International Journal of Solids and Structures 41 (2004) 3353–3377 www.elsevier.com/locate/ijsolstr

Deformation-induced folding systems in thin-walled monolithic hexagonal metallic honeycomb
Dirk Mohr, Mulalo Doyoyo
Impact and Crashworthiness Laboratory, Massachusetts Institute of Technology, Rm 5–222, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Received in revised form 15 December 2003 Available online 3 March 2004

Abstract Metallic honeycombs exhibit microstructural heterogeneity under large deformation which presents a challenge to the development of mechanical models of the material using classical continuum mechanics. In order to gain insight on this problem, numerical multiaxial experiments are performed on a virtual honeycomb specimen (VHS). This involves a detailed finite element model that represents the plate-like honeycomb microstructure with three-dimensional shell elements obeying an elastic–plastic constitutive law. The VHS is subjected to large combined compressive and shear loading along its tubular direction in displacement-controlled simulations under quasi-static conditions. The observed deformation mechanisms that include plastic collapse and the formation of folding systems are analyzed at the microstructural level and their effects on the mechanical responses at the macroscopic level are discussed in-depth. Mathematical expressions of the characteristics of the folding systems, namely: folding planes, folding directions, hinge line orientations, and compatibility zones are developed and used to determine representative measures of microstructural deformation. An elliptic macroscopic plastic collapse envelope of the honeycomb is analytically and numerically evaluated, while closed-form expressions of compressive and shear strengths are presented. A linear crushing envelope defines the post-collapse behavior. The direction of inelastic deformation is found to be parallel to that of the macroscopic compressive principal stress. This...