Constitutive Models for Lattice Materials

Natural materials are often characterised by a cellular microstructure that allows them to achieve a wide range of mechanical properties. This microarchitecture has provided inspiration for the development of high performance manmade structures and artificial materials. Among cellular solids, lattice materials are characterised by an ordered, periodic, microstructure that can be tailored to achieve specific combinations of stiffness, strength and density. This book presents a methodology for the derivation of constitutive models for lattice materials. Under the hypothesis of linear behaviour, the method has been applied to evaluate the macroscopic stiffness and strength of a selection of two-dimensional and three-dimensional lattices. The performance of different cell topologies have been compared by means of material charts for stiffness, buckling and plastic yielding. The method has also been applied to derive constitutive models for the non linear behaviour of lattices. In particular, macroscopic stress-strain relationships have been obtained capable to capture the effect of geometric non linearity.