EI、Scopus 收录

 引用本文: 陈明祥. 关于返回映射算法中应力的四阶张量值函数[J]. 力学学报, 2010, 42(2): 228-238.
Mingxiang Chen. n the fourth order tensor valued function of the stress in return map algorithm[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(2): 228-238.
 Citation: Mingxiang Chen. n the fourth order tensor valued function of the stress in return map algorithm[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(2): 228-238.

## n the fourth order tensor valued function of the stress in return map algorithm

• 摘要: 针对各向同性材料，基于一组相互正交的基张量，建立了一套有效的相关运算方法. 基张量中的两个分别是归一化的二阶单位张量和偏应力张量，另一个则使用应力的各向同性二阶张量值函数经过归一化构造所得，三者共主轴. 根据张量函数表示定理，本构方程和返回映射算法中所涉及到的应力的二阶、四阶张量值函数及其逆都由这组基所表示. 推演结果表明：这些张量之间的运算，表现为对应系数矩阵之间的简单关系. 其中，四阶张量求逆归结为对应的3\times3系数矩阵求逆，它对二阶张量的变换则表现为该矩阵对3times 1列阵的变换. 最后，对这些变换关系应用于返回映射算法的迭代格式进行了相关讨论.

Abstract: The inversion of a fourth order tensor valued functionof the stress and its transformation to the second order tensor are requiredin the return map algorithm for implicit integration of the constitutiveequation. Based on a set of the base tensors which are mutually orthogonal,this paper presents an effective methodology to perform those tensoroperations for the isotropic constitutive equations. In the scheme, two ofthe base tensors are the second order identity tensor and the deviatoricstress tensor, respectively. Another base tensor is constructed using anisotropic second order tensor valued function of the stress. The three basetensors are coaxial. By making use of the representation theorem forisotropic tensorial functions, all the second order, the fourth order tensorvalued functions of the stress involved can be represented in terms of thebase tensors. It shows that the operations between the tensors are specifiedby the simple relations between the corresponding matrices. The inversion ofa fourth order tensor is reduced to the inversion of corresponding 3\times3 matrix, and its transformation to the second tensor is equivalent totransformation of 3\times 3 matrix to 3\times 1 column matrix. Finally,some discussions are given to the application of those transformationrelationships to the iteration algorithm for the integration of theconstitutive equations.

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈