Numerical finite element formulation of the Schapery non‐linear viscoelastic material model

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Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network (2006, background): “Several variants of Schapery s approach have been proposed to describe the nonlinear time-dependent response of composites (Papanicolaou et al., 2004; Haj-Ali and Muliana, 2004).”
A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials (2011, methodology): “(9), the deviatoric strain tensor enve;tij and the volumetric strain e nve;t kk can be expressed in terms of the hereditary integrals, such that (Haj-Ali and Muliana, 2004): enve;tij ¼ 1 2 gt0J0 þ gt1gt2 XN n¼1 Jn gt1gt2 XN n¼1 Jn 1 expð knDwtÞ knDw t " # Stij 1 2 gt1 XN n¼1 Jn expð knDwtÞqt Dtij;n…”
On the development and parameter identification of Schapery-type constitutive theories (2008, background): “For example, Beijer and Spoormaker (2002), Haj-Ali and Muliana (2004), Henriksen (1984), Hu et al.”