A representation theorem for volume-preserving transformations

被引：19

作者：

Carroll, MM ^{[1
]}

机构：

[1] Rice Univ, Dept Mech Engn & Mat Sci, Houston, TX 77251 USA

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2004年 / 39卷 / 02期

关键词：

partial differential equations; Jacobian; volume-preserving; finite elasticity;

D O I：

10.1016/S0020-7462(02)00167-1

中图分类号：

O3 [力学];

学科分类号：

08 [工学]; 0801 [力学];

摘要：

A general solution is presented for the partial differential equation partial derivativeu/partial derivativex = k(x), where u and x are n-vector fields, partial derivativeu/partial derivativex denotes the Jacobian of the transformation x --> u and k(x) is a scalar-valued function. The solution for the case k(x) = 1 is of special interest because it furnishes a representation theorem for volume-preserving transformations in an n-dimensional space. Such a representation for the case n = 2 was obtained by Gauss. The solution for n = 3, presented here, furnishes a representation for isochoric (volume-preserving) finite deformations, which are important in the mechanics of highly deformable incompressible solid materials. (C) 2003 Elsevier Science Ltd. All rights reserved.

引用

页码：219 / 224

页数：6