# Mesoscale Modelling of the Mechanical Behavior of Metaconcretes
## 1 Introduction  
Artificially structured materials designed to exhibit properties not typically found in nature are metamaterials. Their conceptual foundation dates back to the late 1960s, when [PERSON] [1] proposed the idea of materials with negative refractive indices, sparkingbroader research into the manipulation of waves. Initially explored for electromagnetic applications, metamaterials later demonstrated remarkable capabilities in acoustic domains, where engineered microstructures can selectively filter or redirect sound waves [2; 3]. These systems can show negative effective mass or stiffness by exploiting local resonance phenomena, resulting in band gaps over specific frequency ranges [4; 5]. Since then, numerous metamaterials have been developed, incorporating diverse mechanisms such as locally resonant structures, phononic crystals (PCs), and geometric-based resonators, each tailored to manipulate wave propagation in distinct ways [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. Capitalizing on these properties, civil engineering researchers have introduced metaconcrete, which integrates resonant inclusions into conventional matrices to mitigate dynamic loads such as impact, blast, and seismic excitations [17; 18; 19; 20]. This innovative approach exploits the unique wave-filtering properties of metamaterials to enhance structural resilience under various transient or vibrational conditions. Unlike standard concrete, MC incorporates inclusions similar to rubber-coated steel balls or metallic cores with compliant coatings that resonate locally under dynamic loads [21; 22]. This resonance phenomenon effectively filters or attenuates stress waves that pass through the material, reducing transmitted wave amplitudes and associated damage [23; 24; 25; 26]. Early studies showed that researchers could tailor the resonant behavior by adjusting the geometry, coating thickness, material properties, and volume fraction of the inclusions [19; 27; 28]. Recent work on complex lattice-like inclusions has demonstrated that 3D resonator arrays can enhance vibration damping over a broader frequency range [29; 30; 31]. There are various practical applications of metaconcretes in specific civil engineering problems, such as the dissipation of impulsive loads (e.g., explosions) [32], their use in the design of new seismic protection systems [33; 34], and vibration attenuation [35]. Despite notable advances in dynamic performance, recent studies have highlighted potential compromises in mechanical response when incorporating resonators. In particular, soft coatings, which are vital for local resonance, weaken interfacial bonds and create stress concentrations that undermine the quasistatic load-bearing capacity [36; 37; 38; 39; 40; 41]. Some investigations have reported compressive strength reductions of up to 50% when adding resonators at just 10% by volume in concrete samples, underscoring the need to consider these design trade-offs carefully [36]. Such findings highlight the importance of comprehensively evaluating both dynamic and static requirements to optimize the performance of metaconcretes [42; 43; 40]. The available experimental evidence suggests that adequately adjusting the resonator's stiffness, the coating's thickness, and the volume fraction can yield metaconcretes with compressive strengths comparable to those of conventional concretes [40]. Achieving this balance requires a deep understanding of the underlying failure mechanisms. A growing body of research has employed mesoscale numerical models to elucidate the mechanical response of metaconcretes. For instance, [PERSON] et al. [44] developed a finite-element model of metaconcrete bars subjected to impulsive loading and validated it experimentally. [PERSON] et al. [17] introduced the concept of metaconcrete by substituting conventional aggregates with specifically designed resonant inclusions, demonstrating a significant attenuation of shock waves and vibrations through Finite Element Method (FEM) simulations. [PERSON] et al.