PSI - Issue 66

Domenico Ammendolea et al. / Procedia Structural Integrity 66 (2024) 320–330 Author name / Structural Integrity Procedia 00 (2025) 000–000

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5. Conclusions This work aims to present a novel combined cohesive/bulk homogenization scheme for the efficient multiscale simulation of crack propagation phenomena in anisotropic heterogeneous structures. The resulting multiscale approach relies on the adoption of a Diffuse Interface Model (DIM) at the macroscopic scale, for which both bulk elements and embedded cohesive interfaces behave in a nonlinear manner according to properly homogenized constitutive laws. In particular, the overall nonlinear mechanical response of the bulk in the hardening regime is derived through “offline” computations performed at the microscopic scale ( i.e. , the RUC scale), whereas the overall nonlinear mechanical behavior of the cohesive interface in the softening regime is obtained in the subsequent “online” computational stage, for each embedded macro-interface and for each loading step of the macroscale problem. The main advantage of this approach relies on its extremely high computational efficiency, with respect to classical continuous/discontinuous homogenization approaches implemented in the framework of FE 2 -like methods. In fact, no costly RUC analyses are required to deriving the constitutive response of embedded cohesive elements after strain localization has occurred. The present continuous/discontinuous multiscale model has been applied to investigating crack propagation in a pre-cracked porous heterogeneous beam, chosen as a benchmark example, and subjected to a pure Mode-I loading case. The numerical results reported in Section 4 have highlighted that the present strategy can capture macroscopic strain localization phenomena due to microcrack propagation in a very accurate and computationally efficient way, especially if compared with direct analyses performed on fully detailed finite element models. Concluding, as a potential future development of this work, the proposed multiscale approach could be applied to more complex failure scenarios, involving multiple crack propagation, interactions with interfacial debonding, as well as global mixed-mode loading conditions. Finally, the present cohesive/bulk homogenization scheme could be generalized to incorporate the effect of finite deformations on the fracture properties of soft composites, in line with what was done, for instance, in Greco et al. (2016). Acknowledgements Domenico Ammendolea, Fabrizio Greco, Lorenzo Leonetti and Paolo Lonetti gratefully acknowledge financial support by the European Union – Next Generation EU – for the Research Grant PRIN 2022 PNRR No. P2022PE8BT "SUSTainable composite structures for energy-harvesting and carbon-storing BUILDings (SUSTBUILD)". References Ammendolea, D., Greco, F., Leonetti, L., Lonetti, P., Pascuzzo, A., 2023a. A numerical failure analysis of nano-filled ultra-high-performance fiber-reinforced concrete structures via a moving mesh approach. Theoretical and Applied Fracture Mechanics 125, 103877. Ammendolea, D., Greco, F., Leonetti, L., Lonetti, P., Pascuzzo, A., 2023b. Fatigue crack growth simulation using the moving mesh technique. Fatigue and Fracture of Engineering Materials and Structures 46(12), 4606–4627. Ammendolea, D., Greco, F., Leonetti, L., Lonetti, P., Pascuzzo, A., Penna, R., 2023c. A moving mesh-based numerical investigation of the failure response of nano-filled ultra-high-performance concrete structures. Procedia Structural Integrity 47, 488–502. Belytschko, T., Loehnert, S., Song, J.-H., 2008. Multiscale aggregating discontinuities: A method for circumventing loss of material stability. International Journal for Numerical Methods in Engineering 73(6), 869–894. Bertoldi, K., Vitelli, V., Christensen, J., van Hecke, M., 2017. Flexible mechanical metamaterials. Nature Reviews Materials 2, 17066. Cauvin, A., Testa, R.B., 1999. Damage mechanics: basic variables in continuum theories. International Journal of Solids and Structures 36, 747– 761. Coenen, E.W.C., Kouznetsova, V.G., Geers, M.G.D., 2012. Multi-scale continuous–discontinuous framework for computational homogenization–localization. Journal of the Mechanics and Physics of Solids 60(8), 1486–1507. De Maio, U., Greco, F., Lonetti, P., Pranno, A., 2024. A combined ALE-cohesive fracture approach for the arbitrary crack growth analysis. Engineering Fracture Mechanics 301, 109996. De Maio, U., Greco, F., Luciano, R., Sgambitterra, G., Pranno, A., 2023. Microstructural design for elastic wave attenuation in 3D printed nacre like bioinspired metamaterials lightened with hollow platelets. Mechanics Research Communications 128, 104045.