A note on the derivation of the derivatives of invariants of stretch tensor to the right Cauchy-Green tensor

作     者：TIAN Dongyan, JIN Ming and DUI Guansuo (Institute of Engineering Mechanics, School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing 100044, China) 

作者机构：Institute of Engineering Mechanics School of Civil Engineering and Architecture Beijing Jiaotong University Beijing 100044 China 

出 版 物：《Progress in Natural Science:Materials International》 (自然科学进展·国际材料(英文))

年 卷 期：2006年第16卷第1期

页      面：96-99页

核心收录：

学科分类：08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0702[理学-物理学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Supported by the school foundation of Beijing Jiaotong University (Grant No. TJ2002J0180) 

主　　题：continuum mechanics invariant strain energy tangent modulus. 

摘      要：A new approach for the derivation of the principal invariants of the stretch tensor with respect to the right Cauchy- Green tensor is presented in this paper. According to the definition of the derivation of tensor function, the three first-order derivatives for the principal invariants of the stretch tensor are obtained through derivation directly to the right Cauchy-Green tensor by incremental method. Then the three second-order derivatives are yielded by the derivation to the right Cauchy-Green strain tensor directly. Furthermore, an explicit expression of the tangent modulus of the general Varga material is given as an example.