Failure

Failure#

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Fig. 61 Figure 6.14b Hartsuijker and Welleman (2007)#

Von Mises failure model#

Von Mises assumed failure if the deviatoric stress exceeds a limit value \(s_{max}\):

\[\frac{1}{3}\left((\sigma_1-\sigma_2)^2 + (\sigma_2-\sigma_3)^2 + (\sigma_3-\sigma_1)^2\right) \leq s_{max}^2\]

This is treated in chapter 6.1, 6.2 and 6.4 of the lecture notes Introduction to Continuum Mechanics (Hartsuijker and Welleman, 2007).

Tresca’s failure model#

Tresca assumed failure if the shear stress exceeds a certain limit value \(c\):

  • \(|\sigma_1 - \sigma_2| \leq 2c\)

  • \(|\sigma_2 - \sigma_3| \leq 2c\)

  • \(|\sigma_3 - \sigma_1| \leq 2c\)

This is treated in chapter 6.3 and 6.4 of the lecture notes Introduction to Continuum Mechanics (Hartsuijker and Welleman, 2007).

Exercises#

  • Additional question Problems 3 in chapter 5.3 of the lecture notes Introduction to Continuum Mechanics (Hartsuijker and Welleman, 2007). Answers are available in chapter 5 of the lecture notes.

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