Some results of a numerical estimating of the stability of the FCC metal two-level constitutive model

Abstract

An important property of constitutive models is the stability of the response change histories obtained under various perturbations of an input data (history of influences and initial conditions) and a model operator. It is associated with the stochastic nature of material properties at different structural-scale levels and thermomechanical influences. Stability analysis is especially significant to justify the applicability of new constitutive models for describing modern technological processes, for instance, those focused on the design of novel functional materials. Multilevel physically-oriented constitutive models of materials hold the most promise for solving such problems. They are able to provide an explicit description of the inelastic deformation mechanisms, the material structure rebuilding and the changes in the physical and mechanical properties of the material determined by its state. Use of the approach developed by the authors and described in detail in the paper in the previous issue of the journal made it possible to evaluate the stability of multilevel constitutive material models under various perturbations of the initial conditions, the history of influences, and parametric operator perturbations. It includes an analysis of the norms of their deviations and the integral norm of deviation of perturbed solutions from the base ones obtained in calculations with unperturbed parameters. In this paper, the application of the proposed approach has been illustrated by studying a two-level constitutive model of the FCC polycrystal. The obtained results demonstrate the stability of this model to the calculated perturbations.