A unified elasto-viscoplastic model for rate-dependent materials

This paper presents a generalized elasto-viscoplasticity framework for modelling material behaviour under static, impact, and potentially cyclic loading. A theoretical equivalence between the classical Cowper–Symonds formulation and Chaboche’s viscoplasticity law is established, demonstrating that both can be expressed within a unified constitutive structure. Based on this equivalence, a new procedure is proposed for identifying elastoplastic and viscoplastic parameters directly from tensile, compressive, or strain-controlled tests performed at different strain rates. The method eliminates the need for additional creep or relaxation experiments and enables decomposition of the stress–strain response into elastoplastic and viscoplastic contributions. Several variants of the viscoplasticity law are introduced, each satisfying relevant physical constraints, and a regression-based strategy is employed for robust parameter identification. The framework is validated using four materially diverse datasets: X2CrNi18-9 stainless steel, Ti6Al4V titanium alloy, short glass fibre-reinforced polybutylene terephthalate (PBT), and hydroxyl-terminated polybutadiene (HTPB) propellant. In all cases, excellent agreement with experimental data is obtained. The proposed formulation further enables prediction of stress–strain behaviour at the limiting cases of zero and infinitely high strain rates, which cannot be accessed experimentally. The results demonstrate that a single constitutive law can capture rate-dependent responses across metals, polymers, and elastomers, making it suitable for structural analyses under monotonic loading, with potential extension to cyclic, multiaxial, and thermo-mechanical conditions. • Unified elasto-viscoplastic law for static, impact, and potentially cyclic loading. • Demonstrates equivalence between Cowper–Symonds and Chaboche formulations. • Material parameters identified directly from standard strain-rate-controlled tests. • Predicts stress–strain response at zero and infinite strain rates beyond experiments. • Validated on metals, polymers, and elastomers with superior accuracy to Perzyna law.