Thermal Stresses and Theorem on Decomposition  

作　　者：Valeriy Lokhov Yuriy Nyashin 

机构地区：[1]Department of Theoretical Mechanics and Biomechanics,Perm National Research Polytechnic University

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》2014年第2期175-179,共5页南京航空航天大学学报（英文版）

摘　　要：The thermal expansion strain is considered as a special case of eigenstrain.The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents:Impotent eigenstrain(not causing stress in any point of a body)and nilpotent eigenstrain(not causing strain in any point of a body).According to this theorem,the thermal stress can be easily found through the nilpotent eigenstrain.If the eigenstrain is an impotent one,the thermal stress vanishes.In this case,the eigenstrain must be compatible.The authors suggest a new approach to measure of eigenstrain incompatibility and hence to estimate of thermal stresses.The thermal expansion strain is considered as a special case of eigenstrain. The authors proved the theo- rem on decomposition of eigenstrain existing in a body into two constituents： Impotent eigenstrain （not causing stress in any point of a body） and nilpotent eigenstrain （not causing strain in any point of a body）. According to this theorem, the thermal stress can be easily found through the nilpotent eigenstrain. If the eigenstrain is an im- potent one, the thermal stress vanishes. In this case, the eigenstrain must be compatible. The authors suggest a new approach to measure of eigenstrain incompatibility and hence to estimate of thermal stresses.

关 键 词：EIGENSTRAIN thermal stresses DECOMPOSITION impotent eigenstrain nilpotent eigenstrain functional space 

分 类 号：O34[理学—固体力学]