Coupled Plastic Wave Propagation and Column Buckling

Abstract

The plastic buckling of columns is explored in a regime where plastic wave propagation and lateral buckling are nonlinearly coupled. Underlying the work is the motivation to understand and quantify the dynamic crushing resistance of truss cores of all-metal sandwich plates where each truss member is a clamped column. Members are typically fairly stocky such that they buckle plastically and their load carrying capacity decreases gradually as they buckle, even at slow loading rates. In the range of elevated loading rates of interest here, the columns are significantly stabilized by lateral inertia, resisting lateral motion and delaying buckling and loss of load carrying capacity to relatively large overall plastic strains. The time scale associated with dynamic axial behavior, wherein deformation spreads along the column as a plastic wave, is comparable to the time scale associated with lateral buckling such that the two phenomena are coupled. Several relevant problems are analyzed using a combination of analytical and numerical procedures. Material strain-rate dependence is also taken into account. Detailed finite element analyses are performed for axially loaded columns with initial imperfections, as well as for inclined columns in a truss core of a sandwich plate, with the aim of determining the resistance of the column to deformation as dependent on the loading rate and the relevant material and geometric parameters. In the range of loading rates of interest, dynamic effects result in substantial increases in the reaction forces exerted by core members on the faces of the sandwich plate with significant elevation in energy absorption.