Overlapping-Field Modeling (OFM) of periodic lattice metamaterials

Abstract

Intensive studies are devoted to establish the relation between macro continuum properties and micro-structural parameters for lattice structures. In this paper, we first realize that the discrete displacements on grids sometimes violate the continuity assumed by the Cauchy-Born hypothesis, which calls for an extension to the usual homogenization procedures. To eliminate such a micro–macro disagreement, a new method called the Overlapping-field model (OFM) is proposed. Grids in a lattice may be divided into a series of types. The displacement distribution among each type of grids is deemed continuous. Displacement relations among all types of lattice grids are derived according to the energetic minimum principle. Each type of grid can be chosen to calibrate macro properties like the continuum stiffness tensor, which is grid type-dependent and can be transformed from type to type. The present model has been validated by comparing with literature and clarifying some fundamental issues remaining in this field. It has also been applied to investigate lattices with cells relatively more complex than those reported in existing studies.