The Quasi-static And Impact Crushing Of Periodic Cellular Structures

Cellular materials have attracted increasing attention in recent years,due to their excellent mechanical properties compared with traditional materials,such as light weight,superior specific stiffness and strength,high energy absorption capability and so on.In this dissertation,the crushing behavior of three new periodic cellular materials are investigated analytically and numerically to explore the relationship between the microscopic structures and the macroscopic mechanical properties,i.e.,auxetic double arrowhead honeycombs(DAHs),hierarchical honeycombs and folded structures.Analytical solutions of the Young's modulus and the Poisson's ratio of DAHs are derived.Based upon the deformation modes of the honeycombs under quasi-static,low velocity and high velocity impacts,theoretical models for the collapse stress are also developed.Obtained results show that the collapse stress under quasi-static and low velocity impacts depends upon the two re-entrant angles responsible for negative Poisson's ratio,while under high velocity impacts the effect of negative Poisson's ratio diminishes and the collapse stress is only influenced by the relative density.Moreover,the analytical results of the collapse stress of uniform DAHs are successfully adapted to interpret the simulated plateau stress of functionally graded DAHs under impact loading.A two-scale method is proposed in order to investigate the in-plane uniaxial collapse response of a second order hierarchical honeycomb(i.e.,a regular hexagonal honeycomb with its cell walls consisting of an equilateral triangular honeycomb).Its failure modes under quasi-static crushing and dynamic impact are systematically explored by finite element simulations.Analytical expressions for the quasi-static collapse stress of the hierarchical honeycomb loaded in two in-plane directions are obtained.The analytical quasi-static collapse stress models are later extended to dynamic crushing.Both numerical and analytical results show that the hierarchical honeycomb has an improved collapse stress over traditional hexagonal honeycombs.The improvement is found to be more pronounced for low velocity impact than for high velocity impact.Base on the Miura origami,three types of folded structures with different stacking orders are proposed and developed.It is found that the folded structure with a horizontal connection has superior energy absorption capacity in three orthogonal directions,owing to the combined bending and stretching deformation of the constituent flat plates of the folded structures.For the folded structures with a longitudinal connection,it presents a biaxial negative Poisson's ratio,which implies transverse shrink in the in-plane two directions under out-of-plane compression.This special property can lead to improved energy absorption capacity.Wierzbicki model for the collapse analysis of thin-walled structures is extended to the folded structures by introducing an inclination angle.It can be concluded that the connection between Miura-ori layers has a great influence on the mechanical properties of the folded structures.The developed theoretical models for the energy absorption of the above three new pattern cellular materials provide a fundation for engineering applications.