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A proposal of a novel geometrical measure of material effort

Wacławiak Krzysztof

Engineering Transactions

2022

Vol. 70, iss. 2

183--199

A stress tensor may be presented as a surface delimited by a stress vector located at angles α1, α2, α3 in relation to axes x, y, z. Geometrically, it outlines a domain and is linked to the loading. In this study, the area of such a surface and the volume of the domain were determined, along with their cross-sections with reference to areas and circumferences. Different stresses were also compared. This article presents cases of uniaxial, biaxial, triaxial tension and pure shear for an isotropic solid body. The analysis of a stress tensor in this conceptual work does not involve any material features, yet yields interesting results, particularly in the case of pure shear and uniaxial tension.

Limit Condition for Anisotropic Materials with Asymmetric Elastic Range

Ostrowska-Maciejewska J., Pęcherski R. B., Szeptyński P.

Engineering Transactions

2012

Vol. 60, iss. 2

125-138

In the paper a new proposition of an energy-based hypothesis of material effort is introduced. It is based on the concept of influence functions introduced by Burzyński and on the concept of decomposition of elastic energy density introduced by Rychlewski. A new proposition enables description of a wide class of linearly elastic materials of arbitrary symmetry exhibiting strength differential effect.