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Characterizing the non‐proportional and out‐of‐phase extent of tensor paths
Author(s) -
Bishop J. E.
Publication year - 2000
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1046/j.1460-2695.2000.00355.x
Subject(s) - scalar (mathematics) , tensor (intrinsic definition) , cartesian tensor , symmetric tensor , cauchy stress tensor , tensor field , invariant (physics) , tensor density , path (computing) , mathematics , phase (matter) , mathematical analysis , geometry , physics , computer science , exact solutions in general relativity , mathematical physics , quantum mechanics , programming language
Scalar measures are developed for characterizing the non‐proportional and out‐of‐phase extent of any symmetric second‐order tensor path. These scalar measures are constructed by introducing the concept of the principal axes of the tensor path. These measures are independent of the parameterization of the tensor path. As required these measures are invariant under coordinate transformations. For an example, these measures are used to characterize the stress history in the combustion dome of an internal‐combustion automotive engine.