Journal Article10.1007/BF00261375
A continuum theory of elastic material surfaces
2.9K
TL;DR: 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.
read more
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
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Some fundamental aspects of surface modelling
TL;DR: In this article, the authors focus on four aspects of surface modelling: delineation of the (scale-dependent) geometrical boundary of a body via molecular considerations, identification of the highly inhomogeneous interfacial region between a body and its exterior, and its modelling as a bidimensional continuum involving interfacial excess quantities.
80
Effects of surface tension and electrochemical reactions in Li-ion battery electrode nanoparticles
TL;DR: In this paper, the size and shape-dependency of the chemo-mechanical behavior of spherical and ellipsoidal nanoparticles in Li-ion battery electrodes are investigated by a stress-assisted diffusion model and 3D finite element simulations.
80
A continuum theory of surface piezoelectricity for nanodielectrics
TL;DR: In this article, a phenomenological continuum theory of surface piezoelectricity accounting for the linear superficial interplay between electricity and elasticity is formulated primarily for elastic dielectric materials.
79
A Surface Cauchy-Born model for silicon nanostructures
Harold S. Park,P. A. Klein +1 more
TL;DR: In this article, a surface Cauchy-Born approach is proposed to model non-centrosymmetric, semiconducting nanostructures such as silicon that exist in a diamond cubic lattice structure.
79
Size dependent dynamic analysis of nanoplates
TL;DR: In this article, size-dependent transverse vibration of nanoplates is investigated and surface properties which include surface elasticity and residual stresses are taken into account Elasticity modulus of the bulk part is considered dependent on size as well as temperature Kirchhoff theory of laminated plates is used to derive the governing differential equation of nanoplate structure
78
References
•Book
Physical chemistry of surfaces
Arthur W. Adamson
- 01 Jan 1960
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.
12.2K
The Non-Linear Field Theories of Mechanics
Clifford Ambrose Truesdell,Walter Noll +1 more
- 01 Jan 1965
3.3K
The Linear Theory of Elasticity
Morton E. Gurtin
- 01 Jan 1973
TL;DR: Linear elasticity is one of the more successful theories of mathematical physics and its pragmatic success in describing the small deformations of many materials is uncontested The origins of the three-dimensional theory go back to the beginning of the 19th century and the derivation of the basic equations by Cauchy, Navier, and Poisson The theoretical development of the subject continued at a brisk pace until the early 20th century with the work of Beltrami, Betti, Boussinesq, Kelvin, Kirchhoff, Lame, Saint-Venant, Somigl
1K
The Surface Tension of Solids
R Shuttleworth
- 01 May 1950
TL;DR: In this paper, a distinction is made between the surface Helmholtz free energy F, and the surface tension γ, which is the tangential stress (force per unit length) in the surface layer; this stress must be balanced either by external forces or by volume stresses in the body.
1K