Reinforced concrete (RC) structures are susceptible to crack initiation and propagation during service, making accurate numerical simulation of crack behavior essential for assessing structural durability and safety. Current numerical approaches for simulating concrete cracking include smeared/continuum approaches, extended finite element method (XFEM), phase-field methods, and meso-mechanical models. In particular, smeared/continuum approaches (e.g., smeared crack and plastic-damage models such as CDP) indirectly reflect cracking through diffusive damage fields without providing explicit geometric information on crack locations and propagation paths. The XFEM module in commercial software is further restricted to first-order elements and encounters difficulties in simulating multi-crack propagation. These limitations indicate that further development of complementary crack-simulation frameworks is warranted. To this end, this paper presents a cracking simulation framework for RC members within the theoretical framework of the Specified Stress Method, adopting an adaptive degree-of-freedom strategy to balance computational accuracy and efficiency. The method introduces inelastic strain as an additional unknown and establishes a variational principle and the corresponding virtual work equation. Concrete cracking is described by specifying the stress on the crack plane to zero, so that the crack-surface stress remains zero after cracking, thereby avoiding the issue of damage reversibility and improving computational convergence. The method requires neither a predefined crack path nor remeshing after cracking. Unlike smeared/continuum approaches that rely on diffusive damage fields, the crack propagation paths, distribution characteristics, and evolution of multiple cracks are characterized through the spatial distribution of cracked integration points within the finite element mesh. In the present implementation, crack initiation is governed by the maximum tensile stress criterion, and a linear elastic constitutive model is adopted for concrete as a deliberate simplification to establish and verify the core computational mechanism of the framework. The proposed method was examined through three numerical examples. First, comparison with theoretical solutions confirmed the algorithm’s correctness in simulating cracking in heterogeneous RC tension members. Second, comparison with experimental results demonstrated qualitatively consistent crack propagation trends and load–displacement responses for RC beams under mixed-mode cracking; the calculated ultimate load of the plain concrete beam is lower than the experimental value, which is attributable to the use of the maximum tensile stress criterion without fracture energy considerations, and certain crack morphology deviations are observed due to the neglect of reinforcement–concrete bond-slip. Third, a multi-crack simulation of an under-reinforced RC beam showed that, whereas the XFEM module in ABAQUS captures only a single dominant crack near the mid-span, the proposed algorithm predicts multiple distributed cracking zones on both sides of the mid-span, qualitatively consistent with the typical flexural cracking behavior of under-reinforced RC beams; the algorithm also supports second-order elements (e.g., C3D20R) unavailable in the ABAQUS XFEM implementation. While the method is still in an exploratory stage, these results confirm the feasibility and potential of the Specified Stress Method as a complementary framework for RC cracking simulation, providing a basis for further development.
Conventional finite element methods suffer from critical drawbacks in simulating concrete crack propagation, including mandatory frequent remeshing, mesh distortion-induced numerical divergence and accuracy loss. Furthermore, robust crack evolution and autonomous crack path tracking remains challenging for existing algorithms. To overcome these limitations, this study develops a numerical model based on the Vector Form Intrinsic Finite Element (VFIFE) method for reinforced concrete (RC) shear walls. The proposed model adopts a discrete particle system, which eliminates the need for mesh rezoning and effectively avoids mesh distortion, and enables autonomous crack propagation direction selection via local stress-strain field judgment. The interaction between concrete and reinforcement across crack interfaces is represented using an equivalent interfacial spring formulation, which enables the evaluation of bond stress induced by crack opening. Comprehensive quasi-static tests were conducted on nine RC shear wall specimens with varying axial compression ratios, reinforcement ratios and aspect ratios for model validation. Numerical results show good agreement with experimental observations in crack patterns, propagation paths and damage distributions. Simulated horizontal crack heights have errors within 5%, and diagonal crack heights within 10%. The model also accurately captures crack opening widths and evolution of local bond stress induced by crack opening. Parametric studies show that higher axial compression and edge reinforcement ratios suppress crack growth, while larger aspect ratios promote cracking. Compared with conventional crack-tracking finite-element methods, the proposed VFIFE model maintains stable crack propagation through particle splitting and interfacial-spring mechanism without remeshing or global stiffness-matrix reconstruction, thereby reducing mesh-intervention cost and preserving crack-path accuracy. This VFIFE-based approach features high efficiency and stability, serving as a reliable tool for damage assessment and performance analysis of RC structures.
Hongmei Zhang, Yangyang Bao, Yuanfeng Duan et al.· International Journal of Str...· 0 citations
Rigorous application of continuum damage mechanics (CDM) models coupled with crack propagation schemes can predict crack branching or zigzag trajectories near the crack tip, even when the macroscopic crack growth is straight. This arises from oscillations in the local damage field and is consistent with experimental observations of ductile tearing; however, it complicates finite element simulations. This study investigates this behavior through two crack propagation strategies in finite element simulations. The first, termed the Mesoscale Crack Advance (MCA) approach, explicitly tracks changes in crack trajectory based on the evolving local damage field. The second, termed the Process Zone Element (PZE) approach, represents damage and crack advance in an averaged sense over a material's characteristic length. Both approaches produce similar results. Despite its simplified formulation, the PZE approach captures the essential features of ductile crack propagation and provides a computationally efficient, practical alternative for simulating ductile crack growth and brittle fracture.
A. Ziccarelli, A. Kanvinde, G. Deierlein· Fatigue & Fracture of En...· 0 citations
Abstract This study examines crack initiation and propagation in AISI D2 punch tools subjected to cyclic and impact loading using the Finite Element Method (FEM) and the Extended Finite Element Method (XFEM). FEM analysis is employed to identify stress concentration areas and potential failure points, while XFEM facilitates efficient simulation of crack growth paths without the need for re-meshing. The Johnson–Cook constitutive and damage models are applied to accurately capture the elastoplastic behavior and fracture characteristics of AISI D2 under realistic industrial punching conditions. Results show that crack evolution occurs in distinct stages, from stable propagation to catastrophic failure, closely linked to Von Mises stress and plastic strain accumulation. These numerical predictions are corroborated by microstructural observations in failed punch head. The study also highlights the superior ability of XFEM to predict crack trajectories compared to conventional FEM, providing valuable insights into fracture mechanisms. The findings offer practical guidance for improving punch tool design through geometry optimization, material selection, and surface engineering. Furthermore, this research emphasizes the critical role of predictive numerical modeling in extending tool life, minimizing downtime, and enhancing reliability in industrial sheet metal forming processes.
Abdelwaheb Zeidi, Khaled Elleuch, Ş. Atapek et al.· Materials Testing· 0 citations
While reinforced concrete offers wide applicability and low cost, cracking remains a critical factor impairing its durability, a challenge that can be addressed by optimizing reinforcement configuration and digital structural modeling to inhibit crack propagation. The rapid advancement of digital technology provides a novel approach to optimizing the spatial distribution of these reinforcement parameters, ensuring a more resilient and durable composite structure. Focusing on digital technology-driven enhancement of the crack resistance of reinforced concrete structures, this study systematically explores the application mechanisms and empirical effects of parametric modeling and finite element analysis in this field. Firstly, it summarizes the cracking mechanisms of reinforced concrete structures and the current state of digital technology applications. Secondly, a parametric modeling framework for reinforced concrete structures based on Python+Grasshopper is established, clarifying the correlation between key design parameters and crack resistance. Thirdly, using ABAQUS finite element analysis software, a refined finite element model considering material nonlinearity and interface bond-slip is developed to conduct numerical simulations of crack resistance. Finally, the reliability of parametric modeling and finite element analysis is verified through typical component tests, and an optimization scheme for crack resistance based on digital technology is proposed. The results indicate that parametric modeling enables efficient iteration and precise control of design parameters for reinforced concrete structures integrated with optimized reinforcement configurations, while finite element analysis can accurately predict how material and interface parameters influence the initiation and propagation laws of structural cracks. When paired with electromagnetic or other nondestructive inspection data, the parametric model may further support structural damage assessment.
Concrete readily develops cracks under service loads, which poses severe risks to the overall safety of engineering structures. In this work, the discrete element method (DEM) integrated with PFC2D 5.0 numerical software is adopted to construct a mesoscale concrete numerical model containing pre-existing internal fractures, and uniaxial compressive loading simulations are subsequently carried out. Unlike previous studies that predominantly examined isolated fracture parameters, this work systematically investigates the coupled effects of fracture inclination angle, length, and quantity on crack propagation mechanisms at the mesoscale, and for the first time establishes a quantitative relationship between microcrack spatial distribution patterns and macroscopic mechanical degradation. Parametric analyses are performed to quantify the influences of fracture geometric characteristics, including fracture inclination angle (30°, 45°, 60°), fracture length (short, long and extra-long), fracture quantity (4, 8 and 16), as well as the comparison between intact and fractured concrete specimens. The fracture quantities of 4, 8, and 16 are selected to represent low, medium, and high levels of initial defect density within the concrete matrix, corresponding to approximately 1%, 2%, and 4% of the total specimen area, respectively, thereby enabling a systematic investigation into the progressive deterioration of mechanical performance with increasing internal damage severity. The whole evolution process of crack initiation, crack propagation and ultimate failure patterns of concrete is systematically explored. Numerical results reveal that specimens with larger fracture angles exhibit higher compressive strength yet generate abundant newly formed microcracks, whereas low-angle prefabricated fractures are prone to triggering abrupt brittle failure. Specimens embedded with shorter fractures achieve superior mechanical strength and develop denser, more intensive microcrack distributions; in contrast, long pre-existing fractures drastically degrade compressive strength while limiting the generation of secondary cracks. Reducing the number of internal defects simultaneously improves compressive strength and expands the coverage range of the induced fracture network. Specimens with 16 prefabricated fractures deliver the weakest mechanical performance, owing to the excessively high initial defect density inside the matrix. In comparison with fractured samples, intact concrete without pre-set fractures achieves better comprehensive performance in terms of compressive strength, deformation compatibility and uniform microcrack development. A core conclusion drawn from this study is that the total quantity of microcracks cannot serve as a direct indicator to evaluate the damage degradation degree of concrete; instead, the spatial distribution pattern of microcracks dominates the deterioration level. Evenly scattered microcrack populations maintain relatively high residual strength, whereas the concentrated coalescence of microcracks into continuous penetrating macrocracks leads to an abrupt decline in structural load-carrying capacity. The findings of this research can provide theoretical references for stability evaluation and safety diagnosis of defective concrete structures in practical engineering.
Haiying Mao, Jun Zhen, Zuodong Zhou et al.· Materials· 0 citations
Concrete structures in service are frequently subjected to sustained loading, which may lead to crack propagation at high load levels and the subsequent reduction in structural stiffness. Therefore, investigating the crack propagation process is essential for evaluating structural performance. This study investigates the crack propagation process of three-point bending beams under sustained loading through experimental tests and numerical simulations. First, creep fracture tests are conducted under sustained load levels of 0.90, 0.85, 0.80, and 0.75. The results indicate that as the load level increases, the nonlinear characteristics of concrete become more pronounced, the creep fracture lifetime decreases exponentially, and both the crack mouth opening displacement and crack propagation length gradually decrease with increasing sustained load level. Subsequently, numerical simulations are performed to calculate the creep fracture lifetime, crack mouth opening displacement, and crack length under different sustained load levels. In these simulations, the viscoelastic behavior of concrete is represented using a two-element Kelvin chain model, and the decay of cohesive stress in the fracture process zone is described through the tension-softening constitutive model proposed in the previous research. A crack propagation criterion based on initial fracture toughness
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is employed. The numerical results exhibit good agreement with the experimental results, confirming the validity of the proposed method in predicting the creep fracture behavior of concrete. These findings provide a reference for estimating the creep fracture lifetime of concrete structures under sustained loading.
Xiaoyan Han, Hongwei Wang, Shaodong Shen et al.· Journal of materials in civi...· 0 citations
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