On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

The main goal of this work is to test the possibility of a newly introduced constitutive law to model the behaviour of the isotropic elastic-perfectly plastic material which is exposed to large elastoplastic deformations. The proposed constitutive relation is based on the hypo-elastic relation and the inelastic INTERATOM model. The verification of the model is done by its implementation into the commercial software ABAQUS/Standard via the user subroutine UMAT. For that purpose, the large simple shear problem is studied where selected objective corotational rates, i.e. the logarithmic rate, the Jaumann rate and the Green-Naghdi rate, are individually implemented in the aforementioned constitutive relations. The obtained results are compared mutually and with the relevant literature. The proposed constitutive model is also used to test the behaviour of the part of a real engineering structure, i.e. a seismic isolator, in order to obtain the correct input data for further analysis of superstructure behaviour due to seismic excitation.

Size Scaling of Plastic Deformation in Simple Shear: Fractional Strain-Gradient Plasticity and Boundary Effects in Conventional Strain-Gradient Plasticity

A recently developed model based on fractional derivatives of plastic strain is compared with conventional strain-gradient plasticity (SGP) models. Specifically, the experimental data and observed model discrepancies in the study by Mu et al. (2016, “Dependence of Confined Plastic Flow of Polycrystalline Cu Thin Films on Microstructure,” MRS Com. Res. Let. 20, pp. 1–6) are considered by solving the constrained simple shear problem. Solutions are presented both for a conventional SGP model and a model extension introducing an energetic interface. The interface allows us to relax the Dirichlet boundary condition usually assumed to prevail when solving this problem with the SGP model. We show that the particular form of a relaxed boundary condition does not change the underlying size scaling of the yield stress and consequently does not resolve the scaling issue. Furthermore, we show that the fractional strain-gradient plasticity model predicts a yield stress with a scaling exponent that is equal to the fractional order of differentiation.