Deriving a lattice model for neo-Hookean solids from finite element methods

Abstract

Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for lattices with regular shapes. Here, we derive a lattice model for neo-Hookean solids directly from finite element methods (FEM). The proposed lattice model can handle complicated geometries and tune the material compressibility without significantly increasing the complexity of the model. Distinct lattices are required for irregular structures, where the lattice spring stiffness can be pre-calculated with the aid of FEM shape functions. Multibody interactions are incorporated to describe the volumetric deformation. We validate the lattice model with benchmark tests using FEM. The simplicity and adoptability of the proposed lattice model open possibilities to develop novel numerical platforms for simulating multiphysics and multiscale problems via integrating it with other modeling techniques.