Fracture of Lattice Materials from Low to High Relative Density
Abstract
Lattice materials have highly tunable mechanical properties that are controlled by their internal geometry and base material behavior. While fracture models for low-density lattices are well-established, the fracture of lattices at relative densities above 30% remains largely unexplored. Here, we present an analytical model that combines homogenization methods and blunt-crack fracture theory to predict the fracture toughness of triangular and hexagonal lattices over a wide range of relative densities. Finite element modeling corroborates the analytical framework and demonstrates a shift in failure mechanisms between low and high relative density regimes. At high relative densities, failure is dominated by nodal stress concentrations, which are strongly influenced by the local crack-tip geometry and the macroscopic crack path. Significant stress redistribution is observed as the relative orientation and lattice fillet radius are varied, resulting in increased fracture toughness relative to baseline geometries. Furthermore, quasi-brittle poly(methyl methacrylate) (PMMA) lattices achieve about a 1.6x enhancement in fracture toughness relative to perfectly brittle lattices as failure is delayed by localized plasticity. Notably, some quasi-brittle lattices are found to exceed the fracture toughness of their base material -- a feature only possible when the cell size is large compared to the base material's plastic radius. Experiments on lattice fracture specimens made from laser-cut PMMA validate the finite element results, but highlight the stochastic nature of failure in brittle lattice materials, especially at higher relative densities.
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BibTeX
@misc{taylor2026fracture,
title = {{Fracture of Lattice Materials from Low to High Relative Density}},
author = {Adam P. Taylor and Sage Fulco and Kevin T. Turner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36166},
eprint = {2609.36166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36166},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fracture of Lattice Materials from Low to High Relative Density
AU - Adam P. Taylor
AU - Sage Fulco
AU - Kevin T. Turner
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36166
UR - https://arxiv.org/abs/2609.36166
AB - Lattice materials have highly tunable mechanical properties that are controlled by their internal geometry and base material behavior. While fracture models for low-density lattices are well-established, the fracture of lattices at relative densities above 30% remains largely unexplored. Here, we present an analytical model that combines homogenization methods and blunt-crack fracture theory to predict the fracture toughness of triangular and hexagonal lattices over a wide range of relative densities. Finite element modeling corroborates the analytical framework and demonstrates a shift in failure mechanisms between low and high relative density regimes. At high relative densities, failure is dominated by nodal stress concentrations, which are strongly influenced by the local crack-tip geometry and the macroscopic crack path. Significant stress redistribution is observed as the relative orientation and lattice fillet radius are varied, resulting in increased fracture toughness relative to baseline geometries. Furthermore, quasi-brittle poly(methyl methacrylate) (PMMA) lattices achieve about a 1.6x enhancement in fracture toughness relative to perfectly brittle lattices as failure is delayed by localized plasticity. Notably, some quasi-brittle lattices are found to exceed the fracture toughness of their base material -- a feature only possible when the cell size is large compared to the base material's plastic radius. Experiments on lattice fracture specimens made from laser-cut PMMA validate the finite element results, but highlight the stochastic nature of failure in brittle lattice materials, especially at higher relative densities.
ER -