连续胶体材料化学-力学耦合有限元理论及其在ABAQUS中UEL程序实现

Finite element theory of chemo-mechanical coupling and the program implementation of UEL in ABAQUS for the continuous colloidal material

基于哈密顿原理,得到水凝胶的化学-力学耦合控制方程的等效积分形式和有限元形式。在整体坐标系下推导出用形函数表示的化学-力学耦合应变矩阵和单元刚度矩阵,并且得到在局部坐标系下的离散化形式。结合ABAQUS软件,编制了用户单元子程序UEL,通过数值算例验证了所开发单元的正确性,为在ABAQUS软件中实现各种耦合问题的有限元UEL编程提供了参考依据。

Based on Hamilton＇s principle,the equivalent integral forms of chemo-mechanical coupling governing equations and corresponding finite element forms are obtained.The strain matrix and element stiffness matrix represented by shape functions in chemo-mechanical coupling are derived in the global coordinate system.Discrete forms of element stiffness matrix are acquired in the local coordinate system.The user element subroutine UEL is programmed in ABAQUS finite element package.The numerical example shows the validity of the UEL developed,which can provide some references for the programming realization of UEL in ABAQUS software for various coupling problems with the form of the finite element.