A stochastic approach for calculating elastic constants of polymer lattice structures based on spectral ultrasonic data

Abstract

Additively manufactured polymer lattices are increasingly used in biomedical and structural applications due to their tunable mechanical properties and architectural similarity to biological materials. However, accurately resolving their anisotropic elastic response remains challenging due to fabrication inconsistencies, energy loss mechanisms, and differences between static and dynamic characterization techniques. In this study, a dynamic technique, resonant ultrasound spectroscopy (RUS) was applied to a stereolithography-fabricated body-centered tetragonal (BC-Tetra) lattice composed of a polyurethane-like resin. Elastic constants were extracted from both experimental and model (FEA) eigenfrequencies using a particle swarm optimization (PSO) scheme with modified parameter tuning to improve exploration of the non-convex inversion space. Comparison of inverted elastic tensors showed strong agreement for the axial stiffness,$C_{33}$ and shear-related coefficients $C_{44}$​ and $C_{66}$, , while in-plane stiffness constants $C_{11}$​ and $C_{12}$​ and the axial coupling term $C_{13}$ exhibited the greatest variance, reflecting inversion sensitivity and the limited number of resonances below the continuum cutoff. Engineering moduli derived from RUS were internally consistent and in-plane values agreed closely with FEA predictions, but quasi-static measurements of the in-plane moduli $E_1=E_2$ and out-of-plane modulus $E_3$ were 20 % and 32 % lower, respectively. This divergence highlights fundamental differences in compliance across loading regimes: quasi-static compression is strongly influenced by strut bending, resin pooling, and boundary effects, whereas RUS probes free–free global vibrational modes that enforce affine deformation at the scale of the entire lattice, suppressing local compliance mechanisms and yielding higher effective moduli. Our study is an effort to test the boundaries of RUS for high-loss polymer lattices and to develop practices that could eventually reduce operator dependence.