SECOND ORDER TENSOR INVARIANTS IN CONTINUUM MECHANICS USING THE LAGRANGIAN FORMULATIONS
The paper presents for second order tensors a simple account of invariant theory from the point of view of its application to continuum mechanics. It is demonstrated that working with the tensors themselves instead of working with their components exclusively, leads not only to certain added convenience in manipulation, but also to enhanced understanding of the concepts of eigenvalues, eigenvectors and invariations of second order tensors. In addition, it is shown that in general curvilinear coordinate systems (Lagrangian point of view in continuum mechanics) the classical computer techniques can be applied provided the mixed tensor components are used. In particular invariants, eigenvalues and eigenvectors are explicit functions of the deformation process that the curvilinear coordinate system is undergoing. Finally, a general numerical scheme is given in order to be used and implemented in a computer code.
Bibliographic Reference: EUR 9165 EN (1984) MF, 30 P., BFR 120, BLOW-UP COPY BFR 150, EUROFFICE, LUXEMBOURG, POB 1003
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Record Number: 1989122104100 / Last updated on: 1987-01-01
Available languages: en