JP LIMIT STATE CRITERION FOR BRITTLE MATERIALS
J.Podgórski, Technical University of Lublin, Faculty of Civil Engineering, Poland
The three failure criteria (Fig. 1) had been considered to analysis:
§ author’s (PJ) criterion, proposed in 1986 , which limit state depends on three tensor invariants (I1, J2, J3)
§ well known Drucker-Prager criterion, (I1, J2)
§ classical Huber-Mises criterion (J2 )
Limit curves described by eqs. (1), (2), (3) in biaxial stress state are shown in Fig. 1. Fig. 2 shows “tension meridian” and “compression meridian” of the PJ and Drucker-Prager limit surface in t0 – s0 plane and Fig. 3 shows isometric view of this surfaces.
The PJ criterion was proposed by one of the author’s (J.P.) in 1986  in the form:
- function describing the shape of limit surface in deviatoric plane,
- mean stress,
- octahedral shear stress,
- first invariant of the stress tensor,
- second and third invariant of the stress deviator,
- alternative invariant of the stress deviator,
- material constants.
Classical failure criteria, like Huber-Mises, Tresca, Drucker-Prager, Coulomb-Mohr as well as some new ones proposed by Lade, Matsuoka Ottosen, are particular cases [cf. 1,2] of the general form (1) PJ criterion.
Material constants can be evaluated on the basis of some simple material test results like:
§ fc - failure stress in uniaxial compression,
§ ft - failure stress in uniaxial tension,
§ fcc - failure stress in biaxial compression at s1/s2 = 1,
§ f0c - failure stress in biaxial compression at s1/s2 = 2,
§ fv - failure stress in triaxial tension at s1/s2/s3 = 1/1/1,
For concrete or rock-like materials some simplifications can be taken on the basis of test results in biaxial stress state and R. M. Haythornthwaite “tension cutoff” hypotesis:
fcc=1.1 fc , f0c=1.25 fc , fv= ft.
With notation used in eq. (1) well-known Drucker–Prager criterion can be written:
Two material constants C0 and C1 can be evaluated on the basis of uniaxial test results like
ft and fc .
Classical criterion proposed by T. Huber and R. von Mises can be obtained by simplification of the general form (1):
Material constant C0 , in this analysis, is evaluated with uniaxial tension failure stress ft.
Fig. 1. Limit curves in biaxial state of stress
Fig. 2. PJ and Drucker-Prager limit surface cross section by t0 – s0 plane.
Fig. 3. PJ and Drucker-Prager limit surface – isometric view.
 J. Podgórski (1985). General Failure Criterion for Isotropic Media. Journal of Engineering Mechanics ASCE, 111, 2, 188-201.
 Podgórski J.: Limit state condition and the dissipation function for isotropic materials.
Archives of Mechanics, 36(1984) 3, 323-342.