Some basic principles in dynamic theory of viscoelastic materials with voids

作     者：LUO En LI WeiHua 

作者机构：Department of Applied Mechanics and EngineeringSun Yat-sen UniversityGuangzhou 510275China 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2007年第50卷第3期

页      面：370-378页

核心收录：

学科分类：08[工学] 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 National Natural Science Foundation of China (Grant No. 10172097) the Scientific Foundation of the Ministry of Education of China for Doctoral Program (Grant No. 20030558025) 

主　　题：dynamic theory of viscoelastic materials with voids principle of virtual work reciprocal theorem simplified Gurtin-type variational principle complementary relation 

摘      要：According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo, some basic principles in the dynamic theory of viscoelastic materials with voids can be estab- lished systematically. In this paper, an important integral relation in terms of con- volutions is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem, but also to derive systemati- cally the complementary functionals for the eight-field, six-field, four-field simpli- fied Gurtin-type variational principles and the potential energy-functional for the two-field one in the dynamic theory of viscoelastic materials with voids by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.