Stability of Crystal Plasticity Constitutive Models: Observations in Numerical Studies and Analytical Justification

In designing accurate constitutive models, it is important to investigate the stability of the response obtained by means of these models to perturbations in operator and input data because the properties of materials at different structural-scale levels and thermomechanical influences are stochastic in nature. In this paper, we present the results of an application of the method developed by the authors to a numerical study of the stability of multilevel models to different perturbations: perturbations of the history of influences, initial condition perturbations, and parametric operator perturbations. We analyze a two-level constitutive model of the alpha-titanium polycrystal with a hexagonal closed packed lattice under different loading modes. The numerical results obtained here indicate that the model is stable to perturbations of any type. For the first time, an analytical justification of the stability of the considered constitutive model by means of the first Lyapunov method is proposed, and thus the impossibility of instability in models with modified viscoplastic Hutchinson relations is proved.