On the Space of Stress Invariants

Abstract

The representation of stress through its three invariants I1 ,I2 , and I3 has been examined. It has been shown that all possible states of stress are mapped into a connected region of the space of stress invariants that is bounded by two surfaces which meet in a cusp on a curve which corresponds to states of isotropic stress. All other states of stress for which two principal stresses are equal, lie on this surface. The I1 axis corresponds to one-dimensional states of stress. Two-dimensional stresses are represented by a connected region of the I1 –I2 plane. The negative half of the I2 axis corresponds to pure shear. The positive half of the I2 axis, and the I3 axis, do not correspond to any states of stress. The representation of yield surfaces in this space has also been considered.