Periodic Averaged Force Method for Lattice Materials with Mechanical Nonlinearity at Medium Strain

Low relative-density or nonlinear meso-structured lattice materials often exhibit macroscopic nonlinear behavior, whose investigation traditionally requires costly full-scale finite element models or experiments. The Representative Volume Element (RVE) method and periodic displacement field assumptions are also widely used for the simulation of lattice materials, which is more suitable for high relative-density materials with significant limitations for nonlinear lattice materials. In this work, a novel Periodic Averaged Force (PAF) Method integrated with the finite element framework is proposed, applicable especially to thin-walled, low relative-density structures with nonlinear behavior. Using honeycomb material and the zigzag chiral lattice material as two examples, nonlinear in-plane mechanical properties and meso-structural deformation were evaluated via the full scale finite element modelling method, the RVE method, and the proposed PAF method. Results show the proposed PAF method predicts low relative-density honeycomb properties under large deformation (up to 10% strain) with under 10% error—compared to over 100% for the RVE method under the same conditions—while closely approximating the in-situ displacement field and significantly reducing computational time versus conventional full scale finite element analysis.