Applied and Interdisciplinary Mathematics Seminar

University of Michigan

Fall 2005
Friday, 14 October, 3:10-4:00pm, 1084 East Hall

Breaking spaghetti by impact: stress and buckling in brittle rods

Andrew Belmonte

W. G. Pritchard Laboratories
Department of Mathematics
Penn State University, USA


Abstract

What happens to uncooked spaghetti if you hit it at 50 mph? This question combines fundamental aspects of elasticity and material science, from nonequilibrium Euler buckling to the failure of brittle solids. I will present an experimental study of the dynamic buckling and fragmentation of slender rods - including pasta, teflon, glass, and steel - due to rapid impact. By combining the results of Saint-Venant with elastic beam theory, we obtain a preferred buckling wavelength from the coupled partial differential equations for stress and deformation. Experimentally, we find that the distribution of fragment lengths has peaks near 1/2 and 1/4 of the buckling wavelength. Such preferred fragment sizes represent the influence of the deterministic buckling process on the more random fragmentation processes.