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Abstract:
This paper deals with the numerical simulation of the dynamic failure of an aluminium plate under air-blast loading. Constitutive modelling based on the fractional viscoplasticity is used. The material model is non-local due to the properties of the applied fractional differential operator and is implemented as user material in the engineering finite element computation code ABAQUS. It is important that the numerical simulations are contrasted with experiments. Numerical outcomes clearly show the applicability of the adopted modelling for the description of salient stages of dynamic structural failure.

Keywords:
fractional viscoplasticity, rate sensitivity, plastic anisotropy, non-locality, damage mechanics

Abstract:
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.

Keywords:
fractional viscoplasticity, strain localization, extreme dynamics

Abstract:
This paper presents a general numerical scheme for the fractional plastic flow rule, dedicated to a wide class of materials manifesting the non-normality of plastic flow and induced plastic anisotropy. To determine the vector of the plastic flow, a special numerical procedure has been developed, which is applicable for any smooth and convex yield function. The obtained approximation is verified based on an analytical solution. The paper also presents a set of numerical results for the generalised Drucker–Prager model

Keywords:
Non-normality, Plastic anisotropy, Fractional calculus, Return mapping algorithm

Abstract:
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.

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

Abstract:
In this paper, an implementation of fractional plastic flow rule in the framework of implicit and explicit procedures is under consideration. The fractional plastic flow rule is obtained from a generalisation of the classical plastic flow rule utilising fractional calculus. The key feature of this new concept is that in general, the non-associative flow is obtained without necessity of additional potential assumption. If needed, the model can cover the anisotropy induced by plastic deformation. Illustrative examples showing the unusual flexibility of this model are also presented.

Keywords:
non-normality of plastic flow, fractional calculus, return mapping algorithm

Abstract:
The objective of the present article is to show the formulation for elastic-viscoplastic material model accounting for intrinsic anisotropic microdamage. The strain-induced anisotropy is described by the evolution of the intrinsic microdamage process — defined by the second-order microdamage tensor. The first step of the possibility of identification procedure (calibration of parameters) are also accounted and illustrated by numerical examples.

Keywords:
microdamage, anisotropy