Temporal homogenization formula for viscoelastic-viscoplastic model subjected to local cyclic loading

In this study, a temporal homogenization formula was developed to predict the response fields (i.e., stress, strain, and displacement) of a viscoelastic-viscoplastic model under local cyclic loading. It is the first attempt to apply the temporal homogenization formula of constitutive equations with higher-order differential forms on the viscoelastic-viscoplastic model. The temporal homogenization formula is classified into two types: non-updated temporal homogenization formula and updated temporal homogenization formula. Initial boundary value problem was classified into the global initial boundary value problem and the local initial boundary value problem. To verify this method, two examples were used: (i) when a uniaxial cyclic load is applied to a one-dimensional bar and (ii) when a multiaxial cyclic load is applied to a three-dimensional bar. On comparing the accuracy of the non-updated and the updated temporal homogenization formula, it can be clearly seen that the updated temporal homogenization formula yielded more accurate results.