Learning finite viscoelasticity with DAVIS: A supervised framework for generalized standard materials

Abstract

This work revisits the recently proposed data-adaptive viscoelasticity (DAVIS) framework, a spline-based formulation of finite viscoelasticity within the generalized standard materials setting. DAVIS enables a data-driven representation of equilibrium and non-equilibrium constitutive functions while retaining thermodynamic consistency and supporting parameter identification via finite element model updating. The present contribution focuses on improving the robustness and identifiability of non-equilibrium branches in generalized Maxwell-type models. To this end, two extensions of the original formulation are introduced. First, the spline representation is reformulated in terms of curvature-based variables, which is especially convenient to enforce monotonicity and convexity constraints by construction through a smooth parameter mapping. Second, the adaptation of interpolation domains is decoupled from the inner parameter identification by means of a staggered, block-alternating strategy: spline coefficients are optimized for fixed domain endpoints, while the endpoints are updated in an outer loop based on smooth statistics of sampled invariants. This separation alleviates an inherent scaling ambiguity between interpolation domains and spline coefficients that can impair conditioning in viscoelastic inverse problems. The underlying constitutive model remains the finite strain viscoelasticity framework of Reese and Govindjee. The proposed identification strategy is assessed for homogeneous uniaxial loading-unloading tests, which facilitates the study of identifiability and robustness of non-equilibrium branches.