PSI - Issue 66

Sobhan Pattajoshi et al. / Procedia Structural Integrity 66 (2024) 167–174 Pattajoshi et al./ Structural Integrity Procedia 00 (2025) 000–000

173

7

concrete. Consistent with established principles, the modified model revealed more pronounced spalling damage in the higher-strength concrete, as indicated by the intensified red regions in the damage contour. This enhancement underscores the modified model effectiveness in accurately simulating tensile failure and spalling, addressing the shortcomings of the default RHT model. For a concrete strength of 48 MPa at an impact velocity of 749 m/s , the residual velocities observed were as follows: Hanchak et al. reported 615 m/s , the default RHT model predicted 625.25 m/s (a 1.67% increase), and the modified damage model yielded 625.38 m/s (a 1.69% increase). Meanwhile, for a concrete strength of 140 MPa at a velocity of 743 m/s , the residual velocities recorded were 544 m/s as per Hanchak et al., 607.47 m/s (an 11.67% increase) with the default RHT model, and 605.35 m/s (an 11.28% increase) with the modified damage model. In the default RHT model, the cracks that form in concrete under stress tend to follow straight paths. This is true for both concrete panels with strengths of 48 MPa and 140 MPa . However, when we compare the two, the crack paths in the 140 MPa concrete are noticeably straighter than those in the 48 MPa panel as presented in Fig. 2. But when we introduce the tensile cracking damage model, which takes into account the strain caused by cracking, the crack paths no longer remain straight. Instead, they shift and change direction with each increase in the cracking strain, which is a more realistic representation of how cracks should behave in concrete. This more dynamic crack pattern, influenced by the ongoing strain, can be observed and compared in Fig. 2 and Fig. 3, where the improved model shows cracks that no longer follow simple straight lines but take a more complex path as they develop. 4. Conclusion The modified damage model with the incorporation of the cracking strain provides a more realistic depiction of concrete damage and dynamic crack path compared to the default RHT model and other recent modifications. It accurately simulates the exponential strength softening under hydrostatic tension, which was a limitation. Numerical simulation of the ballistic impact on concrete targets validates the efficacy of modified damage model in reproducing the damage diameter and residual velocity of the projectile. References Song, J. H., & Eun, H. C. (2021). Improvement of flexural and shear strength of RC beam reinforced by glass fiber-reinforced polyurea (GFRPU). Civil Engineering Journal , 7 (3), 407-418. Anderson Jr, C. E. (1987). An overview of the theory of hydrocodes. International journal of impact engineering , 5 (1-4), 33-59. ANSYS Inc. (2022). ANSYS Autodyn User Manual 2022 R2 . ANSYS Inc. Pattajoshi, S., Ray, S., & Joshi, Y. K. (2024). Dynamic behaviour of multi-layer composite against single and multiple projectile impact loading. Theoretical and Applied Fracture Mechanics , 129 , 104189. Pattajoshi, S., & Ray, S. (2022, August). Dynamic Fracture Behavior of Layered Composite Under High Strain Rate Loading. In International Symposium on Plasticity and Impact Mechanics (pp. 305-322). Singapore: Springer Nature Singapore. Kishen, J. C., Ramaswamy, A., & Ray, S. computational modeling of dynamic fracture of layered composite under various strain-rate loading. Krieg, R. D., & Krieg, D. B. (1977). Accuracies of numerical solution methods for the elastic-perfectly plastic model. Bresler, B., & Pister, K. (1956). Strength of concrete under combined stresses. Drucker, D. C., & Prager, W. (1952). Soil mechanics and plastic analysis or limit design. Quarterly of applied mathematics , 10 (2), 157-165. William, K. J., & Warnke, E. P. (1975). Constitutive model for the triaxial behavior of concrete. Ottosen, N. S. (1977). A failure criterion for concrete. Journal of the Engineering Mechanics Division , 103 (4), 527-535. Li, Q. M., & Meng, H. (2003). About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test. International Journal of solids and structures , 40 (2), 343-360. Shkolnik, I. E. (2008). Influence of high strain rates on stress–strain relationship, strength and elastic modulus of concrete. Cement and Concrete Composites , 30 (10), 1000-1012. Chen, X., Wu, S., & Zhou, J. (2014). Quantification of dynamic tensile behavior of cement-based materials. Construction and Building Materials , 51 , 15-23. Hillerborg, A. (1985). The theoretical basis of a method to determine the fracture energy GF of concrete. Materials and structures , 18 , 291-296. Bi ć ani ć , N., & Pearce, C. J. (1996). Computational aspects of a softening plasticity model for plain concrete. Mechanics of Cohesive ‐ frictional Materials: An International Journal on Experiments, Modelling and Computation of Materials and Structures , 1 (1), 75-94. Holmquist, T. J., & Johnson, G. R. (2011). A computational constitutive model for glass subjected to large strains, high strain rates and high pressures. Malvar, L. J., Crawford, J. E., Wesevich, J. W., & Simons, D. (1997). A plasticity concrete material model for DYNA3D. International journal of impact engineering , 19 (9-10), 847-873.