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Theory Manual Version 3.6
 Subsubsection 5.6.5.3: Specific Strain Energy Up Subsection 5.6.5: Constitutive Models for Damage and Yield Criteria Subsubsection 5.6.5.5: Maximum Normal Stress 

5.6.5.4 Von Mises Stress

For this criterion it is assumed that damage or yield is initiated by increases in the von Mises (or effective) stress, . Thus, where is the deviatoric part of . To evaluate the damage surface normal in this case, we must use the chain rule, From the hyperelasticity relation in eq.(5.6.2-5) it can be shown that where is the fourth-order spatial elasticity tensor associated with the strain energy density . Then, it can be shown that where From the von Mises criterion in eq.(5.6.5.4-1), it can be shown that Substituting Eqs.(5.6.5.4-5)-(5.6.5.4-6) into eq.(5.6.5.4-4) provides the surface normal .
 Subsubsection 5.6.5.3: Specific Strain Energy Up Subsection 5.6.5: Constitutive Models for Damage and Yield Criteria Subsubsection 5.6.5.5: Maximum Normal Stress