Von Mises criterion

Definition

The von Mises criterion is a mathematical formula used in engineering and materials science to predict yielding of materials under complex loading conditions. It defines a yield surface in terms of the state of stress, and it allows for determining whether a material will yield based on the combination of its principal stresses. This criterion connects the concepts of principal stresses and maximum shear stress by focusing on the idea that yielding occurs when the distortional energy reaches a critical level.

5 Must Know Facts For Your Next Test

1. The von Mises criterion is often referred to as the 'distortion energy theory' because it relates to the energy associated with deforming a material.
2. For ductile materials, the von Mises criterion is typically more reliable than maximum shear stress theory for predicting failure under multi-axial stress states.
3. The yield condition can be mathematically expressed as: $$\sigma_{1}^{2} + \sigma_{2}^{2} + \sigma_{3}^{2} - \sigma_{1}\sigma_{2} - \sigma_{2}\sigma_{3} - \sigma_{3}\sigma_{1} = \sigma_{Y}^{2}$$ where $$\sigma_Y$$ is the yield strength.
4. In practice, engineers use the von Mises criterion to design components that will not fail under expected load conditions, ensuring structural integrity.
5. The von Mises criterion applies well for isotropic materials but may need modifications for anisotropic or composite materials where directional properties affect yielding.

Review Questions

• How does the von Mises criterion relate to the failure of materials under complex loading conditions?
  • The von Mises criterion provides a way to assess whether a material will yield when subjected to multiple stresses acting simultaneously. It does this by combining the effects of all principal stresses into a single measure, which reflects the distortional energy in the material. When this energy exceeds a certain threshold related to the material's yield strength, failure is predicted to occur.
• Compare and contrast the von Mises criterion with other yield criteria like the Tresca criterion.
  • While both the von Mises and Tresca criteria are used to predict yielding in materials, they differ fundamentally in their approach. The Tresca criterion focuses on maximum shear stress and predicts yielding based on the largest difference between principal stresses. In contrast, the von Mises criterion takes into account all principal stresses simultaneously and relies on distortion energy. This makes the von Mises criterion generally more accurate for ductile materials subjected to complex loading.
• Evaluate how understanding the von Mises criterion can impact material selection and design decisions in engineering applications.
  • Understanding the von Mises criterion is crucial for engineers when selecting materials and designing components, as it influences decisions about safety and performance under load. By applying this criterion, engineers can ensure that chosen materials can withstand expected stress levels without yielding. This knowledge directly affects material selection, influencing costs, durability, and safety standards, especially in critical applications such as aerospace and civil engineering.

Related terms

Principal Stresses: The normal stresses acting on specific planes where shear stress is zero, providing key information about the state of stress in a material.

Shear Stress:

The stress that acts parallel to the surface of a material, causing it to deform by sliding along a plane.

Yield Strength:

The amount of stress at which a material begins to deform plastically and will not return to its original shape when the load is removed.