摘要
讨论完全弹性体的有限弹性变形问题．根据变形可恢复性，采用两种参考系度量应力分量，导出恒等式式中（δｉｋ＋ｕｉ，ｋ）Ｓｋｙ＝σｉｙ为有限变形梯度张量，Ｓｉｙ为Ａ参考系中的Ｋｉｒｃｈｈｏｆｆ应力张量，σｉｙ为Ｂ参考系中的Ｅｕｌｅｒ应力张量．上式即为有限弹性变形的本构方程．有限弹性变形的解法为首先在Ｂ参考系中采用经典线性理论解出σｉｙ，而后代入上式，ｕｉ与Ｓｉｙ可解．
This paper discusses the problem of finite elastic deformation. According to the recoverability of elastic deformation,the identical formula is derived by using the stress component of measure in two reference systems: Where, (δik+ui,k)is a gradien tensor of finite displacement; Siy mean stress components in two reference systems respectively. The constitutive equation has not only quantitatively described the stress tensor Siy and the gradient tensor of the deformation , but also the recover ability of the deformation qualitively.This paper also provides the theoretical basis for finite elastic deformation. are derivedby using the classical theory first of all,then the displacement vector ui and stress component Siy are solved by equation above.
基金
国家煤炭部科学基金
关键词
可恢复性
同态方程
本构方程
弹性变形
变形
finite elastic deformation
homomorphic equation
constitutive equation
conservation of geometry
