欧拉描述的有限应变固结控制方程之矩阵表述

Matrix Formulation of Eulerian Governing Equations of Finite Strain Consolidation Theory

采用Voigt规则建立了欧拉描述的有限应变固结控制方程的矩阵表述形式.同时将Truesdell率型本构关系引入到欧拉描述的有限应变固结理论中,阐明了Truesdell率与常用的Jaumann率之间的关系.结果表明,欧拉描述的有限应变固结控制方程的矩阵形式要比T.L.和U.L.两种物质描述方法的矩阵形式简洁;当忽略Truesdell率型本构矩阵中的某子矩阵时,就退化为Jaumann率型本构矩阵.可供有限元编程分析参考.

Using Voigt rule, the matrix formulation of governing equations of finite strain consolidation with Eulerian description is proposed in this paper. With the introduction of Truesdell derivative into the constitutive equation of finite strain consolidation theory with Eulerian description, comparison is made between Truesdell derivative and Jaumann derivative. The results show that the matrix formulation of governing equations of finite strain consolidation with Eulerian description has a more simple form than those with both T.L. and U.L. descriptions. The constitutive matrix using TruesdeU derivative can be reduced to that using Jaumarm derivative, when a sub-matrix is ignored. The conclusions could be provided for finite element programming.