Avalanche dynamics of fiber bundle models

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model CDFBM . Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models

Brittle to ductile transition in a fiber bundle with strong heterogeneity

We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0≤α≤1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition αc which separates two qualitatively different behaviors: Below the critical point, the failure of the bundle is brittle, characterized by an abrupt damage growth within the breakable part of the system. Above αc, however, the macroscopic response becomes ductile, providing stability during the entire breaking process. The transition occurs at an astonishingly low fraction of strong fibers which can have importance for applications. We show that in the ductile phase, the size distribution of breaking bursts has a power law functional form with an exponent μ=2 followed by an exponential cutoff. In the brittle phase, the power law also prevails but with a higher exponent μ=92. The transition between the two phases shows analogies to continuous phase transitions. Analyzing the microstructure of the damage, it was found that at the beginning of the fracture process cracks nucleate randomly, while later on growth and coalescence of cracks dominate, which give rise to power law distributed crack sizes.

Universality class of fiber bundles with strong heterogeneities

We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0 ≤ α ≤ 1 of fibers is unbreakable, while the remaining 1 - α fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components αc which separates two qualitatively diferent regimes of the system: below αc the burst size distribution is a power law with the usual exponent Ƭ= 5/2, while above αc the exponent switches to a lower value Ƭ = 9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena

Critical ruptures in a bundle of slowly relaxing fibers

We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime ʧ of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life tʄ and the characteristic time tm of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of ʧ from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Fixed points on torus fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.

Coincidence points of fiber maps on S-n-bundles

In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Coincidences of self-maps on Klein bottle fiber bundles over the circle

The main purpose of this work is to study coincidences of fiber-preserving self-maps over the circle S 1 for spaces which are fiberbundles over S 1 and the fiber is the Klein bottle K. We classify pairs of self-maps over S 1 which can be deformed fiberwise to a coincidence free pair of maps. © 2012 Pushpa Publishing House.

Fracture and resistance-curve behavior in hybrid natural fiber and polypropylene fiber reinforced composites

This article presents the results of a combined experimental and theoretical study of fracture and resistance-curve behavior of hybrid natural fiber- and synthetic polymer fiber-reinforced composites that are being developed for potential applications in affordable housing. Fracture and resistance-curve behavior are studied using single-edge notched bend specimens. The sisal fibers used were examined using atomic force microscopy for fiber bundle structures. The underlying crack/microstructure interactions and fracture mechanisms are elucidated via in situ optical microscopy and ex-situ environmental scanning microscopy techniques. The observed crack bridging mechanisms are modeled using small and large scale bridging concepts. The implications of the results are then discussed for the design of eco-friendly building materials that are reinforced with natural and polypropylene fibers.

Time-resolved fluorescence spectroscopy of white-spot caries in human enamel

The objective is to differentiate noncavitated caries enamel through time-resolved fluorescence and to find excitation and emission parameters that can be applied in future clinical practice for detection of caries lesions that are not clearly visible to the professional. Sixteen human teeth with noncavitiated white-spot caries were selected for this work. Fluorescence intensity decay was measured by using an apparatus based on the time-correlated single-photon counting method. An optical fiber bundle was employed for sample excitation (440 nm), and the fluorescence collected by the same bundle (500 nm) was registered. The average lifetime for sound enamel was 7: 93 +/- 0: 09, 2: 46 +/- 0: 04, and 0: 51 +/- 0: 02 ns, whereas for the carious enamel the lifetimes were 4: 84 +/- 0: 06, 1: 35 +/- 0: 02, and 0: 16 +/- 0: 01 ns. It was concluded that it is possible to differentiate between carious and sound regions by time-resolved fluorescence and that, although the origin of enamel fluorescence is still uncertain, the lifetime values seem to be typical of fluorophores like collagen I. (C) 2010 Optical Society of America

Computer-Assisted Numerical Analysis for Oxygen and Carbon Dioxide Mass Transfer in Blood Oxygenators

A two-dimensional numeric simulator is developed to predict the nonlinear, convective-reactive, oxygen mass exchange in a cross-flow hollow fiber blood oxygenator. The numeric simulator also calculates the carbon dioxide mass exchange, as hemoglobin affinity to oxygen is affected by the local pH value, which depends mostly on the local carbon dioxide content in blood. Blood pH calculation inside the oxygenator is made by the simultaneous solution of an equation that takes into account the blood buffering capacity and the classical Henderson-Hasselbach equation. The modeling of the mass transfer conductance in the blood comprises a global factor, which is a function of the Reynolds number, and a local factor, which takes into account the amount of oxygen reacted to hemoglobin. The simulator is calibrated against experimental data for an in-line fiber bundle. The results are: (i) the calibration process allows the precise determination of the mass transfer conductance for both oxygen and carbon dioxide; (ii) very alkaline pH values occur in the blood path at the gas inlet side of the fiber bundle; (iii) the parametric analysis of the effect of the blood base excess (BE) shows that V(CO2) is similar in the case of blood metabolic alkalosis, metabolic acidosis, or normal BE, for a similar blood inlet P(CO2), although the condition of metabolic alkalosis is the worst case, as the pH in the vicinity of the gas inlet is the most alkaline; (iv) the parametric analysis of the effect of the gas flow to blood flow ratio (Q(G)/Q(B)) shows that V(CO2) variation with the gas flow is almost linear up to Q(G)/Q(B) = 2.0. V(O2) is not affected by the gas flow as it was observed that by increasing the gas flow up to eight times, the V(O2) grows only 1%. The mass exchange of carbon dioxide uses the full length of the hollow-fiber only if Q(G)/Q(B) > 2.0, as it was observed that only in this condition does the local variation of pH and blood P(CO2) comprise the whole fiber bundle.

Examining the Agreement of Structural Loss Measured With Heidelberg Retinal Tomograhy and Functional Loss With Standard Automated Perimetry (SAP; Octopus), Pulsar Perimetry (PP), and Moorfields Motion Displacement Test (MDT) Perimetry

Purpose: To examine the relationship of functional measurements with structural measures. Methods: 146 eyes of 83 test subjects underwent Heidelberg Retinal Tomography (HRTIII) (disc area<2.43, mphsd<40), and perimetry testing with Octopus (SAP; Dynamic), Pulsar (PP; TOP) and Moorfields MDT (ESTA). Glaucoma was defined as progressive structural or functional loss (20 eyes). Perimetry test points were grouped into 6 sectors based on the estimated optic nerve head angle into which the associated nerve fiber bundle enters (Garway-Heath map). Perimetry summary measures (PSM) (MD SAP/ MD PP/ PTD MDT) were calculated from the average total deviation of each measured threshold from the normal for each sector. We calculated the 95% significance level of the sectorial PSM from the respective normative data. We calculated the percentage agreement with group1 (G1), healthy on HRT and within normal perimetric limits, and group 2 (G2), abnormal on HRT and outside normal perimetric limits. We also examined the relationship of PSM and rim area (RA) in those sectors classified as abnormal by MRA (Moorfields Regression Analysis) of HRT. Results: The mean age was 65 (range= [37, 89]). The global sensitivity versus specificity of each instrument in detecting glaucomatous eyes was: MDT 80% vs. 88%, SAP 80% vs. 80%, PP 70% vs. 89% and HRT 80% vs. 79%. Highest percentage agreement of HRT (respectively G1, G2, sector) with PSM were MDT (89%, 57%, nasal superior), SAP (83%, 74%, temporal superior), PP (74%, 63%, nasal superior). Globally percentage agreement (respectively G1, G2) was MDT (92%, 28%), SAP (87%, 40%) and PP (77%, 49%). Linear regression showed there was no significant trend globally associating RA and PSM. However, sectorally the supero-nasal sector had a statistically significant (p<0.001) trend with each instrument, the associated r2 coefficients are (MDT 0.38 SAP 0.56 and PP 0.39). Conclusions: There were no significant differences in global sensitivity or specificity between instruments. Structure-function relationships varied significantly between instruments and were consistently strongest supero-nasally. Further studies are required to investigate these relationships in detail.