An Improved Finite Element Modeling Method for Triply Periodic Minimal Surface Structures Based on Element Size and Minimum Jacobian

TL;DR

This paper introduces a two-parameter voxel modeling approach for TPMS structures that improves mesh convergence, accuracy, and efficiency by controlling element size and Jacobian, validated through numerical analysis.

Contribution

The study develops a novel two-parameter voxel method incorporating element size and Jacobian control, enhancing simulation stability and convergence for TPMS structures.

Findings

Simulation stabilizes at MJ of 0.3

Proposed method outperforms traditional voxel modeling in convergence and accuracy

Effective in analyzing graded TPMS structures

Abstract

Triply periodic minimal surface (TPMS) structures, a type of lattice structure, have garnered significant attention due to their lightweight nature, controllability, and excellent mechanical properties. Voxel-based modeling is a widely used method for investigating the mechanical behavior of such lattice structures through finite element simulations. This study proposes a two-parameter voxel method that incorporates joint control of element size and minimum Jacobian (MJ). Numerical results indicate that the simulation outcomes tend to stabilize when the MJ reaches 0.3. The grid convergence index (GCI), based on Richardson extrapolation, is introduced to systematically assess the numerical convergence behavior of both voxel models and the proposed two-parameter voxel models. This provides a systematic and objective framework for evaluating discretization errors and mesh convergence in TPMS modeling. Compared with traditional voxel method, the proposed method exhibits superior mesh convergence, solution accuracy, and computational efficiency. Furthermore, the two-parameter voxel method also shows excellent applicability in the analysis of graded TPMS structures, exhibiting even better convergence behavior than in uniform structures.