Developing a four-dimensional lattice spring model for mechanical responses of solids

Gao-Feng Zhao

In this work, a four-dimensional lattice spring model is developed for studying the mechanical responses of solids. Our resultsindicate that the Poisson’s ratio limitation of the classical lattice spring model defined in three-dimensional space can be releasedby introducing an extra fourth-dimensional interaction. The fourth-dimensional lattice spring model adopts central interactionsonly, and it can naturally represent the nonlinear dynamic responses of solids without special treatment of rigid body rotationor incremental integration of non-central/non-local interaction as used in the traditional methods. Applicability of the model isillustrated from a few numerical examples.