Parabolic mohr failure criterion in terms of invariants for brittle isotropic materials

The modified Mohr/Coulomb failure criterion with a linear envelope in the r egion of sheer fracture for brittle isotropic materials generates in princi pal stress space a cone-shaped failure surface with straight meridians. The cross-sections in the deviatoric planes are similar irregular hexagons, wh ich expand with increasing hydrostatic pressure. This is in contradiction t o the experimental results, i.e. for concrete, indicating parabolic meridia ns and cross-sections. whose shape changes from nearly triangular to nearly circular. A better approximation to the test data is obtained by choosing a parabolic Mohr envelope in combination with a limit circle. The criterion is given in Lode coordinates as well as in terms of the invariants of the stress tensor.