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

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

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

Dynamic fields at the tip of sub-Rayleigh and supershear frictional rupture fronts

The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracture-mechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction.Comment: 20 pages including 11 figure

Transcranial Direct Current Stimulation in Obsessive Compulsive Symptoms: A Personalised Approach

Peer reviewe

Investigating the Acceptability and Tolerability of tDCS in Patients with OCD - A Feasibility Study

© 2021 University of Hertfordshire.Introduction: Obsessive Compulsive Disorder (OCD) is a neuropsychiatric disorder which often proves refractory to current treatment approaches1. Transcranial Direct Current Stimulation (tDCS), a non-invasive form of neurostimulation, with potential for development as a self-administered intervention, has shown potential as a safe and efficacious treatment for OCD in a small number of trials2. The two most promising stimulation sites are located above the orbitofrontal cortex (OFC) and the supplementary motor area (SMA). The aim of this feasibility study was to inform the development of a definitive trial, focussing on the acceptability, safety of the intervention, feasibility of recruitment, adherence and tolerability to tDCS and study assessments and the size of the treatment-effect. Due to COVID-19 this study was paused in March 2020 and restarted in July 2020, consequently facing the challenges of recruiting and continuing face-to-face research during the pandemic. This abstract presents acceptability and safety of the intervention as well as the feasibility of recruitment, adherence and tolerability of tDCS in patients with OCD. Method: Potential participants were identified from OCD clinics, primary health care services (e.g. IAPTs), charity/support networks, advertisements and trust databases across two sites (Hertfordshire Partnership and Southampton). Individuals were screened, then randomised if eligible, receiving three courses of tDCS (SMA, OFC and sham), randomly allocated and given in counterbalanced order. Each course comprised four sessions of 20-minute stimulations, delivered over two consecutive days, separated by at least a four-week washout period. Participants were evaluated at baseline, 1, 2 and 4 hours after stimulation. Follow-up assessments were conducted via telephone at 24 hours, 7 and 14 days following the last stimulation of each round with a final assessment 28 days after the third round. Intervention-related adverse events (AEs) were also recorded at each time point, using a questionnaire specific to tDCS3. Results: A total of 135 individuals were identified as potentially eligible (through clinics or self-referral), of which 36 consented to eligibility screening. Four withdrew consent/were lost to follow up, so screening was completed for 32. Subsequently, 16 were excluded through ineligibility (n=9), withdrawal (n=2) or loss to follow up (n=1), with the remaining 20 randomised. One participant withdrew prior to intervention round one and another prior to round two, both due to COVID-19 anxiety. All other participants (n=18, 90% of those randomised) completed all three intervention rounds. However, one individual was unable to attend day two of round two due to unconnected ill-health. Across all tDCS types, the most commonly reported AEs were sleepiness (18.7% of sessions), trouble concentrating (13.0%) and headache (12.2%), with other AE types present at <7% of sessions. Itching (0.8%) and scalp pain (1.0%) were reported least often. Discussion: Despite the impact of COVID-19, this study successfully restarted after suspension with few adjustments, meeting the revised target sample with minimal participant drop-out. Reasons for drop-out were unrelated to the intervention itself, with some participants delayed or experiencing pandemic-related anxiety. This study presents a safe intervention which was accepted, adhered to and tolerated by OCD patients, even amid a pandemic.Peer reviewe

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