Dynamic crushing of a one-dimensional chain of type II structures

The development of an analytical model based on a ‘bar–hinge’ idealisation is described. It is used to investigate the structural response of a one-dimensional chain of components each constructed from a pair of slightly bent elastic–plastic struts under axial impact loading. Each component (a typical type II structure) in the chain is modelled as four axially compressible, elastic–plastic, straight bars of infinite bending rigidity connected to each other by elastic–plastic hinges of finite length. A new approach to formulate the constitutive relation between the generalised force and displacement of the bars and hinges is developed. A self-contact algorithm is used for intra-component contact simulation. The ‘bar–hinge’ model is validated using the results from finite-element simulations using ABAQUS. Good agreement is achieved. The analytical model was then used to investigate the crushing features of the chain structure. The effects of the number of the components in the chain and the crookedness angle of the components on the crushing behaviour were studied. It was found that collapse of the components in the chain occurs at the proximal end of the chain first and that the component at the fixed distal end will also collapse at some later time. The single component structure is more ‘inertia sensitive’ than a chain structure of more than two components.