Implementation of Large-Deformation Viscoelastic Models Using the Incremental Variational Formulation with Complex-Step Derivative Approximation

To support product design and performance prediction, this study proposes CSDA–IVF, a material-update framework applicable to finite-strain inelastic analysis. CSDA–IVF applies the complex-step derivative approximation to tensor differentiation within an incremental variational formulation, requiring only the Helmholtz free energy and a dissipation potential to compute internal variables, stresses, and consistent tangent moduli, without analytical tensor derivatives. First derivatives attain machine precision, while generalized complex-step second derivatives achieve fourth-order truncation accuracy. An Abaqus/UMAT implementation for finite-strain viscoelasticity in uniaxial tension and Cook’s bending demonstrates accuracy, Newton convergence, and stability, indicating applicability to advanced material modeling.