Asymptotic analysis of evolution of a neck in extended thin rigid plastic solids

We carry out an asymptotic analysis with natural small geometric parameter of the stress-strain state realized under the stretch of a rigid-plastic rod of round section and of a flat sheet infinite in one direction, taking into account the presence of areas of thinning (a neck) and thickening with respect to the medium size. In examples, we stress qualitative effects of possible inertia-free development of a neck.

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