Fractional-orderuniaxial visco-elasto-plastic models for structural analysis

Three fractional-order models for uniaxial large strains and rate-dependent plastic behavior of materials instructural analysis are proposed. Our approach is a menable to modeling nonlinear and more sophisticated effects namely visco-elasto-plastic response of materials. This approach seamlessly interpolates between the standard elasto-plastic and visco-plastic models in plasticity, taking in to account the history-dependency of the accumulated plastic strain to specify the state of stress. To this end, we propose three models namely i) viscoelasto-plastic with linear hardening plastic model, ii )elasto-viscoplastic model, and iii) visco-elasto-plastic model, which combines the first the second models. We employ afractional-order constitutive law that relates the Kirchhoff stress to its Caputo time-fractional derivative of order α ∈ (0,1]. When α → 0 the standard elasto-plastic (rate-independent) model and when α = 1, the corresponding visco-plastic model is recovered. Since the material behavior is path-dependent the evolution of the plastic strainis achieved by fractional-order time integration of the plastic strain rate with respect to time. The strain rate is then obtained by means of the corresponding plastic multiplier and deriving proper consistency conditions. Finally, we develop a so called fractional return-mapping algorithm for solving the nonlinear system of the equilibrium equations developing in each model

Fractional-orderuniaxial visco-elasto-plastic models for structural analysis

Three fractional-order models for uniaxial large strains and rate-dependent plastic behavior of materials instructural analysis are proposed. Our approach is a menable to modeling nonlinear and more sophisticated effects namely visco-elasto-plastic response of materials. This approach seamlessly interpolates between the standard elasto-plastic and visco-plastic models in plasticity, taking in to account the history-dependency of the accumulated plastic strain to specify the state of stress. To this end, we propose three models namely i) viscoelasto-plastic with linear hardening plastic model, ii )elasto-viscoplastic model, and iii) visco-elasto-plastic model, which combines the first the second models. We employ afractional-order constitutive law that relates the Kirchhoff stress to its Caputo time-fractional derivative of order α ∈ (0,1]. When α → 0 the standard elasto-plastic (rate-independent) model and when α = 1, the corresponding visco-plastic model is recovered. Since the material behavior is path-dependent the evolution of the plastic strainis achieved by fractional-order time integration of the plastic strain rate with respect to time. The strain rate is then obtained by means of the corresponding plastic multiplier and deriving proper consistency conditions. Finally, we develop a so called fractional return-mapping algorithm for solving the nonlinear system of the equilibrium equations developing in each model