100 / 2017-05-20 15:21:08

A novel approach to derive the general expression of spin tensors and strain/stress measures in large deformation based on the characteristic bases

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In the reliability engineering and structural analysis, the large deformation will affect the security of structures and precision control. Particularly, the large deformation exists everywhere in our life and the small deformation hypothesis is an approximate approach to the large deformation by without considering the higher order error term. The rotation phenomenon is a difficult issue in the large deformation analysis. Based on the theory of the second-order tensor and algebra, M.M. Mehrabadi derived the general representation of the relative spin tensor, which is independence from any coordination system. In addition, the logarithmic strain measure (real strain) and the stress measure conjugate to the logarithmic strain have been widely used in structural analysis, such as the Finite element analysis software ABAQUS. Anne Hoger used the complicate theory to derive the general representation of the material time derivative of the logarithmic strain and the stress conjugate to the logarithmic strain. In this paper, based on the characteristic bases theory, we propose a novel approach to derive the general representation of the Euler spin tensor, the Lagrangian spin tensor, the relative spin tensor, the material time derivative of the logarithmic strain and the stress conjugate to the logarithmic strain, and they can be written in a same general form. This analysis process has a clear physical background and is simpler and more concise.