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杨庆生 马连华 刘宝胜. 一种化学-力学耦合连续介质理论与数值格式[J]. 力学学报, 2010, 42(3): 422-431. DOI: 10.6052/0459-1879-2010-3-2008-616
引用本文: 杨庆生 马连华 刘宝胜. 一种化学-力学耦合连续介质理论与数值格式[J]. 力学学报, 2010, 42(3): 422-431. DOI: 10.6052/0459-1879-2010-3-2008-616
Qingsheng Yang, Lianhua Ma, Baosheng Liu. A continuum theory and numerical procedure for chemo-mechanical coupling behavior[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 422-431. DOI: 10.6052/0459-1879-2010-3-2008-616
Citation: Qingsheng Yang, Lianhua Ma, Baosheng Liu. A continuum theory and numerical procedure for chemo-mechanical coupling behavior[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 422-431. DOI: 10.6052/0459-1879-2010-3-2008-616

一种化学-力学耦合连续介质理论与数值格式

A continuum theory and numerical procedure for chemo-mechanical coupling behavior

  • 摘要: 对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.

     

    Abstract: Many continuum media, often described asmultifunctional materials, exhibit multi-field coupling behavior and aresensitive to external environmental stimuli. Chemo-mechanical couplingbehavior for continuum media was investigated in this paper. From the pointview of the thermodynamics and chemical potential, we have obtained theconstitutive equations and governing equations of chemo-mechanical couplingproblem. Energy functional of chemo-mechanical coupling equations has beenestablished by variational principle, and then the equivalent integrationforms and finite element formulation of the coupled governing equations arederived. The chemo-mechanical coupling behaviors of continuum media areanalyzed by numerical examples. The numerical results show that themechanical and chemical fields interact with each other in a medium. Thedeformation of media is caused by the concentration variation. Similarly,the external mechanical force can also induce concentration redistribution.The basic theory and simulation method can be applied to analysis ofchemo-mechanical coupling behavior of continuum media. The chemo-mechanicalcoupling behavior of continuum media can be reflected clearly in the presentmodel.

     

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