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On the theory of fourth-order tensors and their applications in computational mechanics. (English) Zbl 0980.74006
Summary: We give a mathematical treatment of fourth-order tensors 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 as an invariant quantity with respect to any co-ordinate system transformation which justifies the use of absolute notation preferred in this work. As the most important application of fourth-order tensors, we study elastic moduli in a material, and give a spatial description for various hyperelastic models.

MSC:
74B99 Elastic materials
15A72 Vector and tensor algebra, theory of invariants
74S99 Numerical and other methods in solid mechanics
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