Unified formulae of variational bounds for multiphase anisotropic elastic composites

Using the spherical and deviator decomposition of the polarization and strain tensors, we present a general algorithm for the calculation of variational bounds of dimension d for any type of anisotropic linear elastic composite as a function of the properties of the comparison body. This procedure is applied in order to obtain analytical expressions of bounds for multiphase, linear elastic composites with cubic symmetry where the geometric shapes of the inclusions are arbitrary. For the validation, it can be proved that for the isotropic particular case, the bounds coincide with those recently reported by Gibiansky and Sigmund. On the other hand, based on this general procedure some, classical bounds reported by Hashin for transversely isotropic composites, are reproduced. Numerical calculations and some comparisons with other models and experimental data are shown.     

均匀化理论及其在生物力学中的应用

在线弹性理论的范围内,简要介绍了新近发展起来的均匀化理论（ｈｏｍｏｇｅｎｉｚａｔｉｏｎｔｈｅｏｒｙ）,并引入了误差分析方面的一些研究成果．由于均匀化理论可以详尽地考虑材料的微观结构,在生命器官组织的细观力学研究中会起到推动作用．作为应用实例,本文介绍了均匀化理论在密质骨力学性能的数值模拟中的应用．      

Yield design of thin periodic plates by a homogenization technique and an application to masonry wallsCalcul à la rupture des plaques minces périodiques par une technique d'homogénéisation et une application aux murs en maçonnerie

A homogenization method for determining overall yield strength properties of thin periodic plates from their local strength properties is proposed within the framework of the yield design theory. The proposed method is applied to the determination of the in-plane and out of plane strength criterion for masonry described as a regular assemblage of infinitely resistant bricks separated by Coulomb interfaces. To cite this article: K. Sab, C. R. Mecanique 331 (2003).     

LINEARIZATION OF A NONLINEAR PERIODIC BOUNDARY CONDITION RELATED TO CORROSION MODELING

We study galvanic currents on a heterogeneous surface. In electrochemistry, the oxidation-reduction reaction producing the current is commonly modeled by a nonlinear elliptic boundary value problem. The boundary condition is of exponential type with periodically varying parameters. We construct an approximation by first homogenizing the problem, and then linearizing about the homogenized solution. This approximation is far more accurate than both previous approximations or direct linearization. We establish convergence estimates for both the two and three-dimensional case and provide two-dimensional numerical experiments.     

非齐次马氏决策过程的齐次化

该文考虑的是可数状态空间有限行动空间非齐次马氏决策过程的期望总报酬准则．与以往不同的是，我们是通过扩大状态空间的方法，将非齐次的马氏决策过程转化成齐次的马氏决策过程，于是非常简洁地得到了按传统的方法所得的主要结果．     

A multiscale method for semilinear elliptic equations

At present there are many papers, based on multiscale expansion and homogenization theory, to deal with nonlinear problems with microstructure. But there is no systematic method to deal with all of the possible nonlinear partial differential equations since different nonlinear problems gives rise to different multiscale expansions parameters classes. This introduces changes in the consequent process of homogenization. In this paper, a method based on the theory of upper and lower solution is provided. It deals with nonlinear problems by reducing them to a series of linear problems. In addition numerical computations are also presented in the last part of the paper to support our theoretical analysis.     

Error Estimates for the Approximation of the Effective Hamiltonian

We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting. D.G. was partially supported by the Center for Mathematical Analysis, Geometry and Dynamical Systems through FCT Program POCTI/FEDER and by grant POCI/FEDER/MAT/55745/2004.     

Simplified pregnant woman models for the fetus exposure assessment

In this paper, we introduce a study that we carried out in order to validate the use of a simplified pregnant woman model for the assessment of the fetus exposure to radio frequency waves. This simplified model, based on the use of a homogeneous tissue to replace most of the inner organs of the virtual mother, would allow us to deal with many issues that are raised because of the lack of pregnant woman models for numerical dosimetry. Using specific absorption rate comparisons, we show that this model could be used to estimate the fetus exposure to plane waves.     

On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals

Effective elastic moduli for 3D solid–solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in two dimensions with direct numerical integration along the third direction. As a result, the MM method converges much quicker to the exact moduli in comparison with the PWE as the number of Fourier coefficients increases. The MM method yields a more explicit formula than previous results, enabling a closed-form upper bound on the effective Christoffel tensor. The MM approach significantly improves the efficiency and accuracy of evaluating effective wave speeds for high-contrast composites and for configurations of closely spaced inclusions, as demonstrated by three-dimensional examples.     

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ITER超导磁体系统的超导电流传输线导体是由NbTi/Cu管内电缆超导体、辅助绝缘层和接地金属屏蔽层组成的层状复合材料结构。分别采用基于传统的复合材料理论和基于均匀化理论与复合材料损伤理论相结合的方法对超导传输线导体的等效模量进行了理论预测。这些结果为分析和计算超导电流传输线的应力和变形以及热性能提供了必要的参数。