- Stress and strain and the relationship between them can be expressed in tensor formalism.
- The stress tensor is symmetric and can be separated into hydrostatic and deviatoric components.
- The stress state can be expressed by a tensor that has only diagonal components – the principal stress tensor. This is achieved by rotating the axes of the stress tensor, so that the axes are parallel to the forces on the body.
- The measured strain tensor can be separated into a symmetric real strain tensor and an antisymmetric rotation tensor. The real strain tensor can then be separated into dilatational (volume expansion) and deviatoric (shape change) components.
- We can define combinations of the three principal stress components that will cause yield – yield criteria. Different criteria are best used for different materials. The best one for metals is the von Mises yield criterion:
A mathematically simpler approximation to the von Mises yield criterion is the Tresca yield criterion:
- If a yield criterion is plotted in 3D stress space, we have a yield surface.
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