wires and films.

Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities

Abstract: The effect of surface energies, strains, and stresses on the size-dependent elastic state of embedded inhomogeneities are investigated. At nanolength scales, due to the increasing surface-to-volume ratio, surface effects become important and induce a size dependency in the otherwise size-independent classical elasticity solutions. In this letter, closed-form expressions are derived for the elastic state of eigenstrained spherical inhomogeneities with surface effects using a variational formulation. Our results indicate that surface elasticity can significantly alter the fundamental nature of stress state at nanometer length scales. Additional applications of our work on nanostructures such as quantum dots, composites, etc. are implied.

Size-Dependent Eshelby’s Tensor for Embedded Nano-Inclusions Incorporating Surface/Interface Energies

Abstract: The classical formulation of Eshelby (Proc. Royal Society, A241, p. 376, 1957) for embedded inclusions is revisited and modified by incorporating the previously excluded surface/interface Stresses, tension and energies. The latter effects come into prominence at inclusion sizes in the nanometer range. Unlike the classical result, our modified formulation renders the elastic state of an embedded inclusion size-dependent making possible the extension of Eshelby's original formalism to nano-inclusions. We present closed-form expressions of the modified Eshelby's tensor for spherical and cylindrical inclusions. Eshelby original conjecture that only inclusions of the ellipsoid family admit uniform elastic state under uniform stress-free transformation strains must be modified in the context of coupled surface/interface-bulk elasticity. We reach an interesting conclusion in that only inclusions with a constant curvature admit a uniform elastic stale, thus restrict-ing this remarkable property only to spherical and cylindrical inclusions. As an immediate consequence of the derivation of modified size-dependent Eshelby tensor for nano-inclusions, we also formulate the overall size-dependent bulk modulus of a composite containing such inclusions. Further applications are illustrated for size-dependent stress concentrations on voids and opto-electronic properties of embedded quantum dots.

Elastic surface—substrate interactions

Abstract: A theory for three–dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described. The Gurtin–Murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance. This modification yields a model that can be used to describe equilibrium deformations in the presence of compressive–surface stress fields. An associated variational theory is given and material symmetry considerations are discussed. The theory is illustrated by examples.