Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions
Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions
复制标题
具有稳定弱周期性边界条件的化学力学问题的变分一致计算均质化
DOI：
10.1002/nme.6798
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发表时间：
2021
影响因子：
2.9
通讯作者：
Larsson
中科院分区：
文献类型：
--
作者：
Kaessmair;Runesson;Janicke;Steinmann;Larsson
基于代表性体积元（RVE）内位移场、化学势场和（离子）浓度场的一阶延拓的经典假设，发展了一种基于变分一致模型的计算均匀化方法.化学势和浓度作为主要全局场的存在代表了一种混合形式，它具有一定的优点。本文考虑了在可扩展性约束下的Cahn-Hilliard型梯度模型下的非标准扩散问题。相关域上的弱周期边界条件为唯一可解的RVE问题提供了一般变分设置。为了控制边界离散的稳定性，这些边界条件被引入了一种新的方法，从而避免了满足LBB条件的需要：惩罚稳定的拉格朗日乘子公式，它以每个弱周期域（当前问题的三个域）的额外拉格朗日乘子为代价来加强稳定性。特别是，一个整洁的结果是，经典的诺依曼边界条件时，罚款变得非常大。在数值算例中，我们研究了以下特性：不同边界近似的网格收敛性，罚参数选择的敏感性，以及RVE尺寸对宏观响应的影响。
A variationally consistent model‐based computational homogenization approach for transient chemomechanically coupled problems is developed based on the classical assumption of first‐order prolongation of the displacement, chemical potential, and (ion) concentration fields within a representative volume element (RVE). The presence of the chemical potential and the concentration as primary global fields represents a mixed formulation, which has definite advantages. Nonstandard diffusion, governed by a Cahn–Hilliard type of gradient model, is considered under the restriction of miscibility. Weakly periodic boundary conditions on the pertinent fields provide the general variational setting for the uniquely solvable RVE‐problem(s). These boundary conditions are introduced with a novel approach in order to control the stability of the boundary discretization, thereby circumventing the need to satisfy the LBB‐condition: the penalty stabilized Lagrange multiplier formulation, which enforces stability at the cost of an additional Lagrange multiplier for each weakly periodic field (three fields for the current problem). In particular, a neat result is that the classical Neumann boundary condition is obtained when the penalty becomes very large. In the numerical examples, we investigate the following characteristics: the mesh convergence for different boundary approximations, the sensitivity for the choice of penalty parameter, and the influence of RVE‐size on the macroscopic response.
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DOI：
10.1016/j.cma.2010.06.023
发表时间：
2011-01-01
影响因子：
7.2
作者：
Larsson, F.;Runesson, K.;Vafadari, R.
通讯作者：
Vafadari, R.
影响因子：
9.2
作者：
Ying Zhao;P. Stein;Yang Bai;Mamun Al-Siraj;Yangyiwei Yang;Bai-Xiang Xu
通讯作者：
Ying Zhao;P. Stein;Yang Bai;Mamun Al-Siraj;Yangyiwei Yang;Bai-Xiang Xu
影响因子：
5.3
作者：
C. Miehé
通讯作者：
C. Miehé
模拟微异质固体结构尺度材料响应恶化的模型
DOI：
--
发表时间：
2001
期刊：
影响因子：
--
作者：
T. Zohdi;P. Wriggers
通讯作者：
P. Wriggers
影响因子：
4.1
作者：
R. Jänicke;F. Larsson;K. Runesson
通讯作者：
R. Jänicke;F. Larsson;K. Runesson