Micro-mechanical approximation to the stress field around an inclined fiber of FRCC

Matrix spalling or crushing is one of the important mechanisms of fiber-matrix interaction of fiber reinforced cementitious composites (FRCC). The fiber pullout mechanisms have been extensively studied for an aligned fiber but matrix failure is rarely investigated since it is thought not to be a major affect. However, for an inclined fiber, the matrix failure should not be neglected. Due to the complex process of matrix spalling, experimental investigation and analytical study of this mechanism are rarely found in literature. In this paper, it is assumed that the load transfer is concentrated within the short length of the inclined fiber from the exit point towards anchored end and follows the exponential law. The Mindlin formulation is employed to calculate the 3D stress field. The simulation gives much information about this field. The 3D approximation of the stress state around an inclined fiber helps to qualitatively understand the mechanism of matrix failure. Finally, a spalling criterion is proposed by which matrix spalling occurs only when the stress in a certain volume, rather than the stress at a small point, exceeds the material strength. This implies some local stress redistribution after first yield. The stress redistribution results in more energy input and higher load bearing capacity of the matrix. In accordance with this hypothesis, the evolution of matrix spalling is demonstrated. The accurate prediction of matrix spalling needs the careful determination of the parameters in this model. This is the work of further study. (C) 2002 Elsevier Science Ltd. All rights reserved.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Biaxial failure model for fiber reinforced concrete

Steel fiber reinforced concrete (SFRC) is widely applied in the construction industry. Numerical elastoplastic analysis of the macroscopic behavior is complex. This typically involves a piecewise linear failure curve including corner singularities. This paper presents a single smooth biaxial failure curve for SFRC based on a semianalytical approximation. Convexity of the proposed model is guaranteed so that numerical problems are avoided. The model has sufficient flexibility to closely match experimental results. The failure curve is also suitable for modeling plain concrete under biaxial loading. Since this model is capable of simulating the failure states in all stress regimes with a single envelope, the elastoplastic formulation is very concise and simple. The finite element implementation is developed to demonstrate the conciseness and the effectiveness of the model. The computed results display good agreement with published experimental data.

In situ characterization of stickiness of sugar-rich foods using a linear actuator driven stickiness testing device

A stickiness testing device based on the probe tack test has been designed and tested. It was used to perform in situ characterization of drying hemispherical drops with an initial radius 3.5 mm. Tests were carried out in two drying temperatures, 63 and 95 degreesC. Moisture and temperature histories of the drying drops of fructose, honey, sucrose, maltodextrin and sucrose-maltodextrin mixtures were determined. The rates of moisture evaporation of the fructose solution was the fastest while those of the maltodextrin solution was the lowest. A profile reversal was observed when the temperature profiles of these materials were compared. Different modes of failure were observed during the stickiness tests. Pure fructose and honey solutions remained completely sticky and failed cohesively until the end of drying. Pure sucrose solution remained sticky and failed cohesively until complete crystallization occurred. The surface of the maltodextrin drops formed a skin shortly after the start of drying. It exhibited adhesive failure and reached a state of non-adhesion. Addition of maltodextrin significantly altered the stickiness of sucrose solution. (C) 2002 Elsevier Science Ltd. All rights reserved.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimen- sioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation that improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.

A class B switch-mode assisted linear amplifier

A switch-mode assisted linear amplifier (SMALA) combining a linear (Class B) and a switch-mode (Class D) amplifier is presented. The usual single hysteretic controlled half-bridge current dumping stage is replaced by two parallel buck converter stages, in a parallel voltage controlled topology. These operate independently: one buck converter sources current to assist the upper Class B output device, and a complementary converter sinks current to assist the lower device. This topology lends itself to a novel control approach of a dead-band at low power levels where neither class D amplifier assists, allowing the class B amplifier to supply the load without interference, ensuring high fidelity. A 20 W implementation demonstrates 85% efficiency, with distortion below 0.08% measured across the full audio bandwidth at 15 W. The class D amplifier begins assisting at 2 W, and below this value, the distortion was below 0.03%. Complete circuitry is given, showing the simplicity of the additional class D amplifier and its corresponding control circuitry.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.