A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Multiscale numerical modelling of crack propagation in two-dimensional metal plate

A novel multiscale model of brittle crack propagation in an Ag plate with macroscopic dimensions has been developed. The model represents crack propagation as stochastic drift-diffusion motion of the crack tip atom through the material, and couples the dynamics across three different length scales. It integrates the nanomechanics of bond rupture at the crack tip with the displacement and stress field equations of continuum based fracture theories. The finite element method is employed to obtain the continuum based displacement and stress fields over the macroscopic plate, and these are then used to drive the crack tip forward at the atomic level using the molecular dynamics simulation method based on many-body interatomic potentials. The linkage from the nanoscopic scale back to the macroscopic scale is established via the Ito stochastic calculus, the stochastic differential equation of which advances the tip to a new position on the macroscopic scale using the crack velocity and diffusion constant obtained on the nanoscale. Well known crack characteristics, such as the roughening transitions of the crack surfaces, crack velocity oscillations, as well as the macroscopic crack trajectories, are obtained.

A multi-scale numerical modelling of crack propagation in a 2D metallic plate

A new multi-scale model of brittle fracture growth in an Ag plate with macroscopic dimensions is proposed in which the crack propagation is identified with the stochastic drift-diffusion motion of the crack-tip atom through the material. The model couples molecular dynamics simulations, based on many-body interatomic potentials, with the continuum-based theories of fracture mechanics. The Ito stochastic differential equation is used to advance the tip position on a macroscopic scale before each nano-scale simulation is performed. Well-known crack characteristics, such as the roughening transitions of the crack surfaces, as well as the macroscopic crack trajectories are obtained.

The Jama legal narrative part I: The JAMA Model and narrative interpretation patterns

For the purposes of starting to tackle, within artificial intelligence (AI), the narrative aspects of legal narratives in a criminal evidence perspective, traditional AI models of narrative understanding can arguably supplement extant models of legal narratives from the scholarly literature of law, jury studies, or the semiotics of law. Not only: the literary (or cinematic) models prominent in a given culture impinge, with their poetic conventions, on the way members of the culture make sense of the world. This shows glaringly in the sample narrative from the Continent-the Jama murder, the inquiry, and the public outcry-we analyse in this paper. Apparently in the same racist crime category as the case of Stephen Lawrence's murder (in Greenwich on 22 April 1993) with the ensuing still current controversy in the UK, the Jama case (some 20 years ago) stood apart because of a very unusual element: the eyewitnesses identifying the suspects were a group of football referees and linesmen eating together at a restaurant, and seeing the sleeping man as he was set ablaze in a public park nearby. Professional background as witnesses-cum-factfinders in a mass sport, and public perceptions of their required characteristics, couldn't but feature prominently in the public perception of the case, even more so as the suspects were released by the magistrate conducting the inquiry. There are sides to this case that involve different expected effects in an inquisitorial criminal procedure system from the Continent, where an investigating magistrate leads the inquiry and prepares the prosecution case, as opposed to trial by jury under the Anglo-American adversarial system. In the JAMA prototype, we tried to approach the given case from the coign of vantage of narrative models from AI.

Finite element modelling of crack detection tests

Four non-destructive tests for determining the length of fatigue cracks within the solder joints of a 2512 surface mount resistor are investigated. The sensitivity of the tests is obtained using finite element analysis with some experimental validation. Three of the tests are mechanically based and one is thermally based. The mechanical tests all operate by applying different loads to the PCB and monitoring the strain response at the top of the resistor. The thermal test operates by applying a heat source underneath the PCB, and monitoring the temperature response at the top of the resistor. From the modelling work done, two of these tests have shown to be sensitive to cracks. Some experimental results are presented but further work is required to fully validate the simulation results.

Representing and recognizing scenario patterns

This paper presents a formal method for representing and recognizing scenario patterns with rich internal temporal aspects. A scenario is presented as a collection of time-independent fluents, together with the corresponding temporal knowledge that can be relative and/or with absolute values. A graphical representation for temporal scenarios is introduced which supports consistence checking as for the temporal constraints. In terms of such a graphical representation, graph-matching algorithms/methodologies can be directly adopted for recognizing scenario patterns.

Matching case history patterns in case-based reasoning

This paper introduces a mechanism for representing and recognizing case history patterns with rich internal temporal aspects. A case history is characterized as a collection of elemental cases as in conventional case-based reasoning systems, together with the corresponding temporal constraints that can be relative and/or with absolute values. A graphical representation for case histories is proposed as a directed, partially weighted and labeled simple graph. In terms of such a graphical representation, an eigen-decomposition graph matching algorithm is proposed for recognizing case history patterns.

Assessing the performance of crack detection tests for solder joints

This paper presents both modelling and experimental test data to characterise the performance of four non-destructive tests. The focus is on determining the presence and rough magnitude of thermal fatigue cracks within the solder joints for a surface mount resistor on a strip of FR4 PCB. The tests all operate by applying mechanical loads to the PCB and monitoring the strain response at the top of the resistor. The modelling results show that of the four tests investigated, three are sensitive to the presence of a crack in the joint and its magnitude. Hence these tests show promise in being able to detect cracking caused by accelerated testing. The experimental data supports these results although more validation is required.

Computer simulation of crack propagation in power electronics module solder joints

A numerical modelling method for the analysis of solder joint damage and crack propagation has been described in this paper. The method is based on the disturbed state concept. Under cyclic thermal-mechanical loading conditions, the level of damage that occurs in solder joints is assumed to be a simple monotonic scalar function of the accumulated equivalent plastic strain. The increase of damage leads to crack initiation and propagation. By tracking the evolution of the damage level in solder joints, crack propagation path and rate can be simulated using Finite Element Analysis method. The discussions are focused on issues in the implementation of the method. The technique of speeding up the simulation and the mesh dependency issues are analysed. As an example of the application of this method, crack propagation in solder joints of power electronics modules under cyclic thermal-mechanical loading conditions has been analyzed and the predicted cracked area size after 3000 loading cycles is consistent with experimental results.

Muscle activation patterns in shoulder impingement patients

Introduction: Shoulder impingement is one of the most common presentations of shoulder joint problems 1. It appears to be caused by a reduction in the sub-acromial space as the humerus abducts between 60o -120o – the 'painful arc'. Structures between the humeral head and the acromion are thus pinched causing pain and further pathology 2. Shoulder muscle activity can influence this joint space but it is unclear whether this is a cause or effect in impingement patients. This study aimed to observe muscle activation patterns in normal and impingement shoulder patients and determine if there were any significant differences. Method: 19 adult subjects were asked to perform shoulder abduction in their symptomatic arm and non-symptomatic. 10 of these subjects (age 47.9 ± 11.2) were screened for shoulder impingement, and 9 subjects (age 38.9 ± 14.3) had no history of shoulder pathology. Surface EMG was used to collect data for 6 shoulder muscles (Upper, middle and lower trapezius, serratus anterior, infraspinatus, middle deltoids) which was then filtered and fully rectified. Subjects performed 3 smooth unilateral abduction movements at a cadence of 16 beats of a metronome set at 60bpm, and the mean of their results was recorded. T-tests were used to indicate any statistical significance in the data sets. Significance was set at P<0.05. Results: There was a significant difference in muscle activation with serratus anterior in particular showing a very low level of activation throughout the range when compared to normal shoulder activation patterns (<30%). Middle deltoid recruitment was significantly reduced between 60-90o in the impingement group (30:58%).Trends were noted in other muscles with upper trapezius and infraspinatus activating more rapidly and erratically (63:25%; 60:27% respectively), and lower trapezius with less recruitment (13:30%) in the patient group, although these did not quite reach significance. Conclusion: There appears to be some interesting alterations in muscle recruitment patterns in impingement shoulder patients when compared against their own unaffected shoulders and the control group. In particular changes in scapula control (serratus anterior and trapezius) and lateral rotation (infraspinatus), which have direct influence on the sub-acromial space, should be noted. It is still not clear whether these alterations are causative or reactionary, but this finding gives a clear indication to the importance of addressing muscle reeducation as part of a rehabilitation programme in shoulder impingement patients.

Singular stresses at the tip of a crack terminating at frictional interface of fibre reinforced composites

The stress singularities at the tip of a crack that terminates at a frictional interface between two layers in anisotropic composites are investigated. The order of stress singularities is determined by solving the characteristic equations obtained from the boundary conditions and the frictional interface conditions for the cases concerned. The interface is assumed to be governed by Coulomb's law of friction. Numerical results are presented for the cases with a crack terminating at a frictional interface of a fibre reinforced composite, and it is shown that there is a big difference of stress singularities between cases with and without considering friction along the interface.