Truss-like Discrete Element Method Applied to Damage Process Simulation in Quasi-Brittle Materials
Abstract
:1. Introduction
- Simulating a concrete slab under pure-shear stress and observing how the internal damage process translated into the signals recorded by an AE sensor.
- Subjecting a pre-fissured sandstone beam to a three-point-bending test, carried out experimentally by [41], as well as through simulations performed in this study. The simulated dataset was then used to deepen the understanding of the damage process through comparisons with the corresponding experimental data.
2. Overview of the LDEM Approach
- Introducing small disturbances throughout the mesh with the node coordinates () defined by:
- Defining the material’s specific fracture energy as a random 3D-field, according to a Type-III (Weibull) distribution, where the mean and the variation coefficient would appear as input parameters. This option also considered a spatial correlation () for when .
3. First Application: AE Events in a Simulated Fracture Process
3.1. Model Description
3.2. Results
4. Second Application: Three-Point Bending Test and Comparison to Experimental Data
4.1. Model Description
- was considered a random field with a Weibull distribution, with a mean value computed by considering = , as shown in Figure 11, and using the classical fracture-intensity factor expression for the three-point-bending test, as provided in Equations (13) and (14) [61], yielding = 345,860 Nm, and = = .
- The material porosity used by [41] was in the [0.1 mm–0.8 mm] interval, which was lower than the discretization level adopted in this study. For this reason, we assumed = , meaning that the random generation of each bar would be statistically independent. However, in the same reference, the variations in the tensile stress test were about 6% ( = [3.4 MPa–3.6 MPa]), whereas it was around 10% in [62] for sandstone specimens with the same dimensions. Previous studies using LDEM on tensile specimens with similar sizes showed that to obtain a close to 10%, the bars’ had to be about 65%. The links between the toughness random field properties and the global parameter variations were discussed in more detail in [50,63].
4.2. Results
- A significant part of the experimental AE events occurred below the pre-fissure’s head, whereas almost none appeared in the LDEM simulation. That difference was probably due to unintended damage in the pre-fissure region during the specimen preparation.
- The simulations indicated noticeable AE activities in regions other than along the main crack, such as in the vicinity of the load application (both tests) and in the horizontal direction crossing the top of the main fissure’s head (non-centered case). No such activity occurred in the corresponding regions during the experiments. These discrepancies were probably derived from the determination methods for identifying AE activity: The events in the numerical data were calculated from the kinetic energy produced inside the model, free from the attenuation that affected the signals captured by the sensors.
5. Conclusions
- The first study used simulations to illustrate the LDEM’s ability to emulate the typical results of AE tests, such as the spatial and temporal distributions of signals captured by AE sensors. It also yielded the calculations of the global parameters usually employed in AE methods for predicting local and global damage-induced instabilities.Those parameters were complemented by capturing the temporal and spatial distributions of the simulated elastic, dissipated, and kinetic energies involved. These were then used in an inverse analysis, linking the signals from the virtual AE sensors with the element-breaking events that caused their emission. These signal patterns were consistent with the system’s kinetic energy progression, i.e., every large-amplitude AE signal could be traced back to a correspondingly significant variation in the energy.By avoiding the numerous hard-to-track variables that characterize any experimental work, this approach showed a clear cause–effect link between the damage processes and the conclusions reached in our AE-based analysis, thus confirming AE coefficients as reliable failure predictors. The extension of this concept to real-world systems is subject to the effects of many extraneous factors, reducing the effectiveness accordingly. Nevertheless, AE analysis remains a valuable method for identifying global tendencies in structures undergoing damage, as indicated by Wilson in their re-normalization group procedure [64], and in other works addressing quasi-brittle materials [1,29,30,60].
- The second application used numerical simulations combined with the AE analysis of the experimental data from an actual pre-fissured sandstone beam undergoing damage. Here, the simulations were used not to mimic the experiment and corroborate the calculations of AE coefficients but to investigate the time–space distributions of the events, so the AE results could be linked to their probable causes in the structure’s interior as the damage progressed. The main points observed in this study are the following:
- –
- The simulation results of the LDEM model were qualitatively similar to the damage patterns observed experimentally, especially regarding the orientation of the major cracks.
- –
- The wave attenuation as it traveled throughout the structure was a primary limitation in identifying damage patterns through AE coefficients because it masked the corresponding signals from the data-acquisition apparatus.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
AE | Acoustic Emission |
CMOD | Crack Mouth-Opening Displacement |
LDEM | Lattice Discrete Element Method |
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E | ||||||||
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70 −1 | 100% | 2.50% | 32 | 2400 −3 | 0.25 | 4 | 4 |
E | |||||||
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−1 | 65% | 15 | 2800 −3 | 0.25 |
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Tanzi, B.N.R.; Birck, G.; Sobczyk, M.; Iturrioz, I.; Lacidogna, G. Truss-like Discrete Element Method Applied to Damage Process Simulation in Quasi-Brittle Materials. Appl. Sci. 2023, 13, 5119. https://doi.org/10.3390/app13085119
Tanzi BNR, Birck G, Sobczyk M, Iturrioz I, Lacidogna G. Truss-like Discrete Element Method Applied to Damage Process Simulation in Quasi-Brittle Materials. Applied Sciences. 2023; 13(8):5119. https://doi.org/10.3390/app13085119
Chicago/Turabian StyleTanzi, Boris Nahuel Rojo, Gabriel Birck, Mario Sobczyk, Ignacio Iturrioz, and Giuseppe Lacidogna. 2023. "Truss-like Discrete Element Method Applied to Damage Process Simulation in Quasi-Brittle Materials" Applied Sciences 13, no. 8: 5119. https://doi.org/10.3390/app13085119