I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Earthquake response of steel braces and braced steel frames

This thesis consists of three parts. Chapter 2 deals with the dynamic buckling behavior of steel braces under cyclic axial end displacement. Braces under such a loading condition belong to a class of "acceleration magnifying" structural components, in which a small motion at the loading points can cause large internal acceleration and inertia. This member-level inertia is frequently ignored in current studies of braces and braced structures. This chapter shows that, under certain conditions, the inclusion of the member-level inertia can lead to brace behavior fundamentally different from that predicted by the quasi-static method. This result is to have significance in the correct use of the quasi-static, pseudo-dynamic and static condensation methods in the simulation of braces or braced structures under dynamic loading. The strain magnitude and distribution in the braces are also studied in this chapter.

Chapter 3 examines the effect of column uplift on the earthquake response of braced steel frames and explores the feasibility of flexible column-base anchoring. It is found that fully anchored braced-bay columns can induce extremely large internal forces in the braced-bay members and their connections, thus increasing the risk of failures observed in recent earthquakes. Flexible braced-bay column anchoring can significantly reduce the braced bay member force, but at the same time also introduces large story drift and column uplift. The pounding of an uplifting column with its support can result in very high compressive axial force.

Chapter 4 conducts a comparative study on the effectiveness of a proposed non-buckling bracing system and several conventional bracing systems. The non-buckling bracing system eliminates buckling and thus can be composed of small individual braces distributed widely in a structure to reduce bracing force concentration and increase redundancy. The elimination of buckling results in a significantly more effective bracing system compared with the conventional bracing systems. Among the conventional bracing systems, bracing configurations and end conditions for the bracing members affect the effectiveness.

The studies in Chapter 3 and Chapter 4 also indicate that code-designed conventionally braced steel frames can experience unacceptably severe response under the strong ground motions recorded during the recent Northridge and Kobe earthquakes.

Force chains, friction, and flow: Behavior of granular media across length scales

We study the behavior of granular materials at three length scales. At the smallest length scale, the grain-scale, we study inter-particle forces and "force chains". Inter-particle forces are the natural building blocks of constitutive laws for granular materials. Force chains are a key signature of the heterogeneity of granular systems. Despite their fundamental importance for calibrating grain-scale numerical models and elucidating constitutive laws, inter-particle forces have not been fully quantified in natural granular materials. We present a numerical force inference technique for determining inter-particle forces from experimental data and apply the technique to two-dimensional and three-dimensional systems under quasi-static and dynamic load. These experiments validate the technique and provide insight into the quasi-static and dynamic behavior of granular materials.

At a larger length scale, the mesoscale, we study the emergent frictional behavior of a collection of grains. Properties of granular materials at this intermediate scale are crucial inputs for macro-scale continuum models. We derive friction laws for granular materials at the mesoscale by applying averaging techniques to grain-scale quantities. These laws portray the nature of steady-state frictional strength as a competition between steady-state dilation and grain-scale dissipation rates. The laws also directly link the rate of dilation to the non-steady-state frictional strength.

At the macro-scale, we investigate continuum modeling techniques capable of simulating the distinct solid-like, liquid-like, and gas-like behaviors exhibited by granular materials in a single computational domain. We propose a Smoothed Particle Hydrodynamics (SPH) approach for granular materials with a viscoplastic constitutive law. The constitutive law uses a rate-dependent and dilation-dependent friction law. We provide a theoretical basis for a dilation-dependent friction law using similar analysis to that performed at the mesoscale. We provide several qualitative and quantitative validations of the technique and discuss ongoing work aiming to couple the granular flow with gas and fluid flows.

Deconvolution and elastography based on dimensional ultrasound

This paper is in two parts and addresses two of getting more information out of the RF signal from three-dimensional (3D) mechanically-swept medical ultrasound . The first topic is the use of non-blind deconvolution improve the clarity of the data, particularly in the direction to the individual B-scans. The second topic is imaging. We present a robust and efficient approach to estimation and display of axial strain information. deconvolution, we calculate an estimate of the point-spread at each depth in the image using Field II. This is used as of an Expectation Maximisation (EM) framework in which ultrasound scatterer field is modelled as the product of (a) a smooth function and (b) a fine-grain varying function. the E step, a Wiener filter is used to estimate the scatterer based on an assumed piecewise smooth component. In the M , wavelet de-noising is used to estimate the piecewise smooth from the scatterer field. strain imaging, we use a quasi-static approach with efficient based algorithms. Our contributions lie in robust and 3D displacement tracking, point-wise quality-weighted , and a stable display that shows not only strain but an indication of the quality of the data at each point in the . This enables clinicians to see where the strain estimate is and where it is mostly noise. deconvolution, we present in-vivo images and simulations quantitative performance measures. With the blurred 3D taken as OdB, we get an improvement in signal to noise ratio 4.6dB with a Wiener filter alone, 4.36dB with the ForWaRD and S.18dB with our EM algorithm. For strain imaging show images based on 2D and 3D data and describe how full D analysis can be performed in about 20 seconds on a typical . We will also present initial results of our clinical study to explore the applications of our system in our local hospital. © 2008 IEEE.

Impact of carbon fibre/epoxy corrugated cores

The dynamic compressive response of corrugated carbon-fibre reinforced epoxy sandwich cores has been investigated using a Kolsky-bar set-up. Compression at quasi-static rates up to v 0=200ms -1 have been tested on three different slenderness ratios of strut. High speed photography was used to capture the failure mechanisms and relate these to the measured axial compressive stress. Experiments show significant strength enhancement as the loading rate increases. Although material rate sensitivity accounts for some of this, it has been shown that the majority of the strength enhancement is due to inertial stabilisation of the core members. Inertial strength enhancement rises non-linearly with impact velocity. The largest gains are associated with a shift to buckle modes composed of 2-3 half sine waves. The loading rates tested within this study are similar to those that are expected when a sandwich core is compressed due to a blast event. © 2012 Elsevier Ltd.

Mechanical response of carbon fiber composite sandwich panels with pyramidal truss cores

The combination of light carbon fiber reinforced polymer (CFRP) composite materials with structurally efficient sandwich panel designs offers novel opportunities for ultralight structures. Here, pyramidal truss sandwich cores with relative densities ρ̄ in the range 1-10% have been manufactured from carbon fiber reinforced polymer laminates by employing a snap-fitting method. The measured quasi-static shear strength varied between 0.8 and 7.5 MPa. Two failure modes were observed: (i) Euler buckling of the struts and (ii) delamination failure of the laminates. Micro-buckling failure of the struts was not observed in the experiments reported here while Euler buckling and delamination failures occurred for the low (ρ̄≤1%) and high (ρ̄>1%) relative density cores, respectively. Analytical models for the collapse of the composite cores by these failure modes are presented. Good agreement between the measurements and predictions based on the Euler buckling and delamination failure of the struts is observed while the micro-buckling analysis over-predicts the measurements. The CFRP pyramidal cores investigated here have a similar mechanical performance to CFRP honeycombs. Thus, for a range of multi-functional applications that require an "open-celled" architecture (e.g. so that cooling fluid can pass through a sandwich core), the CFRP pyramidal cores offer an attractive alternative to honeycombs. © 2012 Elsevier Ltd. All rights reserved.

The low velocity impact response of sandwich beams with a corrugated core or a Y-frame core

The low speed impact responses of simply-supported and clamped sandwich beams with corrugated and Y-frame cores have been measured in a drop-weight apparatus at 5 m s-1. The AISI 304 stainless steel sandwich beams comprised two identical face sheets and represented 1:20 scale versions of ship hull designs. No significant rate effects were observed at impact speeds representative of ship collisions: the drop-weight responses were comparable to the ones measured quasi-statically. Moreover, the corrugated and Y-frame core beams had similar performances. Three-dimensional finite element (FE) models simulated the experiments and were in good agreement with the measurements. The simulations demonstrated correctly that the sandwich beams collapsed by core indentation under both quasi-static loading and in the drop-weight experiments. These FE models were then used to investigate the sensitivity of impact response to (i) velocity, over a wider range of velocities than achievable with the drop-weight apparatus, and (ii) the presence of the back face sheet. The dynamic responses of sandwich beams with both front and back face sheets were found to be within 20% of the quasi-static responses for speeds less than approximately 5 m s-1. This suggests that quasi-static considerations are adequate to model the collision of a sandwich ship hull. By contrast, beams without a back face collapsed by Brazier buckling under quasi-static loading conditions, and by core indentation at a loading velocity of 5 m s-1. Thus, dynamic considerations are needed in ship hull designs that do not employ a back face. © 2014 Elsevier Ltd. All rights reserved.

THE VARIATION AND MOVEMENT OF A KIND OF EDDIES IN SHELF SLOPE WATER

Considering the characteristics of the time and space scales of the eddies we established a quasi-static and quasi-geostrophic model to describe their variation and movement in shelf slope water. The analytical solution revealed the main properties of the variation: slow expansion and fast stagnation processes and the law of the eddy motion affected under the background field. All theoretical results are proved by satellite image measurements.

A study of secondary instabilities in postbuckling composite aerostructures

A number of experimental studies have shown that postbuckling stiffened composite panels, loaded in uniaxial compression, may undergo secondary instabilities, characterised by an abrupt change in the buckled mode-shape of the skin between the supporting stiffeners. In this study high-speed digital speckle photogrammetry is used to gain further insight into an I-stiffened panel's response during this transient phase. This energy-dissipating phenomenon will be shown to be able to cause catastrophic structural failure in vulnerable structures. It is therefore imperative that an accurate and reliable methodology is available to predict this phenomenon. The shortcomings of current non-linear implicit solution schemes, found in most commercially-available finite element codes, are discussed. A robust and efficient strategy, which utilises an automated quasi-, static/pseudo-transient hybrid scheme, is presented in this paper and validated using a number of experimental tests. This approach is shown to be able to predict mode-jumping with good accuracy.

An automated hybrid procedure for capturing mode-jumping in postbuckling composite stiffened structures

This paper presents a robust finite element procedure for modelling the behaviour of postbuckling structures undergoing mode-jumping. Current non-linear implicit finite element solution schemes, found in most finite element codes, are discussed and their shortcomings highlighted. A more effective strategy is presented which combines a quasi-static and a pseudo-transient routine for modelling this behaviour. The switching between these two schemes is fully automated and therefore eliminates the need for user intervention during the solution process. The quasi-static response is modelled using the are-length constraint while the pseudo-transient routine uses a modified explicit dynamic routine, which is more computationally efficient than standard implicit and explicit dynamic schemes. The strategies for switching between the quasi-static and pseudo-transient routines are presented

Capturing mode-switching in postbuckling composite panels using a modified explicit procedure

A postbuckling blade-stiffened composite panel was loaded in uniaxial compression, until failure. During loading beyond initial buckling, this panel was observed to undergo a secondary instability characterised by a dynamic mode shape change. These abrupt changes cause considerable numerical difficulties using standard path-following quasi-static solution procedures in finite element analysis. Improved methods such as the arc-length-related procedures do better at traversing certain critical points along an equilibrium path but these procedures may also encounter difficulties in highly non-linear problems. This paper presents a robust, modified explicit dynamic analysis for the modelling of postbuckling structures. This method was shown to predict the mode-switch with good accuracy and is more efficient than standard explicit dynamic analysis. (C) 2003 Elsevier Science Ltd. All rights reserved.

Fluorescence enhancement and energy transfer in apertureless scanning near-field optical microscopy

We investigate the mechanisms for fluorescence enhancement and energy transfer near a gold tip in apertureless scanning near-field optical microscopy. Using a simple quasi-static model, we show that the observed enhancement of fluorescence results from competition between enhancement and quenching, and is dependent on a range of experimental parameters. We find good qualitative agreement with the results of measurements of the effect of both sharp and blunt tips on quantum dot fluorescence, and provide a demonstration of tip-enhanced fluorescence imaging with 60 nm resolution.

Detection of an artificial target with low radar cross-section in presence of backscatter

This paper presents an approach to improve the detection of an artificial target with low radar cross-section in presence of clutter. The target proposed in the paper modulates the phase response of the circularly polarized incident signal by means of rotation. The same physical phenomenon can be used to steer the modulated response in a non-specular direction. The bi-static measurements of the response of the target have demonstrated good agreement with theoretical prediction as well as with full-wave simulation.

A static test method to assess swivel seat strength in frontal impact

Mechanical swivel seat adaptations are a key aftermarket disability modification to any small-to medium-sized passenger vehicle. However, the crashworthiness of these devices is currently unregulated and the existing 20g dynamic sled testing approach is prohibitively expensive for prototype assessment purposes. In this paper, an alternative quasi-static test method for swivel seat assessment is presented, and two different approaches (free-body diagram and multibody modelling) validated through published experimental data are developed to determine the appropriate loading conditions to apply in the quasi-static testing.Results show the two theoretical approaches can give similar results for estimating the quasi-static loading conditions, and this depends on the seatbelt configuration. Application of the approach to quasi-static testing of both conventional seats and those with integrated seat belts showed the approach to be successful and easy to apply. It is proposed that this method be used by swivel seat designers to assess new prototypes prior to final validation via the traditional 20g sled test.

Impact des troubles musculosquelettiques sur les mécanismes du contrôle postural chez les adolescents-hockeyeurs de niveau élite et intervention en Reconstruction Posturale®

Les adolescents-hockeyeurs peuvent être affligés de troubles musculosquelettiques (TMS) résultant d’un excès de tension musculaire lequel peut mener à des déformations ou déséquilibres musculaires ainsi qu’à une attitude posturale inadéquate. Les conséquences de ces changements mènent souvent à une surcharge inutile du système musculosquelettique (SMS), à la perturbation des mécanismes du contrôle postural et éventuellement à l’apparition de douleurs musculaires et articulaires. Les interventions qui s’attaquent aux TMS par une rééquilibration de la tension musculaire sont peu nombreuses. Les interventions qui s’attaquent aux TMS par une normalisation de la tension musculaire sont peu nombreuses. La Reconstruction Posturale® (RP), testée cliniquement, est l’une d’entre elles. Dans un premier temps, cette thèse visait à identifier les caractéristiques du contrôle postural chez les adolescents-hockeyeurs de niveau élite lorsque le système somatosensoriel est mis à l’épreuve en position debout quasi statique pieds nus et en patins. Dans un deuxième temps, nous avons évalué l’impact d’une intervention en RP sur des variables cliniques et biomécaniques, chez ces athlètes qui souffrent de TMS. Soixante-sept adolescents-hockeyeurs de niveau élite âgés de 15 à 18 ans ont participé à l’étude. Le contrôle postural de cinquante-sept joueurs a été évalué en position debout sur deux plateformes de force les yeux ouverts et les yeux fermés, pieds nus sur une surface dure et sur une mousse. De ce groupe, trente-cinq sujets ont également été évalués en patins, les yeux ouverts et les yeux fermés. Par la suite, neuf adolescents-hockeyeurs souffrant de TMS, ont été sélectionnés pour participer au protocole d’intervention thérapeutique en RP qui consistait en l’application de six séances de thérapie prodiguées sur une période de six semaines. Le déplacement du centre de pression (CP) sous les pieds a été calculé dans les directions antéro-postérieure (AP) et médio-latérale (ML). La vélocité moyenne du CP, le déplacement moyen du CP et l’étendue du CP ont été retenus pour rendre compte de la performance du contrôle posturale. D’autre part, l’asymétrie de mise en charge, la trajectoire du CP sous les pieds gauche et droit, le CPc pour rendre compte de la stratégie de chevilles et le CPv pour rendre compte de la stratégie de hanches ont été retenues pour identifier les stratégies utilisées pour maintenir l’équilibre. L’impact de l’intervention en RP a été évalué à l’aide de trois variables cliniques soit la douleur à l’aide de l’échelle visuelle analogue (ÉVA), la capacité fonctionnelle à l’aide d’un un questionnaire autoadministré et des photographies de la posture debout pour rendre compte des variables posturales biomécaniques. Nos résultats montrent que chez les adolescents-hockeyeurs la performance du contrôle postural en position debout statique est davantage perturbée par les changements somatosensoriels en direction ML alors qu’en AP, la perte d’informations visuelles ainsi que des changements somatosensoriels affectent la performance. Dans toutes les conditions expérimentales et dans les deux directions, nous avons observé une vélocité du CP remarquablement élevée, variant entre 18 et 22 mm/s. Au niveau des stratégies et indépendamment de la condition expérimentale, nous avons observé une dominance presque complète de la stratégie de cheville en AP alors qu’en ML, la stratégie de hanche dominait avec une contribution de la stratégie de cheville de plus de 20 %. En patins, en direction ML, aucun changement significatif de la performance n’a été observé. Toutefois en AP, nous avons observé une augmentation significative de la vélocité du CP, yeux ouverts et yeux fermés ainsi qu’une augmentation significative de l’étendue, yeux ouverts seulement. Au niveau des stratégies, la stratégie de cheville domine en AP et la stratégie de hanche domine en ML avec une contribution plus modeste de la stratégie de cheville qui était inférieure à 12 %. Chez les adolescents-hockeyeurs souffrant de TMS, post-intervention, nos résultats indiquent une diminution significative de la douleur et une amélioration des capacités fonctionnelles ainsi que de l’attitude posturale. Pré intervention en direction ML, nous avons observé une contribution significativement plus élevée de la stratégie de cheville au contrôle du CPnet et un retour vers des valeurs normales post-intervention. L’impact de l’intervention thérapeutique sur la performance du contrôle postural s’est avéré non significatif en ML et en AP.