Fractional-order uniaxial visco-elasto-plastic models for structural analysis
J. L. Suzuki, M. Zayernouri, M. L. Bittencourt, and G. E. Karniadakis, “Fractional Order Uniaxial Visco-Elasto-Plastic Models for Structural Analysis”, Computer Methods in Applied Mechanics and Engineering, vol. 308, pp. 443–467, Aug. 2016.
This paper proposes two fractional-order models for uniaxial large strains and visco-elasto-plastic behavior of materials in structural analysis. Fractional modeling seamlessly interpolates between the standard elasto-plastic and visco-elasto-plastic models, taking into account the history (memory) effects of the accumulated plastic strain to specify the state of stress. The evolution of the plastic strain is achieved by fractional-order time integration of the plastic strain rate with respect to time. We further develop a so-called fractional return-mapping algorithm for solving the nonlinear system of the equilibrium equations. The simulation results demonstrate the flexibility of fractional-order modeling using the Caputo derivative to account for rate-dependent hardening and viscous dissipation, and it’s potential to effectively describe complex constitutive laws of engineering materials and especially biological tissues.