In continuum mechanics

Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...

, Haigh–Westergaard stress space, or simply stress space is a 3-dimensional space in which the three spatial axes represent the three principal stresses for a body subject to stress

Stress (physics)

In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

.

Functions of the principal stresses, such as the yield function, can be represented by surfaces in stress space. In particular, the surface represented by von Mises

Von Mises stress

The von Mises yield criterion suggests that the yielding of materials begins when the second deviatoric stress invariant J_2 reaches a critical value k. For this reason, it is sometimes called the J_2-plasticity or J_2 flow theory. It is part of a plasticity theory that applies best to ductile...

yield function is a right circular cylinder, equiaxial to each of the three stress axes.

In 2-dimensional models, stress space reduces to a plane and the von Mises yield surface reduces to an ellipse.