Higher-order gradient continuum modelling of periodic lattice materials

This is the author’s version of a work that was accepted for publication in the Computational Materials Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://dx.doi.org/10.1016/j.commatsci.2011.05.025The dynamic behaviour of periodic lattice materials is investigated using an equivalent higher-order continuum model obtained by homogenisation of the equations of motion. A gradient continuum enriched with higher-order inertia terms is developed using a combination of finite element discretisation of the unit cell and the continualisation approach. The analysis of the dispersion relations shows that the proposed model is able to capture correctly the physical phenomenon of wave dispersion in lattice structures which is overlooked by classical continuum theories