期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 189, 期 2, 页码 419-438出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/S0045-7825(99)00472-7
关键词
fourth-order tensors; tensor algebra; eigenvalue problems; isotropic tensor functions; tangent moduli
Many problems concerned with the mathematical treatment of fourth-order tensors still remain open in the literature. In the present paper they will be considered in the framework of a complete theory involving a set of notations and definitions, a tensor operation algebra, differentiation rules, eigenvalue problems, applications of fourth-order tensors to isotropic tensor functions and some other relevant aspects. A tensor is understood to be an invariant quantity with respect to any co-ordinate system transformation, which justifies the use of absolute notation preferred in this work. As a most important application held of fourth-order tensors, elastic moduli are formulated in a material and a spatial description and given for various hyperelastic material models. (C) 2000 Elsevier Science S.A. All rights reserved.
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