Considerations on elliptical failure envelope associated to Mohr-Coulomb criterion

Abstract

Mohr-Coulomb theory is mostly used in civil engineering as it is suitable for soils, rock, concretes, etc., meaning that the theory is generally used for brittle facture of the materials, but there are cases when it matches ductile behaviour also. The failure envelope described by the Mohr-Coulomb criterion is not completely accurate to the real yield envelope. The ductile or brittle behaviour of materials could not be incorporated in a linear envelope suggested by classic stress state theories and so, there have been a number of authors who have refined the notion of yield envelope so that it would fit better to the actual behaviour of materials. The need of a realistic yield envelope comes from the demand that the failure state should be able to be predicted in a fair manner and with as little errors as possible. Of course, certain criteria will be closer to the actual situation, but there is a constant need to unify and refine the limit stress theories in order to avoid problems as defining boundaries of application areas on numerical programs. Mohr-Coulomb's yield envelope is the most used one on programs, can be reduced to Tresca theory when the materials are conducting a ductile behaviour and has a linear simplified form. The paper presents some considerations with respect to the elliptical failure envelope correlated to the Mohr-Coulomb theory. The equations have been rewritten for triaxial situation to describe a more accurate state of stress that is encountered under real conditions in materials. Using the Mohr's circles to define the yield envelope, the calculus has been made in in order to determine the yield stress at tensile tests.