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

The Incremental Variational Formulation (IVF) provides a thermodynamically consistent framework for inelastic analysis, however evaluating stresses and the consistent tangent modulus ordinarily demands cumbersome higher-order tensor differentiation. To remove this bottleneck, we embed the Complex-Step Derivative Approximation (CSDA) which delivers high-precision first- and second-order derivatives directly into IVF, thereby creating a high-fidelity, implementation-friendly scheme. When applied to a uniaxial tension–unloading simulation of a finite-strain linear viscoelastic solid, the CSDA–IVF response reproduces the reference solution with an average relative error of 0.82%. In addition, Newton–Raphson iterations exhibit clear quadratic convergence, confirming the method’s robust numerical performance. Because CSDA supplies accurate numerical derivatives, analysts are freed from laborious hand-derived tensor calculus and the overhead of configuring automatic-differentiation tools. The proposed CSDA–IVF thus enables straightforward deployment of sophisticated inelastic constitutive models by specifying only the energy potentials, making it well-suited for integration into commercial finite-element platforms.