Institut de Recherche en Génie Civil et Mécanique

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.

Abstract During an earthquake, slip occurs in a localized shear zone that features a heavily granulated fault core that can be characterized as a shear band. We study the formation of this fault core in a granular rock such as sandstone by developing a model of crushable granular media within the framework of Breakage Mechanics. This model accounts for the evolution of the grain size distribution, while also accounting for the co‐evolution of the solid fraction. An enrichment with the Cosserat continuum allows for the model to predict finite‐width shear bands. The model is then calibrated against experimental data taken from tests on Bentheim sandstone, and a parametric study of the mechanical parameters is conducted using linear stability analysis. We find that for deeply‐buried rocks the shear bands have a compactive component, and the initial value of the solid fraction does not play a strong role in the initial band thickness, but can influence the rate of delocalization of the band. Post‐localization behavior is studied with the finite element method, which shows the formation of zones of dilation outside the band in addition to the compaction within the band. Using a modified Kozeny–Carman permeability law, it is shown that within the band the permeability reduces by several orders of magnitude, but can increase outside the band. Our results highlight the importance of modeling grain size and solid fraction evolution as they exert a controlling influence on hydromechanical properties that play an important role in fault formation and seismic slip.

Coupling between creep and damage is studied in order to properly describe tertiary creep of concrete. Evolution of damage is governed by a strain tensor through an energy norm, obtained by weighting total and elastic strain tensor by means of a constant parameter. In fact, previous analyses show that, if coupling between creep and damage rely upon total strains, tertiary creep occurs too early. In this study, damage model with bilinear constitutive law and Benboudjema’s creep model are employed. Numerical simulations provide the structural response after the introduction of the coefficient.

In this paper, two commercial software packages dedicated to the simulation of crack propagation in elastomer components were tested: FLEXPAC and MSC-MARC. Firstly, the theoretical limitations of classical crack propagation laws were examined to demonstrate that actual numerical predictions are limited to very simple loading conditions. Secondly, crack propagation approaches implemented in both softwares were analysed. In order to compare their performances, fatigue experiments are performed. Different rubber components with different pre-cracks were tested under several loading conditions. Crack propagation, i.e. size and direction of the crack, was measured as a function of the number of cycles. Then, these results were compared with crack direction criteria proposed by the two models. It was demonstrated that loading amplitude highly influenced the crack direction and that the models must take this into account in their solver. Finally, limitations of this type of numerical analysis to predict the duration life of rubber components were highlighted.

Calcium silicate hydrate (C-S-H) gel is an amorphous material with a complex, disordered structure that complicates the understanding of its atomic-scale properties. While many studies have investigated ionic diffusion in C-S-H pores, the behavior of sodium ( ) and chloride ( ) ions, particularly in relation to the Ca/Si ratio, is not well understood. In this study, atomistic models of C-S-H were developed with varying Ca/Si ratios, pore sizes, and NaCl concentrations. Molecular dynamics simulations were used to calculate the self-diffusion profiles of and ions. Results indicate that pore size strongly affects diffusivity and adsorption through confinement and electrical double layer effects. The solid surface influences ionic mobility up to approximately 1.2 nm. The Ca/Si ratio has minimal impact on the diffusion profiles of non-adsorbed ions, but its rise enhances mobility near the surface and increases chloride binding capacity, consistent with prior studies.