Institute of Fundamental Technological Research

The paper considers the plastic strain localization phenomenon in the framework of the fractional viscoplasticity. As an illustrative example, full spatial modelling of a tension test under extreme dynamic conditions is presented. The modelling assumes adiabatic conditions including isotropic work hardening-softening effects induced by plastic strains, temperature and damage (scalar). Special attention is paid to additional, compared to the classical Perzyna viscoplasticity, model parameters resulting from application of fractional calculus in the evolution law for plastic strains. It is shown that the proposed formulation allows for high flexibility of modelling of the localization zone with a limited number of model parameters.

fractional viscoplasticity, strain localization, extreme dynamics

The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above mentioned FV properties, together with a detailed discussion on a general 3D numerical implementation for the explicit time integration scheme.

fractional viscoplasticity, rate dependence, plastic anisotropy, non-normality, directional viscosity, explicit/implicit non-locality