Bending It Like Beckham: How to Visually Fool the Goalkeeper

Background: As bending free-kicks becomes the norm in modern day soccer, implications for goalkeepers have largely been ignored. Although it has been reported that poor sensitivity to visual acceleration makes it harder for expert goalkeepers to perceptually judge where the curved free-kicks will cross the goal line, it is unknown how this affects the goalkeeper's actual movements.

Methodology/Principal Findings: Here, an in-depth analysis of goalkeepers' hand movements in immersive, interactive virtual reality shows that they do not fully account for spin-induced lateral ball acceleration. Hand movements were found to be biased in the direction of initial ball heading, and for curved free-kicks this resulted in biases in a direction opposite to those necessary to save the free-kick. These movement errors result in less time to cover a now greater distance to stop the ball entering the goal. These and other details of the interceptive behaviour are explained using a simple mathematical model which shows how the goalkeeper controls his movements online with respect to the ball's current heading direction. Furthermore our results and model suggest how visual landmarks, such as the goalposts in this instance, may constrain the extent of the movement biases.

Conclusions: While it has previously been shown that humans can internalize the effects of gravitational acceleration, these results show that it is much more difficult for goalkeepers to account for spin-induced visual acceleration, which varies from situation to situation. The limited sensitivity of the human visual system for detecting acceleration, suggests that curved free-kicks are an important goal-scoring opportunity in the game of soccer.

Investigation of organic xenobiotic transfers, partitioning and processing in air-soil-plant systems using a microcosm apparatus. Part II:comparing the fate of chlorobenzenes in grass planted soil

A microcosm system was used to investigate and compare transfers of 14C labeled-1,2-dichlorobenzene (DCB), 1,2,4-trichlorobenzene (TCB) and hexachlorobenzene (HCB) in an air-soil-plant system using single grass tillers planted into spiked soil. This study was the second phase of a development investigation for eventual study of a range of xenobiotic pollutants. Recoveries from the system were excellent at >90%. The predominant loss pathway for 14C labeled-1,2-DCB and 1,2,4-TCB was volatilisation with 85% and 76% volatilisation of parent compound and volatile metabolites over 5 weeks respectively. Most of the added label in the hexachlorobenzene spiked system remained in soil. Mineralisation was

Numerical analysis of intralaminar failure mechanisms in composite structures, Part I: FE implementation

This paper presents a three-dimensional continuum damage mechanics-based material model which was implemented in an implicit finite element code to simulate the progressive intralaminar degradation of fibre reinforced laminates. The damage model is based on ply failure mechanisms and uses seven damage variables assigned to tensile, compressive and shear damage at a ply level. Non-linear behaviour and irreversibility were taken into account and modelled. Some issues on the numerical implementation of the damage model are discussed and solutions proposed. Applications of the methodology are presented in Part II

Numerical analysis of intralaminar failure mechanisms in composite structures, Part II: Applications

A three-dimensional continuum damage mechanics-based material model was implemented in an implicit Finite Element code to simulate the progressive intralaminar degradation of fibre reinforced laminates based on ply failure mechanisms. This paper presents some structural applications of the progressive failure model implemented. The focus is on the non-linear response of the shear failure mode and its interaction with other failure modes. Structural applications of the damage model show that the proposed model is able to reproduce failure loads and patterns observed experimentally.

Intralaminar toughness characterisation of unbalanced hybrid plain weave laminates

A numerical and experimental investigation on the mode-I intralaminar toughness of a hybrid plain weave composite laminate manufactured using resin infusion under flexible tooling (RIFT) process is presented in this paper. The pre-cracked geometries consisted of overheight compact tension (OCT), double edge notch (DEN) and centrally cracked four-point-bending (4PBT) test specimens. The position as well as the strain field ahead of the crack tip during the loading stage was determined using a digital speckle photogrammetry system. The limitation on the applicability of the standard data reduction schemes for the determination of intralaminar toughness of composite materials is presented and discussed. A methodology based on the numerical evaluation of the strain energy release rate using the J-integral method is proposed to derive new geometric correction functions for the determination of the stress intensity factor for composites. The method accounts for material anisotropy and finite specimen dimension effects regardless of the geometry. The approach has been validated for alternative non-standard specimen geometries. A comparison between different methods currently available for computing the intralaminar fracture toughness in composite laminates is presented and a good agreement between numerical and experimental results using the proposed methodology was obtained. 

A correction to the analytical solution of the mixed-mode bending (MMB) problem

This paper addresses the analytical solution of the mixed-mode bending (MMB) problem. The first published solutions used a load separation in pure mode I and mode II and were applied for a crack length less than the beam half-span, a <= L. In later publications, the same mode separation was used in deriving the analytical solution for crack lengths bigger than the beam half-span, a > L. In this paper it is shown that this mode separation is not valid when a > L and in some cases may lead to very erroneous results. The correct mode separation and the corresponding analytical solutions, when a > L, are presented. Results, of force vs. displacement and force vs. crack length graphs, obtained using the existing formulation and the corrected formulation are compared. A finite element solution, which does not use mode separation, is also presented

Stiffener debonding mechanisms in post-buckled CFRP aerospace panels

This paper describes the fractographic analysis of five CFRP post-buckled skin/stringer panels that were tested to failure in compression. The detailed damage mechanisms for skin/stiffener detachment in an undamaged panel were characterised and related to the stress conditions during post-buckling; in particular the sites of peak twist (at buckling nodes) and peak bending moments (at buckling anti-nodes). The initial event was intralaminar splitting of the +45 degrees plies adjacent to the skin/stiffener interface, induced by high twist at a nodeline. This was followed by mode II delamination, parallel to +/- 45 degrees plies and then lengthwise (0 degrees) shear along the stiffener centreline. The presence of defects or damage was found to influence this failure process, leading to a reduction in strength. This research provides an insight into the processes that control post-buckled performance of stiffened panels and suggests that 2D models and element tests do not capture the true physics of skin/stiffener detachment: a full 3D approach is required.

The Behavior of compressively loaded stiffener runout specimens - Part II: Finite element analysis

The termination of stiffeners in composite aircraft structures give rise to regions of high interlaminar shear and peel stresses as the load in the stiffener is diffused into the skin. This is of particular concern in co-cured composite stiffened structures where there is a relatively low resistance to through-thickness stress components at the skin-stiffener interface. In Part I, experimental results of tested specimens highlighted the influence of local design parameters on their structural response. Indeed some of the observed behavior was unexpected. There is a need to be able to analyse a range of changes in geometry rapidly to allow the analysis to form an integral part of the structural design process.

This work presents the development of a finite element methodology for modelling the failure process of these critical regions. An efficient thick shell element formulation is presented and this element is used in conjuction with the Virtual Crack Closure Technique (VCCT) to predict the crack growth characteristics of the modelled specimens. Three specimens were modelled and the qualitative aspects of crack growth were captured successfully. The shortcomings in the quantitative correlation between the predicted and observed failure loads are discussed. There was evidence to suggest that high through-thickness compressive stresses enhanced the fracture toughness in these critical regions.

The Behavior of compressively loaded stiffener runout specimens - Part I: Experiments

The development of the next generation of civil and military transport aircraft will inevitably see an increased use of advanced carbon fibre composite material in the primary structure if performance targets are to be met. One concern in this development is the vulnerability of co-cured and co-bonded stiffened structures to through-thickness stresses at the skin-stiffener interfaces, particularly in stiffener runout regions. These regions are a consequence of the requirement to terminate stiffeners at cutouts, rib intersections, or other structural features which interrupt the stiffener load path.

This work presents the results of an experimental programme investigating the failure of thick-sectioned stiffener runout specimens loaded in uniaxial compression. For all tests, failure initiated at the edge of the runout and propagated across the skin-stiffener interface. It was found that the failure load of each specimen was greatly influenced by intentional changes in the geometric features of these specimens. High frictional forces at the edge of the runout were also deduced from a fractographic analysis, indicating a predominantly Mode II initial failure mode.

Postbuckling behaviour of a blade-stiffened composite panel loaded in uniaxial compression

The postbuckling behaviour of a panel with blade-stiffeners incorporating tapered flanges was experimentally investigated. A new failure mechanism was identified for this particular type of stiffener. Failure was initiated by mid-plane delamination at the free edge of the postbuckled stiffener web at a node-line. This was consistent with an interlaminar shear stress failure and was calculated from strain gauge measurements using an approximate analysis based on lamination theory and incorporating edge effects. The critical shear stress was found to agree well with the shear strength obtained from a three-point bending test of the web laminate.