Steady-State Cracks in Viscoelastic Lattice Models II

We present the analytic solution of the Mode III steady-state crack in a square lattice with piecewise linear springs and Kelvin viscosity. We show how the results simplify in the limit of large width. We relate our results to a model where the continuum limit is taken only along the crack direction. We present results for small velocity, and for large viscosity, and discuss the structure of the critical bifurcation for small velocity. We compute the size of the process zone wherein standard continuum elasticity theory breaks down.Comment: 17 pages, 3 figure

Does the continuum theory of dynamic fracture work?

We investigate the validity of the Linear Elastic Fracture Mechanics approach to dynamic fracture. We first test the predictions in a lattice simulation, using a formula of Eshelby for the time-dependent Stress Intensity Factor. Excellent agreement with the theory is found. We then use the same method to analyze the experiment of Sharon and Fineberg. The data here is not consistent with the theoretical expectation.Comment: 4 page

Cognitive deficits in problematic internet use : meta-analysis of 40 studies

© The Royal College of Psychiatrists 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.BACKGROUND: Excessive use of the internet is increasingly recognised as a global public health concern. Individual studies have reported cognitive impairment in problematic internet use (PIU), but have suffered from various methodological limitations. Confirmation of cognitive deficits in PIU would support the neurobiological plausibility of this disorder.AimsTo conduct a rigorous meta-analysis of cognitive performance in PIU from case-control studies; and to assess the impact of study quality, the main type of online behaviour (for example gaming) and other parameters on the findings.METHOD: A systematic literature review was conducted of peer-reviewed case-controlled studies comparing cognition in people with PIU (broadly defined) with that of healthy controls. Findings were extracted and subjected to a meta-analysis where at least four publications existed for a given cognitive domain of interest.RESULTS: The meta-analysis comprised 2922 participants across 40 studies. Compared with controls, PIU was associated with significant impairment in inhibitory control (Stroop task Hedge's g = 0.53 (s.e. = 0.19-0.87), stop-signal task g = 0.42 (s.e. = 0.17-0.66), go/no-go task g = 0.51 (s.e. = 0.26-0.75)), decision-making (g = 0.49 (s.e. = 0.28-0.70)) and working memory (g = 0.40 (s.e. = 0.20-0.82)). Whether or not gaming was the predominant type of online behaviour did not significantly moderate the observed cognitive effects; nor did age, gender, geographical area of reporting or the presence of comorbidities.CONCLUSIONS: PIU is associated with decrements across a range of neuropsychological domains, irrespective of geographical location, supporting its cross-cultural and biological validity. These findings also suggest a common neurobiological vulnerability across PIU behaviours, including gaming, rather than a dissimilar neurocognitive profile for internet gaming disorder.Declaration of interestS.R.C. consults for Cambridge Cognition and Shire. K.I.'s research activities were supported by Health Education East of England Higher Training Special interest sessions. A.E.G.'s research has been funded by Innovational grant (VIDI-scheme) from ZonMW: (91713354). N.A.F. has received research support from Lundbeck, Glaxo-SmithKline, European College of Neuropsychopharmacology (ECNP), Servier, Cephalon, Astra Zeneca, Medical Research Council (UK), National Institute for Health Research, Wellcome Foundation, University of Hertfordshire, EU (FP7) and Shire. N.A.F. has received honoraria for lectures at scientific meetings from Abbott, Otsuka, Lundbeck, Servier, Astra Zeneca, Jazz pharmaceuticals, Bristol Myers Squibb, UK College of Mental Health Pharmacists and British Association for Psychopharmacology (BAP). N.A.F. has received financial support to attend scientific meetings from RANZCP, Shire, Janssen, Lundbeck, Servier, Novartis, Bristol Myers Squibb, Cephalon, International College of Obsessive-Compulsive Spectrum Disorders, International Society for Behavioral Addiction, CINP, IFMAD, ECNP, BAP, the World Health Organization and the Royal College of Psychiatrists. N.A.F. has received financial royalties for publications from Oxford University Press and payment for editorial duties from Taylor and Francis. J.E.G. reports grants from the National Center for Responsible Gaming, Forest Pharmaceuticals, Takeda, Brainsway, and Roche and others from Oxford Press, Norton, McGraw-Hill and American Psychiatric Publishing outside of the submitted work.Peer reviewe

Nonlinear lattice model of viscoelastic Mode III fracture

We study the effect of general nonlinear force laws in viscoelastic lattice models of fracture, focusing on the existence and stability of steady-state Mode III cracks. We show that the hysteretic behavior at small driving is very sensitive to the smoothness of the force law. At large driving, we find a Hopf bifurcation to a straight crack whose velocity is periodic in time. The frequency of the unstable bifurcating mode depends on the smoothness of the potential, but is very close to an exact period-doubling instability. Slightly above the onset of the instability, the system settles into a exactly period-doubled state, presumably connected to the aforementioned bifurcation structure. We explicitly solve for this new state and map out its velocity-driving relation

Crack Front Waves and the dynamics of a rapidly moving crack

Crack front waves are localized waves that propagate along the leading edge of a crack. They are generated by the interaction of a crack with a localized material inhomogeneity. We show that front waves are nonlinear entities that transport energy, generate surface structure and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to crack instabilities, yields both inhomogeneity and scaling behavior within fracture surface structure.Comment: Embedded Latex file including 4 figure

Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture

We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments.Comment: submitted to PRE, Rapid Communication

The Breakdown of Linear Elastic Fracture Mechanics near the Tip of a Rapid Crack

We present high resolution measurements of the displacement and strain fields near the tip of a dynamic (Mode I) crack. The experiments are performed on polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of typical brittle amorphous materials. Over a wide range of propagation velocities ($0.2-0.8c_s$), we compare linear elastic fracture mechanics (LEFM) to the measured near-tip fields. We find that, sufficiently near the tip, the measured stress intensity factor appears to be non-unique, the crack tip significantly deviates from its predicted parabolic form, and the strains ahead of the tip are more singular than the $r^{-1/2}$ divergence predicted by LEFM. These results show how LEFM breaks down as the crack tip is approached.Comment: 4 pages, 4 figures, first of a two-paper series (experiments); no change in content, minor textual revision

Quasi-Static Brittle Fracture in Inhomogeneous Media and Iterated Conformal Maps: Modes I, II and III

The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require solution of the bi-Laplace rather than the Laplace equation. For all cases we can consider quenched randomness in the brittle material itself, as well as randomness in the succession of fracture events. While mode III calls for the advance (in time) of one analytic function, mode I and II call for the advance of two analytic functions. This fundamental difference creates different stress distribution around the cracks. As a result the geometric characteristics of the cracks differ, putting mode III in a different class compared to modes I and II.Comment: submitted to PRE For a version with qualitatively better figures see: http://www.weizmann.ac.il/chemphys/ander

Steady-State Cracks in Viscoelastic Lattice Models

We study the steady-state motion of mode III cracks propagating on a lattice exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity $\eta$ allows for a direct comparison between lattice results and continuum treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques, we explore this comparison as a function of the driving displacement $\Delta$ and the number of transverse sites $N$. At any $N$, the continuum theory misses the lattice-trapping phenomenon; this is well-known, but the introduction of $\eta$ introduces some new twists. More importantly, for large $N$ even at large $\Delta$, the standard two-dimensional elastodynamics approach completely misses the $\eta$-dependent velocity selection, as this selection disappears completely in the leading order naive continuum limit of the lattice problem.Comment: 27 pages, 8 figure

Phase-Field Model of Mode III Dynamic Fracture

We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between ``broken'' and ``unbroken'' states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.Comment: submitted to PR