DOI: 10.5281/zenodo.18808156
title: Accompanying dataset for the paper: "Fracture Toughness of Periodic Beam Lattices"

description: Contributions



G. Molnar did method developement, numerical simulations, validation and article writing.

J. Réthoré did conceptualization, experimental design, funding acquisition and article revision.


Licensing

Creative Commons CC BY 4.0

Funding sources

This work was partly supported by the French Research National Agency program
through the grant ANR-16-CE30-0007-01.

Data structure and information

Simulation data for the article entitled: "Fracture Toughness of Periodic Beam Lattices"



04_Lattice_toughness : Simulation files for the beam model


00_Fun_a : Effect of crack length

01_Fun_a0 : Effect of initial crack length

02_Fun_N : Effect of sample size

03a_Fun_h : Efect of beam heigth

03b_Fun_h_2_h_lm_const : Effect of slenderness

04_Fun_Lm : Effect of beam length

05_Fun_sigc : Effect of tensile strength

06_Fun_E : Effect of Young's modulus



05_Phase-field_homogenization : From beam to phase-field homogenisation


01_DAMAGE_COUPLING : Damage coupling

02_LOCALIZATION : Localization

03a_HOMO_RVE_BEAM : Homogeneous solution using the beam model

03b_HOMO_RVE_PF : Homogeneous solution using the phase-field model

04_PF_LC : Effect of initial crack length vs lc/Lm


01_BEAM_MODEL : Beam model

02_PF_MODEL : Phase-field model





06_Experiment : Experimental results


01_BEAM : Beam model

02_PHASE-FIELD : Phase-field model




Dependencies



Abaqus/Standard 2019 (with FORTRAN subroutine)

MATLAB R2025b


Paper Description

The study tackles the challenge of accurately modeling fracture behavior in beam lattices, which is essential for designing robust architected materials. Our research focuses on evaluating how the lattice's microstructure and material properties affect fracture toughness. We employed finite element simulations based on the Euler-Bernoulli beam theory to investigate crack propagation, using a failure criterion that initiates beam fracture when maximum axial stress exceeds critical strength. Building on observations from these simulations, we developed a multi-phase-field fracture model with Cosserat elasticity to integrate consistent toughness characteristics into a comprehensive framework for lattice design. This model was validated through experimental tests, ensuring a close match between theoretical predictions and physical reality. Our findings reveal that the energy release rate remains relatively stable during crack propagation, underscoring its reliability as a measure of the toughness of periodic lattice structures. We discovered that toughness is predominantly influenced by beam height and material properties such as tensile strength and Young's modulus, while slenderness has minimal impact. Additionally, cracks were observed to preferentially propagate along the lattice's structural directions due to stress localization effects, highlighting the importance of the microstructure in fracture behavior. The implications of this research are significant, suggesting that improved modeling of fracture in lattice structures can enhance material design reliability and optimization. This study bridges the gap between theoretical models and real-world applications, providing valuable insights for the development of advanced materials with tailored fracture properties.