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

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