A geometrical approach to dynamic strain localization in planar motion

A geometrical theory for the time-evolution of strain localization (flow-localization) is discussed. The purpose is to obtain a reduction of the continuum mechanical problem of time-evolution of deformation to one involving few scalar invariants rather than the full field variables and thereby obtain a 'particle-like' description of the evolving localization zones. The present paper deals with these issues on cases restricted to those of planar deformation. Several concepts are introduced in the description, such as path-continuity, stable and unstable localization, width of localization zones, uncertainties in the description of time evolution of localization, coherent and non-coherent flow localization. Simulation results for the high-rate planar extension with rectangular elastic-viscoplastic blocks are used to demonstrate several of the theoretical concepts used. A fully non-linear formulation of the continuum mechanical problem is used accounting for finite deformations as well as irreversible elastic-viscoplastic material behavior. Several characteristic localization phenomena are observed in the simulations such as branching of the critical path of the impact wave, multiple neck formation and elastic-plastic wave interaction.