Engineering Transactions, 70, 3, pp. 239–286, 2022

Parametrization of Cauchy Stress Tensor Treated as Autonomous Object Using Isotropy Angle and Skewness Angle

Andrzej Grzegorz ZIÓŁKOWSKI
Institute of Fundamental Technological Research Polish Academy of Sciences

Intrinsic features (eigenproperties) of the Cauchy stress tensor are discussed. Novelty notions of isotropy and skewness mode angles are introduced for the improved parametric description of spherical (isotropic) and deviatoric (anisotropic) components of stress tensor. The skewness angle is defined with pure shear employed as a comparison reference mode upon observing that pure shear states can be interpreted as elementary (atomic) blocks of any macroscopic deviatoric stress state. An original statistical-physical interpretation of the stress tensor orthogonal invariants is provided. A micromechanical explanation for observed decrease of the stress tensor anisotropy factor values, measured in terms of the tensor orbit diameter, with stress deviator diverging from pure shear mode, is proposed. Explicit reasons explaining why biaxial experimental layouts (simple shear and/or planar shear) are insufficient for the comprehensive characterization of materials properties submitted to complex stress states loadings are presented. New explicit formulas for the triaxiality factor valid for biaxial stress states are delivered.
Keywords: Cauchy stress; oriented geometrical object; isotropy angle; skewness angle; isomorphic cylindrical coordinates; pure shear, comparison reference state; anisotropy factor; biaxial tests; simple shear; planar shear; triaxiality factor.
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DOI: 10.24423/EngTrans.2210.20220809