Variational principles in dissipative electro‐magneto‐mechanics: A framework for the macro‐modeling of functional materials
Variational principles in dissipative electro‐magneto‐mechanics: A framework for the macro‐modeling of functional materials
复制标题
耗散电磁力学的变分原理：功能材料宏观建模的框架
DOI：
10.1002/nme.3127
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发表时间：
2011
影响因子：
2.9
通讯作者：
B. Kiefer
中科院分区：
文献类型：
--
作者：
D. Rosato;B. Kiefer
本文提出了基于增量变分原理的具有电磁-机械耦合的耗散功能材料的宏观、基于连续体的公式和数值实现的一般框架。我们专注于准静态问题，其中机械惯性效应和时间依赖的电磁耦合被优先忽略，时间依赖仅通过可能的速率依赖耗散材料响应进入公式。不可逆耦合过程的潜在变分结构与规范本构建模方法有关，通常针对所谓的标准耗散材料。它被证明对宏观电磁力学中基于连续体的建模的各个方面都有巨大的影响。首先，耦合耗散响应的局部本构模型，即应力、电场和磁场与应变、电位移和磁感应，被证明是基于变分的，受增量最小化和鞍点原则的支配。接下来，讨论了边界值问题公式的含义，边界值问题以最小化原则的形式出现在基于能量的公式中，以鞍点原则的形式出现在基于焓的公式中。此外，耗散电磁力学在宏观水平上的材料稳定性是基于增量势的凹凸性来定义的。我们提供了可选变分结构的全面概述，并讨论了其计算实现的细节，例如本构更新算法和有限元求解器的制定。从本构建模的角度，包括对耦合电磁力学稳定性的理解，表明基于能量的公式是规范的设置。从计算方便的角度来看，基于焓的公式是最方便的设置。对多铁复合材料的数值研究表明，所提出的框架与未来新功能材料的设计有关。版权所有©2011 John Wiley & Sons， Ltd
This paper presents a general framework for the macroscopic, continuum‐based formulation and numerical implementation of dissipative functional materials with electro‐magneto‐mechanical couplings based onincremental variational principles. We focus on quasi‐static problems, where mechanical inertia effects and time‐dependent electro‐magnetic couplings area priorineglected and a time‐dependence enters the formulation only through a possible rate‐dependent dissipative material response. The underlying variational structure of non‐reversible coupled processes is related to a canonical constitutive modeling approach, often addressed to so‐called standard dissipative materials. It is shown to have enormous consequences with respect to all aspects of the continuum‐based modeling in macroscopic electro‐magneto‐mechanics. At first, thelocal constitutive modelingof the coupled dissipative response, i.e. stress, electric and magnetic fields versus strain, electric displacement and magnetic induction, is shown to be variational based, governed by incremental minimization and saddle‐point principles. Next, the implications on the formulation ofboundary‐value problemsare addressed, which appear in energy‐based formulations as minimization principles and in enthalpy‐based formulations in the form of saddle‐point principles. Furthermore, thematerial stabilityof dissipative electro‐magneto‐mechanics on the macroscopic level is defined based on the convexity/concavity of incremental potentials. We provide a comprehensive outline of alternative variational structures and discuss details of their computational implementation, such as formulation of constitutive update algorithms and finite element solvers. From the viewpoint of constitutive modeling, including the understanding of the stability in coupled electro‐magneto‐mechanics, anenergy‐based formulationis shown to be the canonical setting. From the viewpoint of the computational convenience, anenthalpy‐based formulationis the most convenient setting. A numerical investigation of a multiferroic composite demonstrates perspectives of the proposed framework with regard to the future design of new functional materials. Copyright © 2011 John Wiley & Sons, Ltd.
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DOI：
--
发表时间：
1975
期刊：
影响因子：
--
作者：
B. Halphen;Q. Nguyen
通讯作者：
Q. Nguyen
时间依赖性铁电行为的能量材料模型：存在性和唯一性
影响因子：
2.9
作者：
A. Mielke;A. Timofte
通讯作者：
A. Timofte
DOI：
10.1007/bf01587765
发表时间：
1971
期刊：
Zeitschrift für angewandte Mathematik und Physik
影响因子：
--
作者：
B. D. Coleman;E. Dill
通讯作者：
E. Dill
影响因子：
2.8
作者：
Schröder, J;Romanowski, H
通讯作者：
Romanowski, H
DOI：
10.1016/s0045-7825(98)00219-9
发表时间：
1999-04
影响因子：
7.2
作者：
M. Ortiz;L. Stainier
通讯作者：
M. Ortiz;L. Stainier