A Theory of Elasto-Plastic Buckling

Abstract

An elastic element (modulus E) and' a sliding element (yield stress σ _p ) are coupled in series to get a rheological model of an elasto-plastic structure and work-hardening is accounted for by coupling another elastic element (modulus E_s ) parallel to the sliding element. This is applied for the compression, recovery, and recompression curves obtained in copper wire buckling. Agreement between theory and experiment is excellent and it is demonstrated how yield starts on the compression and extension sides of the wire cross section and moves towards the center; a new pair of yield-limit positions appears for a new deformation (strain history). The same theory is applied to paper buckling, where the work-hardening effect mentioned must be introduced and calculated, and it is indicated that buckling involves a "weakening" of the structure compared to extension. It is also demonstrated that a model of frictional-elastic buckling developed for textile fabrics does not fit paper buckling well; this is an indication that the rhe ological coupling is significant.