Stress space

Short description: Mathematical representation of stress in continuum dynamics

Visualisation of a Cauchy stress tensor σ in the Haight-Westergaard stress space

In continuum mechanics, Haigh–Westergaard stress space, or simply stress space is a 3-dimensional space in which the three spatial axes represent the three principal stresses of a body subject to stress. This space is named after Bernard Haigh and Harold M. Westergaard.

In mathematical terms, H-W space can also be interpreted (understood) as a set of numerical markers of stress tensors orbits (with respect to proper rotations group – special orthogonal group SO3); every point of H-W space represents one orbit.[1]

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 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.

## See also

* Bigoni–Piccolroaz yield criterion

## References

1. ↑ Ziółkowski, Andrzej Grzegorz (9 August 2022). "Parametrization of Cauchy Stress Tensor Treated as Autonomous Object Using Isotropy Angle and Skewness Angle". Engineering Transactions 70 (3): 239–286. doi:10.24423/EngTrans.2210.20220809. ISSN 2450-8071. https://et.ippt.gov.pl/index.php/et/article/view/2210.

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