The book reviews section generally accepts for review only those books whose content and level reflect the general editorial policy of Technometrics. Publishers are invited to send books for review to Eric R. Ziegel, Amoco Research Center, Mail Station F-l/C& P.O. Box 3011, Naperville, Illinois 60566-7011. Please include the price of the book. The opinions expressed in this section are those of the reviewers and do not necessarily reflect those of the editorial staff or the sponsoring societies. Listed prices were provided by the publisher when the books were received by Technometrics and may not be current.

Adventures in Stochastic Processes

https://hal.archives-ouvertes.fr/hal-00940462/document

Microstructural effects in elastic composites

The present paper provides details on the new trends in application of asymptotic homogenization techniques to the analysis of composite materials and thin-walled composite structures and their effective properties. The problems under consideration are important from both fundamental and applied points of view. We review a state-of-the-art in asymptotic homogenization of composites by presenting the variety of existing methods, by pointing out their advantages and shortcomings, and by discussing their applications. In addition to the review of existing results, some new original approaches are also introduced. In particular, we analyze a possibility of analytical solution of the unit cell problems obtained as a result of the homogenization procedure. Asymptotic homogenization of 3D thin-walled composite reinforced structures is considered, and the general homogenization model for a composite shell is introduced. In particular, analytical formulas for the effective stiffness moduli of wafer-reinforced shell and sandwich composite shell with a honeycomb filler are presented. We also consider random composites; use of two-point Pade approximants and asymptotically equivalent functions; correlation between conductivity and elastic properties of composites; and strength, damage, and boundary effects in composites. This article is based on a review of 205 references. DOI: 10.1115/1.3090830

Asymptotic Homogenization of Composite Materials and Structures

The introductory and more elementary ideas and results of micromechanics of heterogeneous media are collected in the survey. The central problem under discussion is “homogenization.” It replaces such media by homogeneous ones, which behave macroscopically in the same way and possess certain gross effective properties. These properties are related in a complicated manner to the prescribed internal structure of the medium and their evaluation, in general, represents a profound challenge in any specific situation. A brief historical survey is given, underlying the reappearance of essentially the same “homogenization” quest in numerous guises and contexts over the last two centuries. Within the framework of the volume-averaging approach the basic notions are introduced and some of the central, now classical, results are then derived and discussed such as perturbation expansions, Hashin-Shtrikman’s bounds, variational estimates and Levin’s cross-property relation. A general “one-particle” scheme for approximate evaluation of the effective properties (in the static case) is detailed in its various implementations like selfconsistency, iterated limits and effective field. Illustrations concern conductivity, elasticity, and absorption phenomena in heterogeneous particulate media, as well as a simple self-consistent model for polycrystals’ homogenization.

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Elementary Micromechanics of Heterogeneous Media

A dispersive model is developed for wave propagation in periodic heterogeneous media The model is based on the higher order mathematical homogenization theory with multiple spatial and temporal scales A fast spatial scale and a slow temporal scale are introduced to account for the rapid spatial fluctuations as well as to capture the long-term behavior of the homogenized solution By this approach the problem of secularity, which arises in the conventional multiple-scale higher order homogenization of wave equations with oscillatory coefficients, is successfully resolved A model initial boundary value problem is analytically solved and the results have been found to be in good agreement with a numerical solution of the source problem in a heterogeneous medium

A Dispersive Model for Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales

Applying the method of two-scale asymptotic expansions to the displacement field in periodic elastic structures the completed macroscopic stress-strain relation of such media is derived. This relation contains beside the usually considered local part also weakly nonlocal contributions in the form of strain gradients up to infinite order. Formulae for the determination of the pertaining homogenized material tensors are derived.



Unter Benntzung der Methods der asymptotischen Entwicklung fur die Verschiebungsfelder in periodischen elastischen Strukturen wird die vollstandige makroskopische Spannungs-Dehnungs-Beziehung solcher Medien abgeleitet. Diese Beziehung enthalt neben dem ublieherweise berucksichtigten lokalen Anteil auch schwach nichtlokale Beitrage in Form von Spannungsgradienten bis zur unendlichen Ordnung. Formeln fur die Bestimmung der zugehorig homogenisierten Materialtensoren werden abgeleitet.

Higher-Order Terms in the Homogenized Stress-Strain Relation of Periodic Elastic Media

Foreword. List of Participants. Titles of Contributed Papers. Invited Lectures. Topology Optimization With The Homogenization And The Level-Set Methods G. Allaire. Thin Films Of Active Materials K. Bhattacharya. The Passage From Discrete To Continuous Variational Problems: A Nonlinear Homogenization Process A. Braides, M.S. Gelli. Approaches To Nonconvex Variational Problems Of Mechanics A. Cherkaev. On G-Compactness Of The Beltrami Operators T. Iwaniec et al. Homogenization And Optimal Design In Structural Mechanics T. Lewinski. Homogenization And Design Of Functionally Graded Composites For Stiffness And Strength R. Lipton. Homogenization For Nonlinear Composites In The Light Of Numerical Simulations H. Moulinec and P. Suquet. Existence And Homogenization For The Problem - div a(x, Du) = F When a(x,) Is A Maximal Monotone Graph In For Every x F. Murat. Optimal Design In 2-D Conductivity For Quadratic Functionals In The Field P. Pedegral. Linear Comparison Methods For Nonlinear Composites P. Ponte Castaneda. Models Of Microstructure Evolution In Shape Memory Alloys T. Roubicek. Stochastic Homogenization: Convexity And Nonconvexity J.J. Telega. Final remarks. Index.

Nonlinear homogenization and its applications to composites, polycrystals and smart materials

A novel estimation of temperature changes inside soft tissues has been proposed in sub-ablation range, i.e. ≈ 20 ◦C−48 ◦C. This estimation has been obtained by studying statistical properties of backscattered ultrasonic signals. Two different procedures of heating/cooling have been performed in which the RF echoes have been registered from soft tissue phantom in the first procedure, and from soft tissue in vitro in the second one. Calculated envelopes of signals registered in time points during heating/cooling experiments have been treated as a statistical sample drawn from a random variable with three different distributions, namely the Rayleigh distribution, the Nakagami distribution, and the K-distribution. The histograms obtained in subsequent time moments have been fitted to the three distributions. Dependencies of their shape and scale parameters on temperature have been calculated. It is concluded that the shape parameter of the K-distribution can be chosen as the best marker of temperature changes in both experiments. The choice of the marker has been made by analysis of temperature dependencies of all calculated parameters and by comparing the quality of fitting all histograms to the considered distributions. Besides, the chosen marker as a function of temperature exhibits the closest shape to temperature/time function experimentally measured.

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Temperature Measurement by Statistical Parameters of Ultrasound Signal Backscattered from Tissue Samples

Temperature monitoring is essential for various medical treatments. In this work, we investigate the impact of temperature on backscattered ultrasound echo statistics during a high intensity focused ultrasound treatment. A tissue mimicking phantom was heated with a spherical ultrasonic transducer up to 56 ◦C in order to imitate tissue necrosis. During the heating, an imaging scanner was used to acquire backscattered echoes from the heated region. These data was then modeled with the homodyned K distribution. We found that the best temperature indicator can be obtained by combining two parameters of the model, namely the backscattered echo mean intensity and the effective number of scatterers per resolution cell. Next, ultrasonic thermometer was designed and used to create a map of the temperature induced within the tissue phantom during the treatment.

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Temperature Monitoring during Focused Ultrasound Treatment by Means of the Homodyned K Distribution

https://satoss.uni.lu/members/andrzej/papers/MG10.pdf

Barbara Gambin

Papers

Higher-Order Terms in the Homogenized Stress-Strain Relation of Periodic Elastic Media

Nonlinear homogenization and its applications to composites, polycrystals and smart materials

Temperature Measurement by Statistical Parameters of Ultrasound Signal Backscattered from Tissue Samples

Temperature Monitoring during Focused Ultrasound Treatment by Means of the Homodyned K Distribution

Stochastic modelling of the eukaryotic heat shock response