PSI - Issue 66

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

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1. Introduction Concrete, a versatile composite material, is made from a combination of aggregates and chemical additives, designed for various functional applications, which gives it a non-uniform structure. It has long been a fundamental material in both construction and defense sectors due to its exceptional compressive strength, durability, and its inherent resistance to both fire and water. These qualities allow for the development of strong, long-lasting structures with superior performance. Over recent years, researchers have focused on strengthening concrete by incorporating reinforcing materials [1]. However, one critical mechanical characteristic of concrete is its vulnerability to cracking when subjected to tensile forces. Due to its brittle nature, once cracks initiate, the structural integrity is significantly compromised, undermining its protective capabilities and safety. In high-stress environments like explosions or high-velocity impacts, the fracture mechanism in concrete often manifests through tensile failure, driven by the propagation of cracks. This can result in phenomena such as spalling or scabbing, where fragments or debris break off, creating additional hazards. Understanding how concrete responds to high strain rates and tensile stresses is crucial for ensuring the safety and stability of structures in such scenarios. This makes research on these topics of utmost importance. Dynamic load experiments often face challenges related to setting up appropriate testing environments and capturing rapid, short-lived events. As a result, numerical simulations using hydrocodes [2, 3, 4, 5] have become a preferred alternative for predicting structural performance and experimental results. Developing an advanced constitutive model that accurately simulates concrete dynamic tensile behavior, including crack initiation and fracture, is essential. Such a model should not only describe the material elastoplastic behavior through a yield surface but also account for nonlinear hardening and softening effects under different stress states [6]. Moreover, it should capture the degradation of tensile strength resulting from crack formation. While several yield criteria have been proposed over the years to describe brittle material behavior under various loads [7, 8, 9, 10], most models fail to represent the time-dependent, dynamic response of concrete under high-impact loading conditions [11, 12, 13], especially the crack-induced stiffness reduction [14, 15]. Recent developments have sought to improve these models by introducing yield surfaces that can account for such effects [16, 17]. Among these, the RHT model [18] has gained significant popularity as a concrete material model in commercial software, mainly applied in high-strain rate analyses like impact and penetration studies. In this paper, a crack softening mechanism has been incorporated into the standard RHT model to better simulate the dynamic tensile response of concrete. Initially, single-element simulations were employed to verify the effectiveness of the modified model. After validation, the model was applied in more extensive numerical simulations. The integration of crack softening into the RHT model represents a notable advancement in simulating and predicting dynamic behavior of concrete, which could significantly enhance the safety and efficiency of structural designs in real-world applications.

Nomenclature p

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Hydrodynamic pressure of material Normalised pressure ( p/ � ) Uniaxial compressive strength Uniaxial tensile strength

Strain rate

Reference strain rate

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Lode angle

Elastic strength surface Failure strength surface Residual strength surface Fractured strength surface Parabolic cap function Dynamic increase factor

Elastic strength along radial path Failure strength along radial path