Journal ArticleDOI
A continuum theory of elastic material surfaces
TLDR
In this paper, a mathematical framework is developed to study the mechanical behavior of material surfaces, and the tensorial nature of surface stress is established using the force and moment balance laws using a linear theory with non-vanishing residual stress.Abstract:
A mathematical framework is developed to study the mechanical behavior of material surfaces. The tensorial nature of surface stress is established using the force and moment balance laws. Bodies whose boundaries are material surfaces are discussed and the relation between surface and body stress examined. Elastic surfaces are defined and a linear theory with non-vanishing residual stress derived. The free-surface problem is posed within the linear theory and uniqueness of solution demonstrated. Predictions of the linear theory are noted and compared with the corresponding classical results. A note on frame-indifference and symmetry for material surfaces is appended.read more
Citations
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Journal ArticleDOI
Size-dependent elastic properties of nanosized structural elements
Ronald E. Miller,Vijay B. Shenoy +1 more
TL;DR: In this article, a simple model is constructed to predict the size dependence of the effective stiffness of the structural element, and the important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulation of the bulk.
Journal ArticleDOI
Surface stress in solids.
Morton E. Gurtin,A. Ian Murdoch +1 more
TL;DR: In a recent paper as mentioned in this paper, a general theory of surface stress was presented and several simple solutions within this theory were discussed, e.g., a simple solution to the problem of surface compression.
Journal ArticleDOI
A general theory of curved deformable interfaces in solids at equilibrium
TL;DR: In this paper, the deformation of a curved interface between solid phases was studied under the assumption of small strains in the bulk phases and neglecting accretion at the interfaces, and the authors showed that the free energy of the interface can depend on the normal and tangential components of the jump in displacement at the interface (stretch and slip), and the average of the projected strain in the tangent plane (average tangential strain).
Journal ArticleDOI
Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy
TL;DR: In this paper, the effect of reduced size on the elastic properties measured on silver and lead nanowires and on polypyrrole nanotubes with an outer diameter ranging between 30 and 250 nm is discussed.
Journal ArticleDOI
Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films
TL;DR: In this paper, a framework is developed to incorporate the surface free energy into the continuum theory of mechanics, and it is demonstrated that the overall elastic behavior of structural elements (such as particles, wires, films) is size-dependent.
References
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Book
Physical chemistry of surfaces
TL;DR: In this paper, the authors discuss the nature and properties of liquid interfaces, including the formation of a new phase, nucleation and crystal growth, and the contact angle of surfaces of solids.
Book
The non-linear field theories of mechanics
TL;DR: A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys as mentioned in this paper, which is not the case in modern physics, since it concerns solely the small particles of matter.
Book
Finite-Dimensional Vector Spaces
TL;DR: The first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces, was the Finite Dimensional Vector Spaces (FDVSP) by Halmos as discussed by the authors.
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Size-dependent elastic properties of nanosized structural elements
Ronald E. Miller,Vijay B. Shenoy +1 more