We propose a modeling framework for finite inelasticity, inspired by the kinematic assumption made by Green and Naghdi in plasticity [1]. In contrast to the classical multiplicative decomposition of the deformation gradient, the present formulation eliminates the need for an intermediate configuration. With the advent of generalized strains, the adopted kinematic setting allows a flexible mechanism for separating inelastic deformation from the total deformation. This allows us to construct models based on general rheological architectures. In particular, when the non-equilibrium free energy adopts a quadratic form, the framework yields a family of finite linear viscoelasticity models, including those by Green and Tobolsky (1946), Miehe and Keck (2000), and Simo (1987) as special cases. Building upon this framework, we further consider the design of structure-preserving schemes. The directionality condition is invoked to construct the algorithm stress for the equilibrium part. For the non-equilibrium part, a corresponding directionality condition is systematically examined, leading to a consistent design strategy for constitutive integration. Based on that, we propose a suite of integration algorithms for the internal state variables. In particular, for finite linear viscoelasticity models, the integration can be performed through explicit update formulas, thereby avoiding Newton-Raphson iterations at local quadrature points. Collectively, the proposed strategy enables a numerical scheme for finite inelasticity that preserves the energy and momentum while maintaining second-order accuracy in time [2]. The proposed modeling framework is validated using a suite of experimental data, demonstrating its effectiveness and potential advantages in characterizing and predicting the mechanical behaviours of real materials. We also provide numerical examples to demonstrate the robustness and long-time accuracy of the proposed structure-preserving algorithms for nonlinear inelastic dynamic problems. REFERENCES [1] J. Liu, C. Zhao, and J. Guan. Modeling finite viscoelasticity based on the Green-Naghdi kinematic assumption and generalized strains, Journal of the Mechanics and Physics of Solids, Vol. 206, 106346, 2026. [2] J. Liu and J.Guan. A continuum and computational framework for viscoelastodynamics: II. Strain-driven and energy-momentum consistent schemes. Computer Methods in Applied Mechanics and Engineering, Vol. 417, 116308, 2023.