Abstract
A geometrical theory for the time-evolution of strain localization(flow-localization) is discussed. The purpose is to obtain a reductionof the continuum mechanical problem of time-evolution of deformation toone involving few scalar invariants rather than the full field variablesand thereby obtain a `particle-like' description of the evolvinglocalization zones. The present paper deals with these issues on casesrestricted to those of planar deformation. Several concepts areintroduced in the description, such as path-continuity, stable andunstable localization, width of localization zones, uncertainties in thedescription of time evolution of localization, coherent and non-coherentflow localization. Simulation results for the high-rate planar extensionwith rectangular elastic-viscoplastic blocks are used to demonstrateseveral of the theoretical concepts used. A fully non-linear formulationof the continuum mechanical problem is used accounting for finitedeformations as well as irreversible elastic-viscoplastic materialbehavior. Several characteristic localization phenomena are observed inthe simulations such as branching of the critical path of the impactwave, multiple neck formation and elastic-plastic wave interaction.
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Sørensen, N.J. A Geometrical Approach to Dynamic Strain Localization in Planar Motion. Nonlinear Dynamics 33, 105–127 (2003). https://doi.org/10.1023/A:1026049828854
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DOI: https://doi.org/10.1023/A:1026049828854