Non-uniqueness, stability and bifurcation analyses in elasto-viscoplastic boundary value problems with no inertia

Huan Wang (1) , Panagiotis Kotronis (1) , Giulio Sciarra (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

The article focuses on non-uniqueness, bifurcation and stability conditions in elasto-viscoplastic boundary value problems when inertia terms are neglected. Analytical and numerical studies are presented to investigate the capability of an elasto-viscoplastic model to regularize the behavior in the occurrence of strain localization with respect to number of strain bands formed and mesh dependency. It is found that elasto-viscoplasticity in a Cauchy medium neither restores the uniqueness of the solution nor provides mesh independent results. A high value of the viscosity parameter can sometimes provide results that are mesh independent, up to a certain limit strain, as it actually modifies the response of the constitutive law by an ad-hoc increase of its hardening branch. On the contrary, coupling elasto-viscoplasticity with a second gradient model that introduces an internal length parameter reproduces realistically the rate dependent behavior and regularizes the results.

Mots clés: Elasto-viscoplasticity; Uniqueness; Strain localization; Regularization; Second gradient; Bifurcation; Linear perturbation analysis; Stability

Domaines: Génie civil

Huan Wang, Panagiotis Kotronis, Giulio Sciarra. Non-uniqueness, stability and bifurcation analyses in elasto-viscoplastic boundary value problems with no inertia. International Journal of Engineering Science, 2022, 177, pp.103714. ⟨10.1016/j.ijengsci.2022.103714⟩. ⟨hal-03688218⟩