Drucker–Prager Yield Criterion - Expressions For A and B

Expressions For A and B

The Drucker–Prager model can be written in terms of the principal stresses as

\sqrt{\cfrac{1}{6}\left} = A + B~(\sigma_1+\sigma_2+\sigma_3) ~.

If is the yield stress in uniaxial tension, the Drucker–Prager criterion implies

\cfrac{1}{\sqrt{3}}~\sigma_t = A + B~\sigma_t ~.

If is the yield stress in uniaxial compression, the Drucker–Prager criterion implies

\cfrac{1}{\sqrt{3}}~\sigma_c = A - B~\sigma_c ~.

Solving these two equations gives

A = \cfrac{2}{\sqrt{3}}~\left(\cfrac{\sigma_c~\sigma_t}{\sigma_c+\sigma_t}\right) ~;~~ B = \cfrac{1}{\sqrt{3}}~\left(\cfrac{\sigma_t-\sigma_c}{\sigma_c+\sigma_t}\right) ~.

Read more about this topic:  Drucker–Prager Yield Criterion

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