Kármán and the development of the material models of concrete

The failure models developed until the 1960ies were defined by the testing equipment: the triaxial loading cell which was developed at the beginning of the last century by Karman. The axial loading was performed with a solid loading plate, the central-symmetric transverse loading through hydraulic pressure. Therefore, the characterization of the failure surface with the hydrostatic normal stress and octahedral shear stress without any reference to deformations was a logical consequence. In 1963 Hilsdorf proposed a brush-type loading equipment. Using brushes Kupfer carried out his wellknown biaxial loading tests which made possible the characterization of concrete strength by means of the principal stresses. In 1977 Ottosen applied in his model for multiaxial strength of concrete the stress invariants. The same did CEB in the Bulletin d’Information N°. 156. Van Mier (1984) applied brushes and proposed a 3D-type representation using contour lines. The MC2010 returned to the Ottosen model and declared concrete as frictional material. Using the principal stresses, a new, transparent (and physically really sound) form of representation of the failure surface showing the strength increase due to bi- and triaxial loading is presented.