A continuum model for lattice structures with geometric and material nonlinearities

An equivalent continuum methodology offers an attractive alternative, or supplement, to classical discrete finite element procedures for the analysis of lattice structures. Effective continuum models can lead to reduced order models of lattice structures which are computationally very efficient. A number of continuum models have recently been proposed for analysis of lattice structures including one developed by the authors. The majority of these models have been concerned with linear analysis although some work has been done in the area of geometrical nonlinearities. To the authors' knowledge none of the existing continuum models have been extended to the analysis of lattices with general (i.e. both geometric and material) nonlinearities. The objective of the work reported herein was the development of a continuum model for general nonlinear analysis of lattice structures. The formulation of a continuum procedure for general nonlinear behavior is given. A continuum finite element is derived and a computational algorithm for nonlinear analysis is outlined. A number of applications of the continuum method for classical elasto-plastic material constitutive behavior are presented and compared to discrete finite element solutions. The examples illustrate the potential economy of the continuum finite element analysis vs classical discrete finite element analysis.