Dynamic Stability of Biaxially Strained Thin Sheets Under High Strain-Rates

Abstract eng:
This work pertains to the stability of structures under rapid loading rates when inertia is taken into account. In contrast to the \Wyused approach using modal analysis to determine the structure’s fastest growing eigenmode — meaningful only for slow loading rates — the present study analyzes the time-dependent response to spatially localized perturbations in structures, in order to understand the initiation of the corresponding failure mechanisms. This approach is followed here to study the stability of rapid biaxial stretching of thin plates. The nonlinear time evolution of a such a perturbation is studied numerically and it is shown that these structures are stable until the time when the condition for the loss of ellipticity is reached. An analytical method, based on linearization, is used to define the size of the influence zone of a point-wise perturbation and we study its dependence on constitutive laws and loading conditions.

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