Dynamic theory for smectic A liquid crystals

A dynamic continuum theory is presented for smectic A liquid crystals in which the usual director n and unit layer normal a do not always necessarily coincide. Most previous dynamic continuum theories equate n with a; the theory developed in this article allows n and a to differ in non-equilibrium situations, work that has been motivated by the recent investigations by Auernhammer et al. (Rheol. Acta 39, 215–222, 2000; Phys. Rev. E 66, 061707, 2002) and Soddemann et al. (Eur. Phys. J. E 13, 141–151, 2004). The usual Oseen constraint () for smectics is not imposed upon the unit normal a. Permeation is also included. After a summary of the complete dynamic equations, an application is given via an example which shows that planar aligned layers of smectic A subjected to an arbitrary periodic disturbance are linearly stable.      

Simulation of crack spacing using a reinforced concrete model with an internal length parameter

Summary A gradient-enhanced smeared crack model and bond-slip interface elements are utilized in finite element simulations of reinforced concrete. The crack model is rooted in an enhanced plasticity theory. It uses the Rankine failure surface dependent on an equivalent inelastic strain measure as well as on its Laplacian. As a result, finitely sized fracture process zones and realistic crack spacings are obtained. A reinforced concrete bar in uniaxial tension is analyzed to demonstrate the regularizing influence of the internal length parameter in the model and to evaluate the influence of the model parameters on the energy dissipation in multiple cracks. A comparison of numerical simulations with experimental results for a beam without shear reinforcement in four-point bending concludes the analysis. Received 4 November 1997; accepted for publication 23 April 1998     

Accuracy assessment of the linear Poisson–Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid–protein complexes

The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson–Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev–Bashford–Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson–Boltzmann model. © 2015 Wiley Periodicals, Inc.     

计算材料科学中桥域多尺度方法的若干进展

材料科学中存在固有的多尺度特性,桥域多尺度方法是在宏观尺度(如连续介质力学)中引入不同的细微观尺度的计算区域,乃至纳米尺度的分子动力学、量子力学计算区域,将不同尺度的研究方法通过一定的数学模型耦合在一起。该方法既能节约计算成本,又能保证所研究问题的物理特性。本文对多尺度方法的基本概念、跨尺度桥域多尺度方法的发展、基本原理、耦合方法和离散方程进行了讨论,给出了几个应用算例,并在最后进行了总结,展望了今后的可能发展方向。     

A method for relaxing parameter constraints in rigid body dynamics

As attractive alternatives to a set of three Euler angles, the rotation of a rigidly deforming body is often represented using four or more parameters. The accompanying parameter constraints introduce generalized constraint forces in the equations of motion which can often negate the benefits of a particular parameterization. In this paper, we discuss situations where the parameter constraints are not imposed. Thus, although the body no longer deforms rigidly, it does deform homogeneously. This allows the theory of a Cosserat point (or, equivalently, the theory of a pseudo-rigid body) to be used to establish equations governing its motion. Earlier work on this topic by O’Reilly and Varadi considered the four Euler parameters and the single Euler parameter constraint. Here, we consider Poincaré's six parameter representation of a rotation tensor, and, complementing earlier work, discuss numerical implementation and representative simulations. One of the contributions of this paper is the development of a viscoelastic Cosserat point, whose equations of motion are free from parameter constraints and singularities, that can be used to approximate the motion of a rigid body.     

A Cosserat shell model for interphases in elastic media

This study is concerned with the modeling of interphases in elastic media in general, and in composite materials in particular. The aim is to replace a boundary value problem consisting of a three-phase configuration, say that of fiber-interphase-matrix, by a simpler problem which involves the fiber and matrix only, plus certain matching conditions which simulate the interphase. The simplest of such known representations replaces a thin interphase by a “perfect contact interface” (a single surface) across which the displacements and tractions are assumed to be continuous. Another classical model replaces a thin and soft interphase by a “spring-type interface”, across which the tractions are continuous, but the displacement field undergoes a discontinuity. In the present paper, a Cosserat shell model of the interphase is derived which successfully models the original interphase in a unified manner, for the full range of its material parameters relative to those of the neighboring media. The model is derived in the setting of three-dimensional linear elasticity with small deformations and displacements. Comparisons with an existing exact solution of a coated fiber in an infinite matrix show that it performs extremely well even for moderately thick interphases.     

结构形状优化设计数值方法的研究和应用

本文论述了连续体结构形状优化设计数值方法的研究和应用进展,讨论了结构模型化、灵敏度分析、优化方法改进、优化实用软件开发以及同CAD技术相结合等问题,介绍了在结构优化设计软件MCADS中采用的方法,并通过工程实例说明了结构形状优化设计的应用及其价值。     

用二级控制法对二维连续体进行形状优化

二级控制的意思是在自然设计变量和有限元网格节点之间加入设计单元，建立自然设计变量控制关键点坐标，关键点控制有限元网格节点，共两层控制关系。后一层控制关系借助有限元形函数描述设计单元，并引入相应的参数坐标，从而实现敏庋分析、结构形状变化的控制和网格的变动控制。本文使用二级控制理论有效地解决了二维连续体结构形状优化的一些困难，将形状优化问题处理成序列二次规划问题求解。使用MSC／PCL语言在MSC／Patran＆Nasntran平台上实现了优化模块的二次开发。本文设计思路的可行性和程序的有效性通过若干算例得到证实。     

PARTITION OF UNITY FINITE ELEMENT METHOD FOR SHORT WAVE PROPAGATION IN SOLIDS

IntroductionIt is known that standard finite element procedure is unable to simulate the wavepropagation with high oscillations or gradients in space in the media with reasonableefficiency and accuracy due to the nature of polynomial interpolation approxi…     

Recovery of small electromagnetic inhomogeneities from partial boundary measurementsIdentification de petites inhomogénéités diélectriques à partir de mesures partielles

We consider for the inverse problem of identifying locations and certain properties of the shapes of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on part of the boundary or dynamic boundary measurements for a finite time interval. Using as weights particular background solutions we develop asymptotic methods based on appropriate averaging of the data. To cite this article: H. Ammari, A.G. Ramm, C. R. Mecanique 330 (2002) 199–205.