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18.104.22.168 Von Mises Stress
For this criterion it is assumed that damage 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.(22.214.171.124-1), it can be shown that Substituting Eqs.(126.96.36.199-5)-(188.8.131.52-6) into Eq.(184.108.40.206-4) provides the surface normal .