Modal Response Improvement of Periodic Lattice Materials with a Shear Modulus-Based FE Homogenized Model

Area of Science:

• Materials Science
• Mechanical Engineering
• Computational Mechanics

Background:

• Lattice materials offer tunable stiffness and energy absorption for industrial use.
• Evaluating large lattice structures is computationally intensive.
• Homogenization-based multi-scale analysis provides an efficient alternative.

Purpose of the Study:

• To introduce a precise and simplified homogenization method for lattice structures.
• To evaluate and compare the anti-vibration performance of different lattice topologies.
• To investigate the trade-off between anti-vibration and loading capacity based on relative density.

Main Methods:

• Proposed an equidistant segmentation (ES) method to approximate periodic boundary conditions (PBCs).
• Applied multi-scale analysis to body-centered cubic (BCC) and triply periodic minimal surface (TPMS) lattices (gyroid, primitive).
• Performed equivalent modal analysis to predict and compare anti-vibration capacities.

Main Results:

• The ES method offers a precise and computationally efficient approach for homogenization.
• TPMS lattices demonstrated higher anti-vibration capacity compared to BCC lattices.
• Lower relative densities in TPMS enhance anti-vibration (frequency resistance), while higher densities improve loading capacity.

Conclusions:

• The ES method is a rational and accurate technique for multi-scale analysis of diverse lattice structures.
• TPMS lattices are promising for applications requiring high anti-vibration performance.
• Relative density is a critical parameter for balancing anti-vibration and loading capacities in TPMS design.