A proposal of a novel geometrical measure of material effort

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.