Given that many properties of solid materials are inherently governed by electronic behavior, analyzing them at the electronic scale is crucial. FP calculations based on density functional theory (DFT) facilitate efficient atomistic-level simulations of essential electronic structure features, including band structures, density of states, and charge-density distributions [24]. The basic workflow of first-principles calculations is illustrated in Fig. 3, which can be divided into six stages from bottom to top:

I.

Model construction and parameter selection: The computational model is established by defining the lattice parameters, atomic occupations, and crystallographic symmetry, providing the foundational structural description for subsequent simulations.

First-principles calculations provide interatomic interaction potentials for molecular dynamics simulations, offering a robust theoretical foundation for studying material behavior at electronic and atomic scales. Furthermore, they supply essential physical parameters that facilitate the transfer of electronic-scale information to mesoscopic and macroscopic levels, thereby supporting parameter transfer and multiscale modeling.

Point defects are prevalent forms of microscopic damage in materials. They can arise intrinsically, such as from vacancies or self-interstitial atoms, or extrinsically through the incorporation of dopant atoms, and they significantly influence the mechanical properties of materials. These defects induce lattice distortions, alter interatomic bonding strengths, and affect the local mechanical stability of atoms, thereby modifying the overall mechanical behavior of the material [25]. Interstitial atoms in metals and hydrogen storage alloys exhibit specific site preferences; by modifying local bonding environments and electronic structure distributions, they can impact structural stability as well as mechanical properties such as strength and plasticity [26,27]. Mosquera-Lois et al. [28] combined first-principles calculations with ML to accurately identify stable defect configurations and elucidate how point defect-induced structural changes influence system energy and electronic structure. Dopant atoms, which form substitutional point defects by replacing host atoms in the lattice, can modulate local atomic occupancy and bonding characteristics, thereby affecting damage mechanisms and crack propagation behavior, ultimately enhancing the mechanical performance and damage tolerance of alloys [29,30]. In summary, point defects influence material strength, plasticity, and mechanical stability by altering lattice distortion, atomic bonding, and electronic structure. The integration of ML with first-principles calculations provides a novel and efficient approach for studying point defects. Fig. 4 illustrates the validation of ML based analyses in point defect studies, offering an effective pathway for investigating the impact of defects on material damage. Collectively, these studies demonstrate that point defects, as microscopic imperfections, profoundly affect mechanical properties, and the combination of artificial intelligence with first-principles methods enables rapid and accurate identification of stable defect configurations, thereby accelerating defect research.

It is noteworthy that, in addition to point defects, interfaces—being a critical microstructural feature in metallic materials—play a key role in determining material properties. Due to discontinuities in atomic arrangement and variations in chemical composition, interfaces are prone to stress concentration, lattice distortion, and local energy fluctuations, which in turn influence dislocation motion, crack propagation, and phase transformation behavior. In nanostructured metals, interfaces possess unique structural characteristics and can serve as effective defect sinks, promoting the recombination of vacancies and interstitial atoms [33]. Moreover, the termination mode, stacking structure, and elemental segregation at interfaces affect interfacial bonding strength and fracture location, thereby governing whether cracks propagate along the interface or into the matrix [34–37]. First-principles and ML studies have further demonstrated that calculating interfacial segregation and binding energies can identify alloying elements that enhance interfacial cohesion and suppress undesirable interfacial reactions [38]. Such elements can optimize interfacial electronic structure and bonding, improving material toughness, reducing the formation of brittle phases, and effectively delaying damage and crack propagation. Taken together, interfacial fracture dominates the strength and toughness of metal composites and represents a critical stage in the damage evolution process, providing essential theoretical guidance for understanding interfacial failure mechanisms and designing toughened composites.

First-principles calculations play a pivotal role in multiscale modeling. As a method independent of empirical interatomic potentials, these calculations enable the determination of key physical parameters, including elastic constants, stacking-fault energies, twin-boundary energies, diffusion barriers, and interfacial bonding energies. Moreover, by capturing fundamental electronic-level interactions, they provide mechanistic insights into the origins of macroscopic mechanical behavior, thereby offering a robust theoretical foundation for materials design and property optimization. Ultimately, first-principles calculations serve not only as an essential tool for understanding the intrinsic properties of metallic materials but also as a critical driving force in advancing multiscale simulation frameworks.

In experimental studies, material damage and fracture are typically characterized at the macroscopic scale, while the fundamental mechanisms underlying these processes occur at the microscopic level. MD simulations facilitate the observation of defect formation, irradiation damage, crack propagation, and other phenomena at the atomic scale, thereby providing deeper insights into material damage and fracture behavior [39–41]. MD is a microscopic simulation method grounded in classical mechanics, specifically Newton’s equations of motion, to describe particle systems. The typical computational workflow, illustrated in Fig. 5, encompasses model parameter loading, simulation initialization, energy minimization, equilibration, and result output. In recent years, advancements in high-performance computing and the development of diverse interatomic potentials have propelled MD into a pivotal paradigm for multiscale scientific research, leading to its widespread application in studies of phase transformations, mechanical behavior, microstructural evolution, and irradiation damage in metallic materials.

Nano-defects, including nanoscale cracks and voids, represent the primary microscopic features governing material damage and fracture. Under applied external loads, voids gradually grow and coalesce, leading to the progressive accumulation of internal damage and significant local density reductions, with microscopic damage eventually developing into macroscopic fracture. As representative microscopic defects, nanoscale voids and cracks markedly influence the yield strength, crack nucleation, and propagation behavior of metallic materials through stress concentration and local structural alterations. Their evolution is closely associated with crack size, loading conditions, and anisotropic deformation mechanisms, thereby accelerating material damage and failure [45–49]. At the atomic scale, these defects dominate the mechanisms of damage evolution and failure, providing crucial theoretical insights for understanding material degradation and fatigue behavior under complex service conditions.

Microstructural features play a critical role in governing damage evolution as well as crack initiation and propagation in metallic materials. Liu et al. [50] investigated the influence of microstructure on fatigue crack growth in steels and observed that materials with more homogeneous microstructures exhibit lower crack growth rates, while the fatigue crack growth threshold decreases with increasing grain size. Yin et al. [15] demonstrated that the refinement and uniform dispersion of the γ’phase in nickel-based superalloys increase phase-boundary density, promote dislocation nucleation and emission, and consequently alleviate crack-tip stress concentration, thereby suppressing crack propagation. Xue et al. [51] further reported that crack growth behavior in the B2 phase of Ti₂AlNb alloys strongly depends on crystallographic orientation, leading to ductile, brittle, or mixed-mode fracture. Their results indicate that crack-tip stress concentration can induce a BCC→HCP phase transformation and the formation of stacking faults, enhancing plastic deformation and improving toughness. Collectively, these studies highlight that microstructural characteristics critically influence mechanical performance by modulating crack propagation pathways and activating distinct plastic deformation mechanisms.

Irradiation damage serves as a significant source of damage in metallic materials, leading to the generation of numerous defects whose accumulation alters the microstructure and substantially degrades mechanical performance. Zhou et al. [52] employed MD simulations to demonstrate that helium bubbles influence the dynamic fracture behavior of aluminum; their expansion and coalescence are governed by dislocation activity, resulting in a reduction of dynamic tensile strength, with the weakening effect intensifying as the bubble volume fraction increases. Liu et al. [53] reported that helium bubbles preferentially agglomerate along the basal plane in α-Zr, with their size dictating variations in strength and ductility. These bubbles facilitate crack propagation along the basal plane and contribute to brittle fracture, thereby affecting the deformation and failure mechanisms of hexagonal close-packed (HCP) metals. Overall, irradiation-induced defects, particularly helium bubbles, reshape the microstructural landscape and modulate dislocation motion and crack-growth pathways. Their size, distribution, and evolution critically determine their influence on the deformation behavior, mechanical properties, and fracture response of irradiated metals.

In summary, the damage and fracture behavior of materials is governed by multiple micro-scale factors. Microdefects, such as nanovoids and nano-cracks, promote crack initiation and propagation through stress concentration, while microstructural features dictate deformation and fracture modes. Irradiation-induced defects, including helium bubbles, further alter the microstructure and degrade mechanical performance. Table 1 compares the characteristics of two representative microscale simulation methods: first-principles calculations and molecular dynamics. First-principles methods facilitate the analysis of defect formation at the electronic scale. however, they are computationally intensive and often lack direct experimental validation. Conversely, MD can elucidate phase transformations and dislocation mechanisms at the atomic scale, although its accuracy is heavily dependent on the selected interatomic potential. In recent years, ML has emerged as a powerful tool in materials science. Fig. 6 illustrates the integration of molecular dynamics with ML, which offers new pathways for predicting and elucidating the formation and evolution of microdefects in materials.

Microscopic-scale numerical simulations have made significant progress in revealing the mechanisms of material damage and fracture, but several common challenges remain: (1)

High computational cost: First-principles calculations can accurately describe point defects, interfaces, and atomic bonding at the electronic level, but they are computationally expensive and limited in time and spatial scales.

The future research directions of microscopic-scale simulations mainly focus on the following aspects: (1)

Cross-scale parameter transfer and model coupling: Incorporating physical parameters obtained from first-principles calculations into MD and higher-scale models to achieve a consistent description of damage mechanisms across scales.

Damage and fracture in metallic materials are highly complex processes rooted in the evolution of micro-scale defects, including lattice imperfections, dislocation activity, void coalescence, and the initiation and propagation of nanoscale cracks. Dislocations play a central role in plastic deformation, and their interactions with other defects largely determine a material’s strength and ductility. DDD grounded in dislocation elasticity theory, neglects atomistic details while explicitly resolving the nucleation, interaction, and motion of individual dislocations [60]. This approach enables DDD to capture the essential features of crystalline plasticity at the mesoscale. As a computational method that operates between atomistic and continuum scales, DDD directly simulates plastic deformation through dislocation evolution, thereby providing detailed insights into the mechanisms and kinetics of dislocation-mediated plasticity. Fig. 7 illustrates the primary workflow of a DDD simulation:

I.

Dislocation initialization, during which dislocation lines are discretized into nodes and segments.

This section reviews recent advances in applying DDD to investigate the role of dislocations in the dynamic damage and fracture of metallic materials, highlighting the underlying mechanisms revealed through mesoscale simulations.

Advanced experimental characterization techniques are essential for revealing crack initiation and the evolution of surface morphology. However, microscale experiments typically capture only the post-deformation configuration of dislocations and microstructures, making it challenging to observe dislocation evolution and its interactions with other defects in a real-time, comprehensive, and in-situ manner. With the rapid development of computational technologies, numerical simulation approaches have become increasingly powerful. Among these, DDD offers distinct advantages in modeling dislocation microstructure evolution and damage accumulation, providing a crucial link between microscopic mechanisms and macroscopic fracture behavior. DDD enables the simulation of key processes such as dislocation density evolution, slip-system interactions, and cross-slip, all of which govern the yielding and strain-hardening behavior of single crystals. The simulation results can accurately capture the macroscopic mechanical response, even under high strain-rate loading conditions [62]. Li et al. [63] examined the compression behavior of Mg single crystals and found that strain hardening is primarily governed by immobile dislocations and dislocation loops generated by basal-plane slip transfer. These defects increase the dislocation density and create obstacles to dislocation motion, thereby controlling the hardening response. As temperature increases, thermally activated processes are enhanced, leading to a further increase in the hardening rate. Collectively, these studies demonstrate that DDD provides a systematic framework for elucidating how dislocation density evolution, slip-system interactions, and cross-slip govern yielding, strain hardening, and fatigue damage evolution in single crystals. They underscore the critical role of microscopic dislocation behavior in shaping macroscopic mechanical responses.

Compared to single-crystal materials, polycrystalline materials exhibit more complex mechanical responses and damage evolution due to their intricate microstructures. Grain boundaries serve not only as significant obstacles and regulators of dislocation motion but also interact with defects such as dislocations, vacancies, and micro voids, influencing the mechanisms of crack nucleation and propagation. In heterogeneous polycrystalline materials, for instance, micro void growth is governed by local dislocation density and dislocation accumulation: small voids grow slowly due to limited dislocation sources, while larger voids more readily propagate into nanoscale cracks [64,65]. Furthermore, in gradient nanocrystalline materials, the distribution of residual stresses affects dislocation nucleation and motion, thereby modifying yield strength and flow stress. The combined effects of gradient structures and non-uniform residual stresses alter dislocation–grain boundary interactions and dislocation density distributions, ultimately influencing damage evolution and crack propagation [66]. Tak et al. [67], through DDD simulations, elucidated the relationships among steady-state creep rate, stress, temperature, and grain size, demonstrating that dislocation pinning at grain boundaries and obstacles affects dislocation mobility, thereby impacting creep behavior and damage evolution. Fig. 8 illustrates the mechanical performance and deformation mechanisms of gradient nanocrystalline aluminum alloys studied via DDD, showing that dislocation accumulation at interfaces generates back stresses that induce synergistic strengthening, resulting in a substantial enhancement of material strength.

These studies systematically elucidate how dislocation density evolution, slip system interactions, and cross-slip in single-crystal materials microscopically regulate yield strength, strain hardening, and fatigue damage evolution, highlighting the critical influence of microscopic dislocation behavior on macroscopic mechanical responses. Overall, DDD demonstrates a unique advantage in revealing the complex mechanical behaviors of polycrystalline materials, including crack propagation, creep, and damage evolution.

In polycrystalline materials, the grain structure and dislocation activity are the primary factors governing mechanical behavior. Under irradiation, dislocation loops and other microstructural perturbations are generated, and the accumulation and interaction of these defects significantly alter the material’s mechanical response and damage evolution. Traditional experiments face challenges in directly resolving the dynamic interactions between microscopic dislocations and irradiation-induced defects; however, DDD simulations can effectively reveal the underlying mechanisms of these processes. Irradiation-induced defects, such as dislocations, vacancy clusters, and nanoscale voids, interact with dislocations to modify plastic deformation behavior, enhancing hardening, regulating local plasticity, and mitigating damage accumulation, while also influencing crack nucleation and propagation. Furthermore, material composition and defect characteristics modulate yield strength and strain localization [69–72]. DDD studies have elucidated the microscopic mechanisms by which irradiation defects control plasticity, hardening, and damage evolution, clarifying their role in governing crack nucleation and propagation.

DDD simulations have elucidated the microscale mechanisms through which dislocation behaviors regulate the mechanical properties and damage evolution of single crystals, polycrystals, and irradiated materials. In single crystals, the evolution of dislocations and interactions among slip systems govern yield strength and the initiation of microcracks. In polycrystalline materials, grain boundaries, residual stresses, and the distribution of micropores alter dislocation motion and crack propagation, thereby influencing damage accumulation. Following irradiation, the formation of dislocation loops, clusters, and nanovoids affects strain localization and cross-slip processes, modifying hardening behavior, retarding damage progression, and ultimately influencing crack-initiation paths. Overall, the DDD method facilitates microscale investigations of dislocation-defect interactions and establishes a quantitative link between microscopic mechanisms and macroscopic mechanical responses. It provides a robust theoretical basis for interpreting damage evolution and crack propagation while offering distinct advantages for materials design and performance prediction.

With the deepening study of the micromechanical behavior and fracture mechanisms of metallic materials, it has become evident that damage at the micron scale plays a critical role in macroscopic failure. Consequently, the crystal plasticity finite element method (CPFEM) has emerged as a pivotal tool for investigating damage evolution at this scale. DDD effectively simulates the microscopic deformation of crystals under external loads, offering valuable insights into dislocation motion, slip, and the interactions that govern plastic deformation [73,74]. Through numerical simulation and analysis, CPFEM elucidates the fundamental behaviors and underlying mechanisms of crystal plasticity. By integrating crystal orientation and slip system constitutive relationships into the finite element framework, CPFEM accurately captures plastic deformation and local damage evolution under applied loads. As a result, it serves as a robust numerical approach for analyzing material mechanical performance and crack propagation. Fig. 9 illustrates the comprehensive numerical procedure for implementing CPFEM in the commercial finite element software ABAQUS through the user-defined subroutine UMAT [75].

In studies of crystalline materials, the CPFEM is widely employed to analyze the mechanical response and fracture behavior of single crystals at the mesoscale, thereby elucidating their underlying deformation mechanisms and fracture characteristics. Wu and Sun [77] demonstrated how microscale slip activity, grain orientation, and strain localization jointly influence the macroscopic mechanical performance of crystalline metals based on CPFEM. By further integrating the cohesive zone model, they successfully captured damage evolution and crack-initiation paths under multiple interacting mechanisms, providing an effective framework for predicting fracture behavior under complex loading conditions. Wang et al. [78] developed a CPFEM model that incorporates slip-system activation and dislocation evolution to investigate nanoscale scratching of single-crystal copper, revealing a strong orientation dependence of stress fields, plasticity, and surface damage. In the case of fretting fatigue in nickel-based single crystals, crystal orientation governs slip-system distribution and slip morphology, thereby shaping both surface and subsurface stress–strain fields; cracks typically propagate along the primary slip band, and the equivalent plastic strain serves as a reliable indicator for crack initiation [79,80]. Overall, CPFEM effectively correlates crystal orientation, slip behavior, and stress–strain evolution, enabling accurate characterization of damage development and crack nucleation under multi-mechanism coupling. This makes CPFEM a robust mesoscale modeling tool for predicting fracture behavior in both single- and polycrystalline materials subjected to complex loading conditions.

The macroscopic mechanical behavior of polycrystalline materials is governed by the coupled effects of microstructural evolution and external loading. By integrating crystal plasticity with other computational approaches, it is possible to capture the spatiotemporal evolution of features such as grain structures, grain boundaries, and voids, thereby quantitatively explaining the heterogeneity of stress–strain fields and the mechanisms of damage evolution. For instance, CPFE simulations of void growth in FCC polycrystals have demonstrated that microstructural heterogeneity suppresses void expansion, indicating that traditional homogeneous isotropic models tend to overestimate void growth rates [81]. Moreover, grain size, shape, orientation, and grain boundary characteristics collectively influence stress distribution, damage initiation, and crack propagation in metallic materials, while dynamic recrystallization, multi-oriented fine-grain structures, and grain boundary effects modulate dislocation nucleation and local strain distribution, significantly affecting overall mechanical performance and failure behavior [82–84]. In summary, these studies, centered on CPFE and combined with molecular dynamics, statistical damage models, and particle swarm optimization, achieve cross-scale characterization from grain boundaries and grains to voids and macroscopic responses under consistent physical constraints. This integrated approach not only captures microstructural evolution and damage initiation but also elucidates macroscopic phenomena and validates underlying mechanisms, providing valuable guidance for material strengthening design and crack propagation studies.

In recent years, the advancement of computational methods and intelligent algorithms has led to an increasing integration of CPFEM with optimization techniques and ML. These approaches not only enhance computational efficiency and predictive accuracy but also provide deeper insights into plastic deformation, structural evolution, and damage formation in polycrystalline materials. Hu et al. [85] coupled CPFEM with particle swarm optimization to develop a multiscale predictive framework that quantitatively characterizes texture evolution and heterogeneous deformation during the compression of polycrystalline copper. They found that spatial variations in grain rotation angles are significant contributors to local heterogeneous deformation and damage initiation. Mao et al. [86] employed a deep learning-driven CPFEM model, which improved stress-strain computation efficiency by 29.3 times. Dorward et al. [87] combined Gaussian processes with Sobol global sensitivity analysis, revealing significant interactions among parameters and identifying certain geometric constants as primary influencers of material yield and hardening behavior. Keshavarz et al. [88] proposed a framework that integrates physics-informed neural networks with CPFEM, incorporating equilibrium equations and constitutive relations as physical constraints to achieve high-fidelity predictions of stress-strain responses, plastic deformation gradients, and dislocation density evolution under large deformation. Although these methods do not directly simulate damage and crack propagation, the combination of CPFEM with other computational approaches effectively and accurately captures localized plasticity, heterogeneous deformation, and the influence of critical parameters in polycrystalline materials, thus providing a robust foundation for subsequent damage and fracture studies.

CPFEM provides a robust connection between microscopic deformation mechanisms and macroscopic material responses, enabling the evaluation of how crystal orientation, grain boundaries, and texture evolution influence stress-strain behavior and crack initiation. When integrated with other computational techniques, CPFEM can accurately reproduce experimentally observed crack initiation sites and propagation paths, thereby enhancing the validation of microscale mechanisms. Furthermore, the incorporation of artificial intelligence approaches, such as deep learning surrogates and physics-informed neural networks, significantly reduces computational costs and improves the generalizability of the models.

The PF is a mesoscale simulation approach particularly well-suited for modeling the evolution of microstructures within materials. Unlike macroscopic models that treat the material as a continuum or microscopic models that focus on localized atomic interactions, the PF method provides a continuous representation capable of accurately capturing the formation and evolution of grains, phase boundaries, and cracks. Since damage and fracture in metallic materials are closely linked to microstructural evolution, the PF method offers an effective means to elucidate the underlying mechanisms governing deformation, damage accumulation, and crack propagation from a mesoscale perspective. The PF method has a broad scope of applicability, encompassing single-grain growth, crack initiation and propagation, phase transformations, solute redistribution, and compositional reconfiguration. This review primarily highlights the use of the PF method to simulate the mechanical degradation of metallic materials during hydrogen embrittlement and further summarizes recent advances in PF–CPFEM coupled frameworks for analyzing deformation and damage evolution.

In recent years, researchers have employed phase-field methods to develop coupled models that address hydrogen diffusion and mechanical behavior, with a particular emphasis on reduced fracture toughness, crack interactions, and the synergistic effects of fatigue and diffusion. These studies have elucidated the mechanisms underlying damage evolution and crack propagation in metals subjected to hydrogen embrittlement. By integrating hydrogen diffusion with mechanical or fatigue behavior within a phase-field fracture framework, researchers can elucidate how hydrogen accumulation results in local degradation of mechanical properties, reduced fracture toughness, and the nucleation and growth of cracks [89–92]. Overall, phase-field approaches not only enhance our understanding of crack initiation, propagation, and fracture toughness degradation under hydrogen embrittlement but also improve the accuracy and computational efficiency of crack growth predictions.

The integration of crystal plasticity finite element (CPFE) and phase-field (PF) methods has emerged as a prominent research focus, as it facilitates the simultaneous consideration of stress evolution and microstructural changes at the continuum scale. This methodology enables a systematic analysis of twin formation mechanisms, interface migration, and interactions with dislocations and cracks. Fig. 10 illustrates the CPFE–PF coupling strategy: the CPFE method resolves the elastic and plastic deformation gradients at material points under prescribed boundary conditions, while the PF model explicitly simulates twin evolution, governed by a non-conserved phase-field equation that drives the minimization of the system’s total energy. Liu et al. [93] employed the CPFE–PF approach to investigate the effects of twins and dislocations on the plastic deformation of hexagonal metals, revealing that twin boundary migration coupled with dislocations significantly alters local stress distributions. However, the driving force for twin boundary migration must be adjusted to eliminate self-stresses induced by boundary defects to avoid biased predictions. To address this issue, Jiang et al. [94] proposed a stress-correction scheme to mitigate self-stress effects, while Mo et al. [95] developed a double-interface model utilizing CPFE–PF, accurately capturing the evolution dynamics of twin fronts and side interfaces, including key characteristics such as interface energy, driving force, and interface velocity. Overall, the CPFE–PF coupling method allows for the concurrent description of mechanical responses and twin microstructural evolution at the continuum scale, providing a robust framework for elucidating twin formation mechanisms, interface migration, and interactions with dislocations, while offering more precise insights into the influence of twinning on the macroscopic mechanical behavior of metals.

The phase-field (PF) method is a powerful tool for investigating damage and fracture in metallic materials at the mesoscopic scale. By explicitly modeling the interaction between hydrogen diffusion and mechanical fields, the PF method facilitates the description of crack initiation, propagation, interaction, and the coupled effects of fatigue and diffusion. Furthermore, the integration of crystal plasticity finite element methods with the phase-field approach (CPFE–PF) allows for the simultaneous consideration of plastic deformation and interfacial evolution. Recent advancements in the PF method present several notable advantages: (1) it eliminates the need for explicit tracking of interface positions; (2) it accurately captures material heterogeneity, defect characteristics, and anisotropy; (3) it does not require predefined microstructural morphologies. Nevertheless, several limitations persist: (1) the computational cost remains relatively high; (2) numerical predictions are often challenging to validate experimentally; (3) the PF framework encompasses numerous material and model parameters, many of which are difficult to determine accurately.

At the mesoscale, the mechanical behavior of materials is significantly influenced by dislocation evolution, grain morphology, and phase-boundary characteristics. The previous sections have reviewed various mesoscale modeling approaches applied to the study of damage and fracture in metallic materials. Under macroscopic loading, subcritical cracks frequently form within crystalline materials, and these micro-defects can substantially alter their mechanical responses. Therefore, characterizing such defects at the mesoscale is essential to enhance the safety and reliability of materials in engineering applications. Table 2 summarizes the primary mesoscale research methods and representative studies, offering a comparative overview of the capabilities of different approaches in elucidating damage evolution and crack behavior.

Mesoscopic scale numerical simulations play an important role in revealing the transitional mechanisms of material damage and crack propagation, serving as a critical bridge between microscopic defect evolution and macroscopic mechanical response. The advantages of mesoscopic-scale simulations include: (1)

Revealing the link between microstructure evolution and macroscopic mechanical behavior.

However, mesoscopic-scale simulations still have several limitations: (1)

High computational cost, which makes direct application to large-scale or long-term engineering problems challenging.