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Derivation of the constitutive relation

LY Li Yu
TW Tzu-Chiang Wang
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The constitutive relation of BMGs can be obtained by combining the yield criterion and the plastic normality rule. The normality rule gives the direction of plastic strain increment, which can be expressed as

This normality rule is described by the nominal stress. Note that f is the flow potential (Eq. (6)) and λ is a coefficient. By substituting the flow potential into the normality rule, we can obtain a relation between the plastic deformation rate and Tij stress, which can be expressed as

The effective plastic strain rate can be expressed as

Similar results can be found in another paper37. Considering the elastic deformation, the strain rate can be written as shown in Eq. (7).

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