A New and Efficient Approach to Determining the Rate of the Second-Order Symmetric Tensor and Its Isotropic Function  

作　　者：Chunyu Meng Mingxiang Chen 

机构地区：[1]Department of Engineering Mechanics,School of Civil Engineering,Wuhan University,Wuhan,430072,China

出　　处：《Acta Mechanica Solida Sinica》2022年第5期867-879,共13页固体力学学报（英文版）

摘　　要：When the rate of a symmetric second-order symmetric tensor is discussed,the spin of the principal axis is involved.This paper proposes a method to establish the basis-free expression of the spin in terms of tensor and its rate by making use of the tensor function representation theorem.The proposed method is simple and the expression of the spin established is compact.To obtain the rate of the isotropic function of a second-order symmetric tensor,the fourth-order tangent tensor needs to be derived,which is the derivative of the tensor function to the second-order tensor.By decomposing the second-order symmetric tensor space into two orthogonal subspaces,the closed-form fourth-order tangent tensor is decomposed into two parts,which are linear mappings in these two orthogonal subspaces,respectively.These two linear mappings are derived in an extremely simple way.Finally,the method proposed in this paper is applied to obtain the expression of the relationship between material logarithmic strain rate and deformation rate.The whole process is simple and avoids tedious operations.

关 键 词：Tensor rate Basis-free spin Tensor function rate Orthogonal space decomposition 

分 类 号：TP212[自动化与计算机技术—检测技术与自动化装置]