Bridging Law Research Articles

John Fletcher Moulton and Guglielmo Marconi: bridging science, Law and industry

Several Fellows of the Royal Society had a role in the achievements of Guglielmo Marconi. Among them was John Fletcher Moulton. An outstanding undergraduate mathematician at Cambridge who maintained a lifelong interest in electricity, Moulton went on to become one of the most formidable lawyers practising in the London courts. His collaboration in the preparation of Marconi's first UK patent in 1897 marked the beginning of an important association with Marconi and the Marconi Wireless Telegraph Company.

Nagel's analysis of reduction: Comments in defense as well as critique

Despite all the criticism showered on Nagel's classic account of reduction, it meets a fundamental desideratum in an analysis of reduction that is difficult to question, namely of providing for a proper identification of the reducing theory. This is not clearly accommodated in radically different accounts. However, the same feature leads me to question Nagel's claim that the reducing theory can be separated from the putative bridge laws, and thus to question his notion of heterogeneous reduction. A further corollary to the requirement that all the necessary conditions be incorporated in an adequate formulation of the putative reducing theory is that the standard example of gas temperature is not reducible to average molecular kinetic energy. As originally conceived, Nagel's conception of reduction takes no account of approximate reasoning and this failure has certainly restricted its applicability, perhaps to the point of making it unrealistic as a model of reduction in science. I suggest approximation can be accommodated by weakening the original requirement of deduction without jeopardizing the fundamental desideratum. Finally, I turn to briefly consider the idea sometimes raised of the ontological reducibility of chemistry.

Residual strength of metal particulate reinforced ceramics with parallel cracks

This work investigates the residual strength of metal particulate reinforced ceramic matrix composites with periodically spaced, parallel cracks. A Fourier transform/integral equation method is used to obtain the stress intensity factor at the tips of the cracks bridged by the plastically stretched metal particulates. The crack bridging of metal particulates is described by a linear softening bridging law that relates the bridging stress and crack opening. The residual strength of the cracked composites is calculated using a stress intensity factor criterion with consideration of crack bridging. Numerical results are presented for three composite systems, i.e., WC/Co, Al 2O 3/Ni, and glass/Al composites to illustrate the effects of interactions between multiple cracks/bridging zones on the residual strength behavior of the reinforced ceramics with parallel cracks. It is found that for given volume fraction of metal particulate and debonding length of the particulate–matrix interface the residual strength increases with decreasing crack spacing. For a given crack spacing, the residual strength initially decreases dramatically with an increase in initial crack length and levels off for long initial cracks.

Determination of tensile crack bridging of PCM-concrete interface subjected to fatigue loading by means of bending test

In this paper, a simple and handy test method for determination of the tensile crack bridging law of PCM-concrete interface is proposed. Based on the fatigue failure mechanism of PCM-concrete interface that is governed by crack propagation as the result of interface bridging degradation, the J-integral method proposed for determining the tension softening relation of concrete under static loading is modified to determine the PCM-concrete interface tensile stress degradation relation. The derived degradation relation is compared to that of normal concrete under cyclic uniaxial tensile tests, and it can be found that the PCM-concrete interface has higher degradation rate so that more attention should be paid to the PCM-concrete interface during the design of PCMretrofitted structures under fatigue loading.

Does Functional Reduction Need Bridge Laws? A Response to Marras

In his recent article ‘Consciousness and Reduction’, Ausonio Marras argues that functional reduction must appeal to bridge laws and thus does not represent a genuine alternative to Nagelian reduction. In response, I first argue that even if functional reduction must use bridge laws, it still represents a genuine alternative to Nagelian reduction. Further, I argue that Marras does not succeed in showing that functional reduction must use bridge laws. 1. Introduction 2. Nagelian Reduction, Functional Reduction, and Bridge Laws 3. Marras on Functional Reduction 4. The Logical Space of ‘Bridge Law’ Views of Reduction 5. [RP] as an Account of Realization 6. Conclusion

Reconsidering the Role of Bridge Laws In Inter-Theoretical Reductions

The present paper surveys the three most prominent accounts in contemporary debates over how sound reduction should be executed. The classical Nagelian model of reduction derives the laws of the target-theory from the laws of the base theory plus some auxiliary premises (so-called bridge laws) connecting the entities of the target and the base theory. The functional model of reduction emphasizes the causal definitions of the target entities referring to their causal relations to base entities. The new-wave model of reduction deduces not the original target theory but an analogous image of it, which remains inside the vocabulary of the base theory. One of the fundamental motivations of both the functional and the new-wave model is to show that bridge laws can be evaded. The present paper argues that bridge laws—in the original Nagelian sense—are inevitable, i.e. that none of these models can evade them. On the one hand, the functional model of reduction needs bridge laws, since its fundamental concept, functionalization, is an inter-theoretical process dealing with entities of two different theories. Theoretical entities of different theories (in a general heterogeneous case) do not have common causal relations, so the functionalization of an entity—without bridge laws—can only be executed in the framework of its own theory. On the other hand, the so-called images of the new-wave account cannot be constructed without the use of bridge laws. These connecting principles are needed to guide the process of deduction within the base theory; without them one would not be able to recognize if the deduced structure was an image of the target theory.

Species Concepts in Biology and Perspectives on Association in Music Analysis

Species Concepts in Biology and Perspectives on Association inMusic Analysis 1? Dora A. Hanninen Twelve years ago while browsing in a bookstore inAnn Arbor, I happened to pick up a book tided Toward a New Philosophy of Biology: Observations of an Evolutionist (1988) by the evolutionary biologist Ernst Mayr. Here was a philosophy of science thatwas entirely different in itsorientation and core issues from the philosophy of science of the 1950s and 1960s (then mostly a philosophy of the physical sciences) that found itsway intoAmerican music theory in its formative years through thewritings ofMilton Babbitt. Instead of universal laws, Mayr emphasized the particularity and contingency of evolutionary history. Instead of bridge laws and theory reduction, he offered a nuanced view of inter-level relations designed to recognize and preserve biology's autonomy as a science.1 As I readmore ofMayr's work, aswell as that by many other writers including Elliott Sober, Phillip Kitcher, 6 PerspectivesofNew Music Michael Ghiselin, Michael Ruse, David Hull, Massimo Pigliucci, and Kim Sterelny, it became clear that core issues in philosophy of biology such as altruism, function, units of selection, and species have a holistic or historical bent that make the field qualitatively different from philosophy of physics or chemistry and much closer in the texture of its thought to contemporary music theory and analysis. Although much of what I read in philosophy of biology seemed to resonate in one way or another with my own thinking about music analysis, given my work with associative sets and associative organization the vast literature on species concepts struck a special chord.2 At a high level of generality, both species and associative sets are categories one forms on the basis of some sort of pattern recognition (e.g., DNA structure or vestigial features in biology; literal or varied repetition in pitch or rhythm inmusic analysis). With categories forming the thread of an analogy between species and associative sets, I began to read the substantial body of work on species concepts not only for its intrinsic interest, but also as an invitation to explore differentways of thinking about associative sets and the roles that association among "like" segments can play inmusic analysis. In "Associative Sets, Categories, and Music Analysis" (Hanninen 2004c), I examined the workings of object formation and category formation inmusic analysis. The current paper continues the discussion at another level, drawing on work on species concepts in biology as an inspiration to contemplate and tryout differentways of interpreting and using associative sets as categories in music analysis. The paper has two parts. Part I provides background on some of the ways that biologists and philosophers of biology have conceptualized species. Here I outline key features and primary challenges of four types of species concepts: the phenetic, biological, phylogenetic, and species as-individuals concepts. My exposition of this preliminary material is a good deal more detailed than, strictly speaking, is actually necessary to support themore basic analogy between species and associative sets that underlies the four perspectives on musical association I develop in Part II. I provide this information in order to give readers a sense of the historical and scientific contexts in which different ways of thinking about species came about: for example, many of the tensions among species concepts in biology reflect exigencies of modeling different sorts of organisms (birds, flowering plants, slime molds, bacteria), or differences in the practices and conceptual cultures of various fields within the life sciences (e.g., molecular biology, ornithology, paleontology). Similarly, one of the points of this paper is to suggest thatmusic analysts, inspired by their own interests, interpretive goals, Species Concepts inBiology 7 and musical context, might try out different ways of thinking about association to seewhere they lead. Part II extracts four central ideas from the species concepts in Part I and uses these to develop four (roughly analogous) perspectives on association for use in music analysis. These focus on morphological similarity, population demographics and processes, associative lineages, and the persistence and transformation of individuals, respectively.3 After outlining each perspective, I provide one or two necessarily brief but suggestive analytic sketches designed to show, first,how an analyst might use each perspective inmusic analysis; and second...

Characterizing delamination of fibre composites by mixed mode cohesive laws

A novel method is used for the determination of mixed mode cohesive laws and bridging laws for the characterisation of crack bridging in composites. The approach is based on an application of the J integral. The obtained cohesive laws were found to possess high peak stress values. Mixed mode cohesive stresses were found to depend on both the normal and tangential crack opening displacements. The bridging laws, which are to be used together with a mode mixity dependent crack tip fracture energy, were found to possess relative low bridging stresses; the peak normal bridging stress was approximately 2 MPa during pure Mode I and the maximum shear stress during pure Mode II was about 10 MPa.

Reinforcing mechanisms in amorphous polymer nano-composites

Despite the large volume of experimental data on the peculiarities of the deformation response of polymer nano-composites published over the last 20 years, models addressing the principal physical reinforcing mechanisms taking into account the appropriate length and time-scales are scarce and not generally accepted. The characteristic length and time-scales in polymer nano-composites are also strongly temperature dependent, which further complicates the theoretical treatment due to principal differences in the behavior of polymers below and above their T g. In addition, the chain mobility above T g also affects nano-composite response below T g due to effects of segmental immobilization on the formation of polymer structure during solidification. It seems evident that the principal reinforcing mechanism above the T g is related to the chain immobilization induced by the presence of rigid high specific surface area inclusions. As a result, the length scale limits of validity of size independent continuum mechanics should be determined since the discrete nature of the matter at the nano-scale prohibits simple scaling down the micromechanics models. In this contribution, the existing reinforcing mechanisms are briefly analyzed in the view of the characteristic length and volume scales in polymers with nano-scale heterogeneities. The results are used to provide a conceptual framework for selecting a suitable molecular dynamics model accounting for molecular details relevant for deformation response of true nano-composites and an identification of possible bridging law between the micro- and nano-length scales.

Property Dualism, Epistemic Normativity and the Limits of Naturalism*

This paper examines some consequences of the (quasi‐)epiphenomenalism implied by a property dualistic view of phenomenal consciousness. The focus is upon the variation of phenomenal content over time. A thought‐experiment is constructed to support two claims. The weaker claim exhibits an incompatibility which arises in certain logically possible situations between a conscious subject’s epistemic norms and the requirement that one be aware of one’s conscious experience. This could be interpreted as providing some epistemic grounds for the postulation of bridging laws between the physical/functional and phenomenal domains. The stronger claim has it that the ontology of property dualism is not properly able to account for the certainty I have of being phenomenally conscious. The problem is viewed as resulting from the neglect of the intensional context involved in a proper representation of the argument for property dualism. It is argued that only a transcendental move can do justice to this certainty I have.

Effect of fiber fatigue rupture on monotonic and cyclic crack bridging laws in discontinuous fiber reinforced composites

Effect of fiber fatigue rupture on monotonic and cyclic crack bridging laws in discontinuous fiber reinforced composites

Experimental study and computer simulation on degradation of z-pin reinforcement under cyclic fatigue

This paper presents an experimental study on the fatigue degradation of the bridging forces of z-pins embedded in polymer laminates. Carbon/epoxy laminate specimens were reinforced in the through-thickness direction with two volume contents and two sizes of z-pins. The specimens were fatigue tested in the through-thickness (mode I) direction to measure the deterioration in the bridging forces of the pins. Degradation of the debonding and friction pull-out forces of the pins with the number of load cycles was determined over a range of fatigue displacements. The degradation of the bridging forces is dependent on the diameter of the pins. Reducing the diameter of the pins reduced the degradation rate of the debonding and friction forces. However, the friction force always degraded more rapidly under fatigue loading than the debonding force. Using the fatigue data and experimental observations, a micromechanics model for calculating the degradation of bridging tractions was developed and the lifetime of z-pinned laminates subjected to mode I fatigue was simulated. In the modeling, z-pins are treated as a series of external forces applied to the DCB laminates which provides bridging forces to the opening crack during delamination. Considering the degradation of bridging force under cyclic loading, the maximum bridging force in the bridging law is assumed to be a power law function decreasing with loading cycles N and maximum z-pin displacement δ max. The classic beam theory is utilized to calculate the energy release rate consumed by the newly created crack surface. The fracture energy method is used as the delamination criterion, in which the unpinned DCB fracture toughness versus loading cycles is assumed as an exponential function determined by previous test results. Computer simulation results show that z-pins can effectively reduce the delamination growth rate under both load-control and displacement-control conditions.

Bridging tractions in mode I delamination: Measurements and simulations

This paper discusses the results of bridging tractions in mode I delamination specimens. Bridging laws determined from a novel technique using distributed strains and an inverse-numerical technique are compared to those obtained using a method based on the experimental measurements of energy release rate and crack opening displacement. Both types of bridging laws are implemented in a numerical model that uses cohesive elements to calculate strains along the FBG and to predict crack growth progression in a double cantilever beam specimen. Global force–displacement responses are well-described by a cohesive model using both experimental bridging laws, however, the J-integral method requires an additional assumption about the length of the bridging zone. In addition, using the cohesive model, the crack tip position and longitudinal strains are more difficult to simulate due to the need for additional parameters (i.e., initial stiffness, maximum stress) required to describe the crack initiation behaviour of the cohesive elements.

Micromechanical model of cross-over fibre bridging – Prediction of mixed mode bridging laws

The fracture resistance of fibre composites can be greatly enhanced by crack bridging. In situ observations of mixed mode crack growth in a unidirectional carbon-fibre/epoxy composite reveal crack bridging by single fibres and by beam-like ligaments consisting of several fibres. Based on the observed bridging mechanism, a micromechanical model is developed for the prediction of macroscopic mixed mode bridging laws (stress-opening laws). The model predicts a high normal stress for very small openings, decreasing rapidly with increasing normal and tangential crack opening displacements. In contrast, the shear stress increases rapidly, approaching a constant value with increasing normal and tangential openings. The solutions for the bridging laws and the resulting toughening due to the bridging stresses are obtained in closed analytical form.

Probing Option Prices for Information

We present a methodology for extracting information from option prices when the market is viewed as knowledgeable. By expanding the information filtration judiciously and determining conditional characteristic functions for the log of the stock price, we obtain option pricing formulae which when fit to market data may reveal this information. In particular, we consider probing option prices for knowledge of the future stock price, instantaneous volatility, and the asymptotic dividend stream. Additionally the bridge laws developed are also useful for simulation based on stratified sampling that conditions on the terminal values of paths.

OS14-2-4 Mode-I Interlaminar Fracture Behavior of Heat-Resistant Composite Materials at High Temperature

In order to develop a High Speed Civil Transport, weight reduction by the use of advanced composite materials is one of the most important technical issues. However, composite laminates have very low interlaminar fracture resistance. Therefore, the interlaminar fracture toughness of composites has consequently become a critical design parameter for the aircraft structures. In this research, mode-I interlaminar fracture behavior of heat-resistant polyimide CFRP (Carbon Fiber Reinforced Plastics) was investigated by way of the double-cantilever-beam (DCB) test at high temperature up to 200℃. In the DCB tests at high temperature, fiber cross-over bridging was observed. In order to evaluate the influence of the bridging zone length on the crack growth resistance curve (R-curve), the DCB tests were conducted using specimens with different thicknesses. Fractographic observations of the fracture surface were performed in order to assess the crack growth behavior. The bridging characteristics were evaluated using a bridging law which describes the relationship between the crack closure traction resulting from the bridging fibers and the local crack opening displacement.

A fibre microbuckling model for predicting the notched compressive strength of composite sandwich panels

Cohesive-zone models have been successfully applied to predicting the damage from notches in engineering materials loaded intension. They have also been used to determine the growth of fibre microbuckling from a hole in a composite laminate under compression. The usual strategy is to replace the in elastic deformation associated with plasticity or microbuckling with a line crack and to assume some form of stress-displacement bridging law across the crack faces. This paper examines recent published experimental data for notched glass-fibre epoxy/honey comb sand wich panels loaded in uniaxial compression. A plastic fibre kinking analysis and a linear softening cohesive-zone model are used for the prediction of the unnotched and open-hole compressive strength and the theoretical results are found to be in a good agreement with experimental data.

Crack bridging law in discontinuous fiber reinforced composites under cyclic loading

Crack bridging law in discontinuous fiber reinforced composites under cyclic loading

Modelling of debonding between old concrete and overlay: fatigue loading and delayed effects

The paper focuses on the propagation of debonding along an interface between a substrate simulating old concrete and a cement-based thin bonded overlay. The aim of the study was to obtain the data necessary for relevant and efficient debonding modelling. The work combined experiment and simulation. Two types of overlay materials were investigated, fibre reinforced mortar (FRM) and plain mortar. Tensile tests were performed to obtain the residual normal stress–crack opening relationship. The shrinkage of the overlay material was characterized by tests on prismatic specimens that showed the evolution of both drying shrinkage and autogenous shrinkage versus time. The substrate—overlay interface was investigated by static tensile tests to provide the relationship between debonding opening and residual normal tensile stress. Its evolution under fatigue loading was assumed to follow a cyclic bridging law for plain concrete. Three-point flexural fatigue tests were then performed on repaired substrate to obtain information on the structural behaviour of the interface. The debonding propagation was monitored by a video-microscope with a magnification of 175× . Relying on the identified and quantified parameters, the above mentioned fatigue tests were modelled by the finite element method using the CAST3M code developed in France by Atomic Energy Commission (CEA). A comparison between model and experimental results shows good agreement and proves the important role of interlocking in the debonding mechanism.

A micromechanical bridging law model for CFCCs

In the present work, a methodology is presented for the assessment of bridging laws for continuous fibre-reinforced ceramic matrix composites based on material properties as well as micromechanics of fibre deformation and failure. A load–displacement model is initially formulated that utilizes weakest-link statistical concepts to analyse and relate the individual contributions of matrix, intact/bridging and failed/pull-out fibres during the composite fracture process. The total and individual contributions to the bridging law and crack growth resistance of the material are determined by identifying the non-elastic part of displacement as crack opening. The model is validated against the experimentally recorded load–displacement behaviour of a notched SiC-fibre-reinforced glass–ceramic matrix composite tested under monotonic tension. The output parameters of the converged regression procedure remain within a small scattering range from the corresponding mean values that compare favourably with known material properties. A parametric analysis of the effect of fibre volume fraction, Weibull modulus of fibres and interfacial shear stress in overall composite performance is presented in view of the ability of the model to serve as an a priori fracture prediction tool.