One-dimensional modeling of necking in rate-dependent materials

Basile Audoly (1) , John Hutchinson (2)

1 LMM - Laboratoire de modélisation en mécanique
2 Computing Department [Lancaster]

This paper presents an asymptotically rigorous one-dimensional analytical formulation capable of accurately capturing the stress and strain distributions that develop within the evolving neck of bars and sheets of rate-dependent materials stretched in tension. The work is an extension of an earlier study by the authors on necking instabilities in rate-independent materials. The one-dimensional model accounts for the gradients of the stress and strain that develop as the necking instability grows. Material strain-rate dependence has a significant influence on the strain that can be imposed on a bar or sheet before necking becomes pronounced. The formulation in this paper enables a quantitative assessment of the interplay in necking retardation due to rate-dependence and that due to the development of hydrostatic tension in the neck. The connection with a much simpler long-wavelength approximation which does not account for curvature induced hydrostatic tension in the neck is also emphasized and extended.

Mots clés: B Beams and columns; B Viscoplastic material; C Stability and bifurcation; C Asymptotic analysis

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]

Basile Audoly, John Hutchinson. One-dimensional modeling of necking in rate-dependent materials. Journal of the Mechanics and Physics of Solids, 2019, 123, pp.149. ⟨10.1016/j.jmps.2018.08.005⟩. ⟨hal-01898154⟩