材料力学和理论力学常使用张量，比如应力张量、应变张量和惯性张量等。张量到底是什么，如何应用？下文做个尝试性探讨。

摘要 应力张量、应变张量和惯性张量等是力学中常见的二阶张量，在力学应用中有重要意义。二阶张量是向量间的线性变换，构成向量空间，向量并矢可作为张量空间的基。本文介绍了张量对向量的作用原理和坐标变换，对常见的力学张量进行说明，分析了力学张量坐标变换、主轴及主值等。使用张量来分析常见的力学张量，有益于明晰力学基本概念，简化力学分析过程和表述形式。

关键词：二阶张量；向量；并矢；向量空间；力学张量

中图分类号：O302    文献标识码：A     文章编号：

Second-OrderTensors with Application in Mechanics

Abstract Stress tensors, strain tensors and inertial tensors et al. are familiar and important second-order tensors in mechanics. The second-order tensor can be defined as an operator acts on a vector or transformation between vectors. Multidimensional Linear vector space is constituted with second-order tensors in which dyads is base tensor. In this paper, actions on vectors and coordinates transformations of the second-tensors are introduced, descriptions of common second-order tensor in mechanics based on basic notion of tensors are presented. Applied tensor in mechanics, it is easy to understand concepts of mechanics and simplify analysis procedure of mechanics.

KeyWords: Second Order Tensors; Vectors; Dyads；Linear Vector Space; Tensors in Mechanics

目录

1 概述... 1

2 张量的一般定义... 2

3 二阶张量及性质... 2

      3.1.笛卡尔张量... 2

      3.2 笛卡尔张量下的向量变换... 3

      3.3张量坐标变换... 3

4.力学中的张量... 4

      4.1应力/应变张量... 4

      4.2惯性张量... 4

5 结语

... 5