A continuum theory of elastic material surfaces

Gurtin, Morton E.; Murdoch, A. Ian

doi:10.1007/bf00261375

Cited by 2,789 publications

(1,451 citation statements)

References 8 publications

Supporting

Mentioning

1,435

Contrasting

Unclassified

Order By: Relevance

“…These questions have received lots of attention during these last decades since the pioneering mathematical works of Gurtin and Murdoch. [23][24][25] Using, for instance, the Chen et al 26 approach, the surface stress is described as symmetric 2×2 tensor σ S in the tangent plane of the curved surface. This latter is seen as a vanishingly thin membrane which can sustain in-plane stresses but offers no resistance for bending.…”

Section: B Bulk and Surface Propertiesmentioning

confidence: 99%

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

Gailhanou

Roussel

2013

Phys. Rev. B

View full text Add to dashboard Cite

By performing atomistic calculations with a tight-binding potential, we study the displacement field induced by a screw dislocation lying along a free 011 Cu cylindrical nanowire. For this anisotropic orientation that is often encountered experimentally, we show that the displacement field u z along the nanowire can be seen as the superposition of three different fields: the screw dislocation field in an infinite medium, the warping displacement field caused by the so-called Eshelby twist, and an additional image field induced by the free surfaces. A Fourier series analysis of this latter image displacement and stress fields is given. For a circular cross section of the wire, this image field corresponds mainly to an additional warping displacement u z ∝ xy. The dissociation mechanism of the dislocation into partials and the surface stress effects being also captured in our simulations, the present study enables one to quantify the various contributions to the formation of the x-ray diffractograms.

show abstract

Section: B Bulk and Surface Propertiesmentioning

confidence: 99%

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

Gailhanou

Roussel

2013

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…This new material parameter can be measured directly from experiment, determined from experiments via inverse analysis, or derived theoretically from micromechanics [11][12][13][14][15][16]. Nowadays there are many concepts dealing with non-local formulations, like general non-local theories [17,18], strain-gradient theories [2,19], micropolar theories [20,21] or theories of material surfaces [22]. Nevertheless, due to the development of new materials and constant miniaturization of electronic or medical devices, the continued progress in this subject is desirable.…”

Section: Introductionmentioning

confidence: 99%

Fractional calculus for continuum mechanics – anisotropic non-locality

Sumelka¹

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

Abstract. In this paper, a generalisation of previous author's formulation of fractional continuum mechanics for the case of anisotropic non-locality is presented. The discussion includes a review of competitive formulations available in literature. The overall concept is based on the fractional deformation gradient which is non-local due to fractional derivative definition. The main advantage of the proposed formulation is its structure, analogous to the general framework of classical continuum mechanics. In this sense, it allows to define similar physical and geometrical meaning of introduced objects. The theoretical discussion is illustrated by numerical examples assuming anisotropy limited to single direction. NotationSection 2and finallywhere] denotes the interval of non-local interaction, and Γ is the Euler gamma functionNext, based on non-standard definition of motion by Eq. (4) the authors define the deformation gradient F α aswhere e a and E A are base vectors in coordinate systems {x a } and {X A }, respectively.

show abstract

“…The surface elasticity theory of Gurtin and Murdoch (1975) and variants thereof have been applied to study the mechanical response of micro-and nanoscale solids. Integral to the theory is the derivation of a set of governing equations and constitutive relations that describe the behaviour of the surface of the bulk object.…”

Section: Introductionmentioning

confidence: 99%

“…Earlier related contributions include those by Scriven (1960) on the dynamics of fluid interfaces. Scriven employed many of the fundamental concepts formalised by Gurtin and Murdoch (1975), including the use of the term surface elasticity (Scriven and Sternling, 1960). The study of the behaviour of fluid surfaces dates back to the work, primarily on the capillary effect, of Laplace, Young and Gibbs.…”

Section: Introductionmentioning

confidence: 99%

A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology

et al. 2014

View full text Add to dashboard Cite

A curvilinear-coordinate-based finite element methodology is presented as a basis for a straightforward computational implementation of the theory of surface elasticity that mimics the underlying mathematical and geometrical concepts.An efficient formulation is obtained by adopting the same methodology for both the bulk and the surface. The key steps to evaluate the hyperelastic constitutive relations at the level of the quadrature point in a finite element scheme using this unified approach are provided. The methodology is illustrated through selected numerical examples.

show abstract

A continuum theory of elastic material surfaces

Cited by 2,789 publications

References 8 publications

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

Fractional calculus for continuum mechanics – anisotropic non-locality

A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology

Contact Info

Product

Resources

About