Experimentally validated multi-scale modeling of 3D printed hyper-elastic lattices

This work deals with mechanical analysis of hyper-elastic lattices in the finite-strain range through multi-scale simulations and experimental testing. It describes designing appropriate unit cells (UCs) and mode-shapes to accurately predict mechanical behaviors of soft lattices in the finite-strain range. Lattices are based on three different types of repeating UCs in triangular, square and hexagonal shapes. Generic planar UCs consisting of beam-like structures are simulated to determine overall constitutive behaviors. In this respect, periodic boundary conditions are introduced in the finite-strain regime. Deformations of the unit cells and lattice are described on the basis of non-linear Green strains. Finite element (FE) solutions coupled with the Mooney–Rivlin constitutive equations are developed and solved using an iterative Newton–Raphson method and a multi-scale strategy. Then, the computational tool is applied to analyze lattice structures fabricated by three-dimensional (3D) printing technology. Samples are tested in tension and compression modes in different directions revealing strong non-linear, directional and load-dependent responses. A detailed analysis of small-scale behavior of unit cells is presented. Large-scale and multi-scale FE models are also implemented to simulate experimental results with high accuracy and computational efficiency. Due to the absence of similar results in the literature, this paper would contribute to understanding of hyper-elastic behaviors of lattices at small-scale and be instrumental in the large-scale design and analysis of soft lattice structures.