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一种化学-力学耦合连续介质理论与数值格式
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.
作者姓名:杨庆生  马连华  刘宝胜
作者单位:北京工业大学工程数值模拟中心 北京工业大学工程数值模拟中心 北京工业大学工程数值模拟中心
基金项目:国家自然科学基金,北京市自然科学基金
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.

关 键 词:连续介质  化学-力学耦合  本构方程  变分原理  有限元
收稿时间:2008-10-09
修稿时间:2009-09-09

A CONTINUUM THEORY AND NUMERICAL PROCEDURE FOR CHEMO-MECHANICAL COUPLING BEHAVIOR
Yang Qingsheng , Ma Lianhua , Liu Baosheng.A CONTINUUM THEORY AND NUMERICAL PROCEDURE FOR CHEMO-MECHANICAL COUPLING BEHAVIOR[J].chinese journal of theoretical and applied mechanics,2010,42(3):422.
Authors:Yang Qingsheng  Ma Lianhua  Liu Baosheng
Affiliation:Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100124, China Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100124, China Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing 100124, China
Abstract:Many continuum media, often described as multifunctional materials, exhibit multi-field coupling behavior and are sensitive to external environmental stimuli. Chemo-mechanical coupling behavior for continuum media was investigated in this paper. From the point view of the thermodynamics and chemical potential, we have obtained the constitutive equations and governing equations of chemo-mechanical coupling problem. Energy functional of chemo-mechanical coupling equations has been established by variational principle, and then the equivalent integration forms and finite element formulation of the coupled governing equations are derived. The chemo-mechanical coupling behaviors of continuum media are analyzed by numerical examples. The numerical results show that the mechanical and chemical fields interact with each other in a medium. The deformation 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 of chemo-mechanical coupling behavior of continuum media. The chemo-mechanical coupling behavior of continuum media can be reflected clearly in the present model.
Keywords:continuum medium  chemo-mechanical coupling  constitutive law  variational principle  finite element method  
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