The 'I3' generalization of the Galileo−Rankine tension criterion

The paper presents a new tension failure criterion which generalizes the so-called Galileo–Rankine formulation. The criterion can be used as a component of the so-called perfectly no-tension model for masonry and cements as well as for establishing a tension cut-off in complex constitutive models for soils, granular materials and powders. The criterion is described by means of a very concise equation based on the third invariant of the stress tensor, approximating the boundaries of the compressive octant of the principal stress space. This sheds new light on the physical significance of the third invariant of the stress tensor. The new criterion has been validated against two known analytical solutions for no-tension materials and also effectively applied for solving two geotechnical and structural engineering problems. The proposed formulation allows for an efficient implementation in finite-element programmes, removing some of the numerical difficulties associated with the Galileo–Rankine criterion.