Haigh-Westergaard stress space

Haigh–Westergaard stress space refers to a three-dimensional coordinate system with three mutually perpendicular axes that represent the three principal stresses of an admissible state of stress in a loaded component. This space is also known as the principal stress space and is used to express the stress tensor as a diagonal matrix, distinguishing between tensile and compressive stresses in a multiaxial stressed state.From: Applied Elasticity and Plasticity [2017], Presenting an explicit step-by-step algorithm for lemaitre's ductile damage model with the crack closure effect in tensile-compressive loadings [2023], Nonlinear Computational Solid Mechanics [2017]

Stress invariants and material tests

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Published in Jamshid Ghaboussi, David A. Pecknold, Xiping Steven Wu, Nonlinear Computational Solid Mechanics, 2017

Jamshid Ghaboussi, David A. Pecknold, Xiping Steven Wu

A general three-dimensional state of stress can be represented as a point with coordinates (σ1, σ2, σ3) in a three-dimensional Cartesian space known as principal stress space (Figure 6.3), in which the coordinate axes are aligned with the principal stress directions. The principal stress space is also sometimes called the Haigh–Westergaard stress space (Mendelson 1968).

Stress–Strain Relations

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Published in Mumtaz Kassir, Applied Elasticity and Plasticity, 2017

Mumtaz Kassir

The Haigh–Westergaard stress space consists of three mutually perpendicular axes with three principal stresses as positional coordinates, which are used to represent any admissible state of stress in a loaded component (Section 2.10). In this section, we utilize the same space to determine the geometrical representation of yield surfaces when plastic deformation first appears in the component.

Presenting an explicit step-by-step algorithm for lemaitre's ductile damage model with the crack closure effect in tensile-compressive loadings

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Published in Mechanics Based Design of Structures and Machines, 2023

Ahmad Reza Shamshiri, Farhad Haji Aboutalebi, Mehrdad Poursina

The stress tensor is simply expressed by the principal stresses in the Haigh-Westergaard stress space as a diagonal matrix to distinguish the tensile and compressive stresses for a multiaxial stressed state:

Haigh-Westergaard stress space

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Stress invariants and material tests

Stress–Strain Relations

Presenting an explicit step-by-step algorithm for lemaitre's ductile damage model with the crack closure effect in tensile-compressive loadings