APPENDIX: List of Printed Papers by G. B. Airy, and List of Books written by G. B. Airy

Airy, George Biddell; Airy, W

doi:10.1017/cbo9780511707131.013

Cited by 43 publications

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“…We describe the stress state of the system by its Airy stress function 35,37 Φ. The stress function must satisfy the biharmonic equation ∇ 4 Φ = 0, and the stresses are then given as suitable derivatives of Φ.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

1997

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We present a systematic study of the effect of crack blunting on subsequent crack propagation and dislocation emission. We show that the stress intensity factor required to propagate the crack is increased as the crack is blunted by up to thirteen atomic layers, but only by a relatively modest amount for a crack with a sharp 60 • corner. The effect of the blunting is far less than would be expected from a smoothly blunted crack; the sharp corners preserve the stress concentration, reducing the effect of the blunting. However, for some material parameters blunting changes the preferred deformation mode from brittle cleavage to dislocation emission. In such materials, the absorption of preexisting dislocations by the crack tip can cause the crack tip to be locally arrested, causing a significant increase in the microscopic toughness of the crack tip. Continuum plasticity models have shown that even a moderate increase in the microscopic toughness can lead to an increase in the macroscopic fracture toughness of the material by several orders of magnitude. We thus propose an atomic-scale mechanism at the crack tip, that ultimately may lead to a high fracture toughness in some materials where a sharp crack would seem to be able to propagate in a brittle manner.When the crack is loaded in mode II, the load required to emit a dislocation is affected to a much higher degree by the blunting, in agreement with the estimates from continuum elasticity. In mode II the emission process is aided by a reduction of the free surface area during the emission process. This leads to emission at crack loadings which are lower than predicted from the continuum analysis of Rice.

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Section: Acknowledgmentsmentioning

confidence: 99%

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

1997

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“…More recently, that is to say, in the late 19th century, it was remarked by Airy [6] that the catenary is also the steady shape of a string being drawn at constant speed, the passage from equilibrium to steady motion only resulting in offsetting uniformly the string's ten- * This paper is dedicated to the memory of Piero Villaggio, who died on the 4th of January 2014, aged 81. † e-mail: eg.virga@unipv.it 1 A similar phenomenon had indeed been documented earlier by J.…”

Section: Introductionmentioning

confidence: 99%

Dissipative shocks in a chain fountain

Virga

2014

Phys. Rev. E

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The fascinating and anomalous behaviour of a chain that instead of falling straight down under gravity, first rises and then falls, acquiring a steady shape in space that resembles a fountain's spray, has recently attracted both popular and academic interest. The paper presents a complete mathematical solution of this problem, whose distinctive feature is the introduction of a number of dissipative shocks which can be resolved exactly.

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“…Significant further developments had to wait until the second half of the twentieth century, when the investigation of solitary water waves of large amplitude was initiated. The linear theory of water waves of small amplitude fails to yield any reasonable approximation to solitary waves [39] and for this reason even the earliest models for solitary waves had to incorporate nonlinear effects 1 . The simplest effective nonlinear approximation to the governing equations for water waves in the shallow water limit is the Korteweg-de Vries (KdV) equation [33]: for small-amplitude long waves there always exists a region in space-time where a balance between nonlinearity and dispersion generates as a leading order approximation to the governing equations for water waves the KdV equation (see the discussion in [12]).…”

Section: Introductionmentioning

confidence: 99%

On the particle paths in solitary water waves

Constantin

2009

Quart. Appl. Math.

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Dedicated to Walter Strauss on his 70th birthday with esteem and friendship.Abstract. We provide the qualitative flow pattern beneath a solitary water wave by describing the individual particle trajectories.Preamble. Hydrodynamics is a research field where Walter Strauss is recognized throughout the world for some groundbreaking contributions. It is also an area of Strauss's work I have had the privilege and pleasure to participate in. The present paper is devoted to one of the most striking manifestations of water waves: solitary waves. Adapting to the context of solitary waves some considerations made for periodic traveling waves in a recent joint work with Strauss [19], we will provide the qualitative flow pattern beneath a solitary water wave by describing the individual particle trajectories, offering a different and simpler approach to the recent results in [11].1. Introduction. Solitary water waves are localized nonlinear waves that propagate steadily. They were first noticed by Scott Russell in 1834, as described in a now famous report on his observations of a large heap of water traveling with undiminished speed or shape over a distance along a Scottish canal [38]:

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APPENDIX: List of Printed Papers by G. B. Airy, and List of Books written by G. B. Airy

Cited by 43 publications

References 0 publications

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

Dissipative shocks in a chain fountain

On the particle paths in solitary water waves

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