Hoffman failure criterion

To account for different strengths in tension and compression, Hoffman added linear terms to Hill s equation (the basis for the Tsai-Hill criterion) [2-23]  

Note for materials with equal strengths in tension and compression that P is 45° and the center of the ellipsoid is at the origin. 

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Figure 2-42 Hoffman Failure Criterion for Glass-Epoxy (Data from Tsai [2-21])...

Figure 2-43 Hoffman Failure Criterion for Graphite-Epoxy (Data from Kim [2-24])...

Figure 2-44 Hoffman Failure Criterion for Boron-Epoxy (Data from Pipes and Cole [2-25])...

Thus, the Tsai-Wu tensor failure criterion is obviously of more general character than the Tsai-Hill or Hoffman failure criteria. Specific advantages of the Tsai-Wu failure criterion include (1) invariance under rotation or redefinition of coordinates (2) transformation via known tensor-transformation laws (so data interpretation is eased) and (3) symmetry properties similar to those of the stiffnesses and compliances. Accordingly, the mathematical operations with this tensor failure criterion are well-known and relatively straightforward. 

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