Pub Date : 2026-01-29DOI: 10.1016/j.tafmec.2026.105484
Wenhui Sun , Yifei Li , Xiaodong Ge , Xiaojian Cao , Xianzheng Zhu , Haizhou Zhou , Shuyang Yu
Fissures in natural rock masses severely weaken bearing capacity and threaten deep engineering stability. Grouting reinforcement is an effective method for restoring integrity and inhibiting crack propagation. In this study, the mechanical properties and fracture mechanisms of 3D-printed rock-like specimens with resin-filled dual flaws under three-point bending are investigated. Digital Image Correlation (DIC) and two-dimensional Particle Flow Code (PFC2D) numerical simulations were integrated to analyze crack evolution under varying inclination angles (α). Resin filling fundamentally reconfigures the failure mechanism, shifting crack propagation from low-energy shear slip to high-energy matrix tension. Unlike unfilled specimens where increasing inclination (α) degrades strength and stress blocking effects as α increased, resin filling restored stress transmission continuity. To quantitatively elucidate this reinforcement, we analyze the mechanism of stress transfer restoration and evaluate the energy evolution using a normalized energy dissipation ratio (Kd). Analysis of the Kd ratio reveals that resin filling stabilizes the energy conversion rate between 70% and 74%, effectively overcoming the brittle collapse observed in unfilled samples. Crucially, at the critical 60° angle, the resin optimizes the energy evolution process by enforcing a transition from interface slip to matrix fracture, providing a theoretical basis for stability assessment in deep engineering projects.
{"title":"Fracture mechanisms of rock-like specimens containing double resin-infilled fissures under three-point bending loading: Sand-based 3D printing experiments and discrete element numerical simulations","authors":"Wenhui Sun , Yifei Li , Xiaodong Ge , Xiaojian Cao , Xianzheng Zhu , Haizhou Zhou , Shuyang Yu","doi":"10.1016/j.tafmec.2026.105484","DOIUrl":"10.1016/j.tafmec.2026.105484","url":null,"abstract":"<div><div>Fissures in natural rock masses severely weaken bearing capacity and threaten deep engineering stability. Grouting reinforcement is an effective method for restoring integrity and inhibiting crack propagation. In this study, the mechanical properties and fracture mechanisms of 3D-printed rock-like specimens with resin-filled dual flaws under three-point bending are investigated. Digital Image Correlation (DIC) and two-dimensional Particle Flow Code (PFC2D) numerical simulations were integrated to analyze crack evolution under varying inclination angles (<em>α</em>). Resin filling fundamentally reconfigures the failure mechanism, shifting crack propagation from low-energy shear slip to high-energy matrix tension. Unlike unfilled specimens where increasing inclination (<em>α</em>) degrades strength and stress blocking effects as <em>α</em> increased, resin filling restored stress transmission continuity. To quantitatively elucidate this reinforcement, we analyze the mechanism of stress transfer restoration and evaluate the energy evolution using a normalized energy dissipation ratio (<em>K</em><sub>d</sub>). Analysis of the <em>K</em><sub><em>d</em></sub> ratio reveals that resin filling stabilizes the energy conversion rate between 70% and 74%, effectively overcoming the brittle collapse observed in unfilled samples. Crucially, at the critical 60° angle, the resin optimizes the energy evolution process by enforcing a transition from interface slip to matrix fracture, providing a theoretical basis for stability assessment in deep engineering projects.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105484"},"PeriodicalIF":5.6,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-29DOI: 10.1016/j.tafmec.2026.105458
Seyed Hadi Bayat, Mohammad Bagher Nazari, Masoud Mahdizadeh Rokhi
In this paper, numerical tools needed to dynamic crack growth analysis in Mindlin-Reissner plate and shell structures are developed in the eXtended Finite Element Method (XFEM) framework. An interaction integral with proper auxiliary fields is introduced to extract mixed-mode Stress Intensity Factors (SIFs) for in-plane (membrane) and out-of-plane (bending) loadings for a dynamically moving crack. Besides, some relations are derived to relate the interaction integral and dynamic SIFs. These SIFs are employed to predict the crack growth direction using the maximum circumferential tensile stress criterion. An alternative relation for the crack growth speed in plates and shells is presented. Several numerical examples are presented to evaluate the accuracy of the results in modeling both quasi-static and dynamic crack growth in plates and shells, with comparisons made to available analytical and experimental data.
{"title":"An interaction integral for dynamic crack growth analysis in Mindlin-Reissner plates and shells","authors":"Seyed Hadi Bayat, Mohammad Bagher Nazari, Masoud Mahdizadeh Rokhi","doi":"10.1016/j.tafmec.2026.105458","DOIUrl":"10.1016/j.tafmec.2026.105458","url":null,"abstract":"<div><div>In this paper, numerical tools needed to dynamic crack growth analysis in Mindlin-Reissner plate and shell structures are developed in the eXtended Finite Element Method (XFEM) framework. An interaction integral with proper auxiliary fields is introduced to extract mixed-mode Stress Intensity Factors (SIFs) for in-plane (membrane) and out-of-plane (bending) loadings for a dynamically moving crack. Besides, some relations are derived to relate the interaction integral and dynamic SIFs. These SIFs are employed to predict the crack growth direction using the maximum circumferential tensile stress criterion. An alternative relation for the crack growth speed in plates and shells is presented. Several numerical examples are presented to evaluate the accuracy of the results in modeling both quasi-static and dynamic crack growth in plates and shells, with comparisons made to available analytical and experimental data.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105458"},"PeriodicalIF":5.6,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-25DOI: 10.1016/j.tafmec.2026.105482
Xingyu Tao , Shuyang Yu , Jun Yu , Yifei Li , Shan Zhao , Jiajie Li
The coupling interaction between bedding and fissures in deep layered rock masses significantly escalates the suddenness and complexity of surrounding rock instability. Consequently, investigating the mechanisms by which weak bedding planes and fissure geometric distributions control rock fracture behavior is of great importance. To address the challenge of experimental discreteness caused by the heterogeneity of natural rocks, additive manufacturing via sand-based 3D printing was employed to produce rock-like samples featuring diverse bedding orientations and double-fissure rock bridge angles. Uniaxial compression tests were conducted, combined with Digital Image Correlation (DIC) and discrete element simulations, to systematically reveal the coupling mechanisms between bedding effects and fissure-induced effects at both macroscopic and mesoscopic scales. The results indicate that: (1) The ultimate fracture manifestations of the samples exhibit significant anisotropy, where the bedding angle and fissure rock bridge inclination jointly determine the load-carrying capacity and overall structural integrity of the rock specimens. (2) Analysis of DIC full-field strain and PFC force chain evolution reveals that low rock bridge inclinations primarily induce stress superposition at crack tips and shear coalescence, manifesting as fissure-dominated failure. Conversely, high rock bridge inclinations trigger a significant stress shielding effect, shifting high-stress zones toward weak bedding planes, which results in splitting along the bedding or mixed-mode failure. (3) Numerical simulations further elucidate the stress propagation laws within the discontinuous medium, confirming the dual role of bedding planes as either stress transmission channels or barrier screens. The results contribute significantly to the theoretical framework of fracture mechanics regarding bedded rock masses containing pre-existing flaws. Furthermore, they offer essential guidance for assessing stability and mitigating geohazards in deep underground projects facing complex geological environments.
{"title":"Coupling effects of bedding and rock bridge inclination on the failure behavior of 3D printed layered sandstone specimens","authors":"Xingyu Tao , Shuyang Yu , Jun Yu , Yifei Li , Shan Zhao , Jiajie Li","doi":"10.1016/j.tafmec.2026.105482","DOIUrl":"10.1016/j.tafmec.2026.105482","url":null,"abstract":"<div><div>The coupling interaction between bedding and fissures in deep layered rock masses significantly escalates the suddenness and complexity of surrounding rock instability. Consequently, investigating the mechanisms by which weak bedding planes and fissure geometric distributions control rock fracture behavior is of great importance. To address the challenge of experimental discreteness caused by the heterogeneity of natural rocks, additive manufacturing via sand-based 3D printing was employed to produce rock-like samples featuring diverse bedding orientations and double-fissure rock bridge angles. Uniaxial compression tests were conducted, combined with Digital Image Correlation (DIC) and discrete element simulations, to systematically reveal the coupling mechanisms between bedding effects and fissure-induced effects at both macroscopic and mesoscopic scales. The results indicate that: (1) The ultimate fracture manifestations of the samples exhibit significant anisotropy, where the bedding angle and fissure rock bridge inclination jointly determine the load-carrying capacity and overall structural integrity of the rock specimens. (2) Analysis of DIC full-field strain and PFC force chain evolution reveals that low rock bridge inclinations primarily induce stress superposition at crack tips and shear coalescence, manifesting as fissure-dominated failure. Conversely, high rock bridge inclinations trigger a significant stress shielding effect, shifting high-stress zones toward weak bedding planes, which results in splitting along the bedding or mixed-mode failure. (3) Numerical simulations further elucidate the stress propagation laws within the discontinuous medium, confirming the dual role of bedding planes as either stress transmission channels or barrier screens. The results contribute significantly to the theoretical framework of fracture mechanics regarding bedded rock masses containing pre-existing flaws. Furthermore, they offer essential guidance for assessing stability and mitigating geohazards in deep underground projects facing complex geological environments.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105482"},"PeriodicalIF":5.6,"publicationDate":"2026-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-23DOI: 10.1016/j.tafmec.2026.105481
Jerome Samuel Stephen , Md Rushdie Ibne Islam
This work presents the development of a finite-strain phase-field formulation for thermo-mechanical brittle fracture within the Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) framework and its comparative assessment with the pseudo-spring model. The proposed formulation extends TLSPH to coupled thermo-mechanical conditions through a multiplicative decomposition of the deformation gradient into elastic and thermal components, enabling consistent treatment of large deformations and temperature-dependent stresses. A hyperbolic regularization of the phase-field evolution equation is adopted to enhance stability and alleviate time-step restrictions inherent in parabolic formulations. Four representative problems are investigated: thermal cracking in a double-notched specimen, expansion-induced fracture in a two-layer cylindrical rock, dynamic crack branching in a notched plate under combined loading, and thermal-shock-induced fracture in ceramics. Results are validated against experimental and numerical data, with quantitative comparisons of crack paths, crack-tip velocity, branching angle, and strain–energy dissipation. The phase-field TLSPH formulation accurately captures continuous and parallel crack evolution under severe thermal gradients, whereas the pseudo-spring model efficiently reproduces multiple small radial cracks in heterogeneous media but exhibits spurious local damage under abrupt thermal shocks. The study establishes a robust particle-based framework for thermo-mechanical fracture and clarifies the relative strengths and limitations of continuum and discrete fracture representations within TLSPH.
{"title":"Development of a finite-strain phase-field formulation for thermo-mechanical brittle fracture in Total Lagrangian SPH and its comparative assessment with pseudo-spring model","authors":"Jerome Samuel Stephen , Md Rushdie Ibne Islam","doi":"10.1016/j.tafmec.2026.105481","DOIUrl":"10.1016/j.tafmec.2026.105481","url":null,"abstract":"<div><div>This work presents the development of a finite-strain phase-field formulation for thermo-mechanical brittle fracture within the Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) framework and its comparative assessment with the pseudo-spring model. The proposed formulation extends TLSPH to coupled thermo-mechanical conditions through a multiplicative decomposition of the deformation gradient into elastic and thermal components, enabling consistent treatment of large deformations and temperature-dependent stresses. A hyperbolic regularization of the phase-field evolution equation is adopted to enhance stability and alleviate time-step restrictions inherent in parabolic formulations. Four representative problems are investigated: thermal cracking in a double-notched specimen, expansion-induced fracture in a two-layer cylindrical rock, dynamic crack branching in a notched plate under combined loading, and thermal-shock-induced fracture in ceramics. Results are validated against experimental and numerical data, with quantitative comparisons of crack paths, crack-tip velocity, branching angle, and strain–energy dissipation. The phase-field TLSPH formulation accurately captures continuous and parallel crack evolution under severe thermal gradients, whereas the pseudo-spring model efficiently reproduces multiple small radial cracks in heterogeneous media but exhibits spurious local damage under abrupt thermal shocks. The study establishes a robust particle-based framework for thermo-mechanical fracture and clarifies the relative strengths and limitations of continuum and discrete fracture representations within TLSPH.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105481"},"PeriodicalIF":5.6,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-23DOI: 10.1016/j.tafmec.2026.105477
Kuldeep Sharma , Rajalaxmi Rath , Tinh Quoc Bui
This study introduces a modified interaction integral (MII) approach within the extended finite element method (XFEM) framework to investigate semipermeable cracks in piezoelectric materials. An iterative technique, based on the iterative capacitor analogy (ICA), is developed to compute the semipermeable crack-face electric displacement condition (). The proposed methodology is validated through three benchmark configurations: center crack, edge crack, and double-edge crack problems. The calculated intensity factors are compared with existing interaction integral methods reported in the literature. For all benchmark cases, the proposed approach demonstrates a notable reduction in percentage error under electro-mechanical loading, especially when the computed is comparable to the applied electrical loading. In scenarios where is relatively small (approximately or less of the applied electrical loading), the variation in percentage error among the interaction integrals remains within 1%. Thus, in such cases, the standard interaction integral can be confidently employed for fracture mechanics analyses involving semipermeable crack-face conditions. To address inconsistencies in existing solutions for semipermeable edge and double-edge crack problems, new distributed dislocation method (DDM)-based solutions are also developed for comparison with XFEM results. Extensive numerical studies, considering variations in electrical and mechanical loads, polarization angles, and material constants, validate the robustness of the proposed approach in minimizing errors in the evaluation of electric displacement intensity factor (EDIF). Furthermore, the enhanced XFEM framework is employed to analyze macro–micro crack interactions and semipermeable crack-face electric displacement conditions in piezoelectric materials with a single edge-type macro-crack and various configurations of parallel micro-crack arrays.
{"title":"A modified interaction integral approach for XFEM analysis of semipermeable cracks in piezoelectric materials","authors":"Kuldeep Sharma , Rajalaxmi Rath , Tinh Quoc Bui","doi":"10.1016/j.tafmec.2026.105477","DOIUrl":"10.1016/j.tafmec.2026.105477","url":null,"abstract":"<div><div>This study introduces a modified interaction integral (MII) approach within the extended finite element method (XFEM) framework to investigate semipermeable cracks in piezoelectric materials. An iterative technique, based on the iterative capacitor analogy (ICA), is developed to compute the semipermeable crack-face electric displacement condition (<span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>y</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span>). The proposed methodology is validated through three benchmark configurations: center crack, edge crack, and double-edge crack problems. The calculated intensity factors are compared with existing interaction integral methods reported in the literature. For all benchmark cases, the proposed approach demonstrates a notable reduction in percentage error under electro-mechanical loading, especially when the computed <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>y</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span> is comparable to the applied electrical loading. In scenarios where <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>y</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span> is relatively small (approximately <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>20</mn><mo>)</mo></mrow></mrow><mrow><mtext>th</mtext></mrow></msup></math></span> or less of the applied electrical loading), the variation in percentage error among the interaction integrals remains within 1%. Thus, in such cases, the standard interaction integral can be confidently employed for fracture mechanics analyses involving semipermeable crack-face conditions. To address inconsistencies in existing solutions for semipermeable edge and double-edge crack problems, new distributed dislocation method (DDM)-based solutions are also developed for comparison with XFEM results. Extensive numerical studies, considering variations in electrical and mechanical loads, polarization angles, and material constants, validate the robustness of the proposed approach in minimizing errors in the evaluation of electric displacement intensity factor (EDIF). Furthermore, the enhanced XFEM framework is employed to analyze macro–micro crack interactions and semipermeable crack-face electric displacement conditions in piezoelectric materials with a single edge-type macro-crack and various configurations of parallel micro-crack arrays.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105477"},"PeriodicalIF":5.6,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.tafmec.2026.105471
Mingchao Wan , Nan Yao , Binyu Luo , Zheng Wan , Yicheng Ye
Layered rock masses, as complex geological media, exhibit mechanical behaviors predominantly controlled by internal weak interlayers and inherent fissures. This study aims to reveal the anisotropic characteristics of the mechanical behavior of layered rock masses under the interaction between weak interlayers and fissures. Uniaxial compression tests were conducted on rock-like specimens containing weak interlayers and prefabricated double fissures, combined with Digital Image Correlation (DIC) and Acoustic Emission (AE) monitoring techniques, to analyze the damage evolution process and the mechanical mechanisms of crack propagation. The results indicate that: (1) The initiation and propagation of tensile wing cracks at the fracture tips exhibit a strong competitive advantage, which weakens as the bedding dip angle increases. (2) The rock bridge serves as a key area for stress concentration and is influenced by the bridging angle β, governing the type of dominant cracks and the pattern of coalescence. (3) The weak interlayer significantly alters the interlayer stress field, inducing cracks to initiate vertically to the interlayer interface or to deflect, while demonstrating typical “barrier” and “guiding” dip effects on tip cracks. (4) The failure mode of the rock mass is primarily characterized by composite failure involving tensile cracking at the tips and penetration through the weak interlayer and hard rock layers. The propagation path is jointly influenced by the fracture dip angle, bridging angle, and the activation state of interlayer shear slip. This study reveals that when the double fissure layout (rock bridge dip angle) is oriented opposite to the dip direction of the weak interlayer, the pillar system is most susceptible to penetrating shear instability failure. Meanwhile, an increase in the bedding dip angle promotes slip along the weak interlayer, which reduces mechanical anisotropy and results in lower overall strength. These findings provide a theoretical reference for optimizing the layout and targeted support design of pillars in multi-layered stratified ore bodies, such as phosphate mines.
{"title":"Research on the mechanical anisotropy and crack propagation in composite rock masses containing weak interlayers and double fissures","authors":"Mingchao Wan , Nan Yao , Binyu Luo , Zheng Wan , Yicheng Ye","doi":"10.1016/j.tafmec.2026.105471","DOIUrl":"10.1016/j.tafmec.2026.105471","url":null,"abstract":"<div><div>Layered rock masses, as complex geological media, exhibit mechanical behaviors predominantly controlled by internal weak interlayers and inherent fissures. This study aims to reveal the anisotropic characteristics of the mechanical behavior of layered rock masses under the interaction between weak interlayers and fissures. Uniaxial compression tests were conducted on rock-like specimens containing weak interlayers and prefabricated double fissures, combined with Digital Image Correlation (DIC) and Acoustic Emission (AE) monitoring techniques, to analyze the damage evolution process and the mechanical mechanisms of crack propagation. The results indicate that: (1) The initiation and propagation of tensile wing cracks at the fracture tips exhibit a strong competitive advantage, which weakens as the bedding dip angle increases. (2) The rock bridge serves as a key area for stress concentration and is influenced by the bridging angle <em>β</em>, governing the type of dominant cracks and the pattern of coalescence. (3) The weak interlayer significantly alters the interlayer stress field, inducing cracks to initiate vertically to the interlayer interface or to deflect, while demonstrating typical “barrier” and “guiding” dip effects on tip cracks. (4) The failure mode of the rock mass is primarily characterized by composite failure involving tensile cracking at the tips and penetration through the weak interlayer and hard rock layers. The propagation path is jointly influenced by the fracture dip angle, bridging angle, and the activation state of interlayer shear slip. This study reveals that when the double fissure layout (rock bridge dip angle) is oriented opposite to the dip direction of the weak interlayer, the pillar system is most susceptible to penetrating shear instability failure. Meanwhile, an increase in the bedding dip angle promotes slip along the weak interlayer, which reduces mechanical anisotropy and results in lower overall strength. These findings provide a theoretical reference for optimizing the layout and targeted support design of pillars in multi-layered stratified ore bodies, such as phosphate mines.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105471"},"PeriodicalIF":5.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.tafmec.2026.105466
Kirill Golubiatnikov , Martin Vild , Frantisek Wald
Design net cross-section resistances for numerical design analyses of weakened tensile plates with real material properties have been established. Datasets of possible resistances for each considered geometry type were generated using a Monte Carlo-based procedure, combining a numerical-analytical approach with statistical functions of real material properties and real thicknesses reported in the literature. The generated datasets and the applied numerical - analytical approach were validated against experimental results. Subsequently, the datasets were statistically evaluated in accordance with EN 1990, and design net cross-section resistances with partial safety factors for tensile resistance were determined. The maximum obtained partial safety factor is 1.22, closely matching the recommended value of 1.23 reported in the literature. The most critical geometry types were smooth double notches, round double notches, and either sharp double notches or a narrow slotted hole. Plates with single holes or slotted holes exhibit lower design resistance than comparable double-notch plates. Additionally, staggered holes reduce resistance, whereas multiple holes in line have little effect. The results provide statistically guaranteed criteria suitable for numerical design analyses with real material properties and support harmonization with Eurocode-based practice.
The findings of this study, particularly the derived design resistances, form a foundation for establishing design failure criteria for numerical design calculations performed with nominal material properties and nominal geometry in a future study.
{"title":"Design net cross-section resistances for numerical design analyses of weakened tensile plates with real material properties","authors":"Kirill Golubiatnikov , Martin Vild , Frantisek Wald","doi":"10.1016/j.tafmec.2026.105466","DOIUrl":"10.1016/j.tafmec.2026.105466","url":null,"abstract":"<div><div>Design net cross-section resistances for numerical design analyses of weakened tensile plates with real material properties have been established. Datasets of possible resistances for each considered geometry type were generated using a Monte Carlo-based procedure, combining a numerical-analytical approach with statistical functions of real material properties and real thicknesses reported in the literature. The generated datasets and the applied numerical - analytical approach were validated against experimental results. Subsequently, the datasets were statistically evaluated in accordance with EN 1990, and design net cross-section resistances with partial safety factors for tensile resistance were determined. The maximum obtained partial safety factor is 1.22, closely matching the recommended value of 1.23 reported in the literature. The most critical geometry types were smooth double notches, round double notches, and either sharp double notches or a narrow slotted hole. Plates with single holes or slotted holes exhibit lower design resistance than comparable double-notch plates. Additionally, staggered holes reduce resistance, whereas multiple holes in line have little effect. The results provide statistically guaranteed criteria suitable for numerical design analyses with real material properties and support harmonization with Eurocode-based practice.</div><div>The findings of this study, particularly the derived design resistances, form a foundation for establishing design failure criteria for numerical design calculations performed with nominal material properties and nominal geometry in a future study.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105466"},"PeriodicalIF":5.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.tafmec.2026.105479
Yuanhao Di , Yifei Li , Qiang Liu , Xianzheng Zhu , Zhengyang Su , Shuyang Yu
In natural rock masses, joints and fissures do not exist independently. They are widely distributed in rock structures at multiple scales and in various forms. In practical engineering, the coupled effect of joints and fissures often induces shear sliding of surrounding rock, block instability, or sudden failure. Serious threats are posed to tunnel lining safety, slope stability, and the long-term service performance of underground engineering. To reveal the failure mechanisms of rock masses under the coupling effects of a serrated joint and double fissures, compression-shear tests were conducted on samples containing a serrated joint and double fissures. Crack initiation, propagation, and coalescence processes of sample under different fissure inclination angles and joint inclination angles were systematically investigated. The corresponding energy evolution characteristics and strength responses were also analyzed. During the experiments, digital image correlation (DIC) technology was introduced. Full-field deformation and strain localization characteristics on the surface of sample were monitored in real time. The stress-controlled mechanism of crack evolution was analyzed in combination with distribution characteristics of the maximum principal stress. Results show that the failure process of samples containing a serrated joint and double fissures exhibits distinct staged characteristics. The failure process of the sample is divided into distinct stages based on combined mechanical indicators, including characteristic stress–strain responses, dominant crack evolution modes, and corresponding energy variation trends. Each stage represents a specific damage state governed by different controlling mechanisms, and transitions between stages are associated with identifiable changes in mechanical response and crack activity. The fissure tips are always the preferred locations for crack initiation. The serrated joint significantly affects crack propagation paths by altering local stress concentration patterns. The formation and development of shear cracks are promoted. The increase in crack number mainly provides channels for energy dissipation. The formation and coalescence of shear cracks determine the concentration degree of energy release and the sudden instability of sample. Samples with different geometric configurations show significant differences in stress distribution, crack evolution modes, and failure patterns. The maximum principal stress contours are in good agreement with DIC strain fields in terms of crack initiation locations and coalescence paths. The findings can provide experimental evidence for understanding failure mechanisms of complex fissured rock masses and for stability analysis of underground engineering.
{"title":"Crack propagation mechanisms in rock-like samples with a serrated joint and double fissures under compression-shear loading","authors":"Yuanhao Di , Yifei Li , Qiang Liu , Xianzheng Zhu , Zhengyang Su , Shuyang Yu","doi":"10.1016/j.tafmec.2026.105479","DOIUrl":"10.1016/j.tafmec.2026.105479","url":null,"abstract":"<div><div>In natural rock masses, joints and fissures do not exist independently. They are widely distributed in rock structures at multiple scales and in various forms. In practical engineering, the coupled effect of joints and fissures often induces shear sliding of surrounding rock, block instability, or sudden failure. Serious threats are posed to tunnel lining safety, slope stability, and the long-term service performance of underground engineering. To reveal the failure mechanisms of rock masses under the coupling effects of a serrated joint and double fissures, compression-shear tests were conducted on samples containing a serrated joint and double fissures. Crack initiation, propagation, and coalescence processes of sample under different fissure inclination angles and joint inclination angles were systematically investigated. The corresponding energy evolution characteristics and strength responses were also analyzed. During the experiments, digital image correlation (DIC) technology was introduced. Full-field deformation and strain localization characteristics on the surface of sample were monitored in real time. The stress-controlled mechanism of crack evolution was analyzed in combination with distribution characteristics of the maximum principal stress. Results show that the failure process of samples containing a serrated joint and double fissures exhibits distinct staged characteristics. The failure process of the sample is divided into distinct stages based on combined mechanical indicators, including characteristic stress–strain responses, dominant crack evolution modes, and corresponding energy variation trends. Each stage represents a specific damage state governed by different controlling mechanisms, and transitions between stages are associated with identifiable changes in mechanical response and crack activity. The fissure tips are always the preferred locations for crack initiation. The serrated joint significantly affects crack propagation paths by altering local stress concentration patterns. The formation and development of shear cracks are promoted. The increase in crack number mainly provides channels for energy dissipation. The formation and coalescence of shear cracks determine the concentration degree of energy release and the sudden instability of sample. Samples with different geometric configurations show significant differences in stress distribution, crack evolution modes, and failure patterns. The maximum principal stress contours are in good agreement with DIC strain fields in terms of crack initiation locations and coalescence paths. The findings can provide experimental evidence for understanding failure mechanisms of complex fissured rock masses and for stability analysis of underground engineering.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105479"},"PeriodicalIF":5.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.1016/j.tafmec.2026.105473
R. A.A. Lima , S. Teixeira de Freitas
Tailoring the stacking sequence of composites bonded joints improves fracture toughness and damage tolerance of the joint by encouraging extrinsic toughening mechanisms, such as crack deflection and crack branching. Previous works show that in composite substrates with tailored laminates, each crack deflection into a new ply can increase the joint's toughness. Still, once a 0° layer is reached, toughness drops abruptly due to sudden delamination. To overcome this limitation, this work explores embedding a co-cured film-adhesive layer to prevent delamination in 0° plies. It examines how the substrate's bending stiffness influences the effectiveness of this toughening strategy. Quasi-static double cantilever beam tests on four different carbon fibre reinforced laminates, with and without the co-cured layer, revealed two regimes: (i) compliant substrates lead to high peel stresses, triggered crack deflection into ±45° plies, enabling bridging and rising R-curves—up to 200% toughness increase; (ii) stiffer substrates suppressed near-tip rotation, and promoted cleavage-like crack growth with minimal toughening.
{"title":"Designing for toughness: How substrate stiffness controls crack path and effective engagement of toughening layers in adhesively bonded CFRP joints","authors":"R. A.A. Lima , S. Teixeira de Freitas","doi":"10.1016/j.tafmec.2026.105473","DOIUrl":"10.1016/j.tafmec.2026.105473","url":null,"abstract":"<div><div>Tailoring the stacking sequence of composites bonded joints improves fracture toughness and damage tolerance of the joint by encouraging extrinsic toughening mechanisms, such as crack deflection and crack branching. Previous works show that in composite substrates with tailored laminates, each crack deflection into a new ply can increase the joint's toughness. Still, once a 0° layer is reached, toughness drops abruptly due to sudden delamination. To overcome this limitation, this work explores embedding a co-cured film-adhesive layer to prevent delamination in 0° plies. It examines how the substrate's bending stiffness influences the effectiveness of this toughening strategy. Quasi-static double cantilever beam tests on four different carbon fibre reinforced laminates, with and without the co-cured layer, revealed two regimes: (i) compliant substrates lead to high peel stresses, triggered crack deflection into ±45° plies, enabling bridging and rising R-curves—up to 200% toughness increase; (ii) stiffer substrates suppressed near-tip rotation, and promoted cleavage-like crack growth with minimal toughening.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105473"},"PeriodicalIF":5.6,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To reveal the mechanisms associated with the fracture of grouted and ungrouted double-fissured rock masses, crack propagation of double-fissured rock masses with different dip angles α is studied by combining experiments and numerical simulations. Rock-like samples are produced through sand-based three-dimensional printing technique, and grouted/ungrouted double-fissured models were constructed through cement grouting. Uniaxial compression experimentation and DIC technology are adopted to evaluate the damage modes and stress-strain properties. A modified particle-based model was established by embedding a particle failure treatment method into SPH method, which reproduces the crack evolution process and is validated against experimental results. The research indicates that mechanical responses of specimens are highly consistent with that of natural sandstone, enabling effective simulation of rock mass properties. Modified SPH method is able to precisely capture interface debonding between grout and rock mass as well as the dynamic crack evolution. For ungrouted specimens, with the rise in fracture dipping angle, the crack initiation position shifts from the middle of the fissures to the outer tips, forming “wing cracks”, and the inner tips tend to directly coalesce. After grouting, peak strength significantly enhanced (with the maximum improvement of 126.9% at α = 0°), the concentrated stress effect is diminished, the crack path transitions to passing the grout, the localized tensile stress zone moves from fissure tips to the interior of the grout. The present research offers experimental and numerical fundamentals for elucidating the mechanical response of grouting-reinforced double-fissured rock masses, meanwhile provides important reference value for stability control in rock engineering.
{"title":"Failure morphologies in grouted and ungrouted double fissured specimens: experiments and SPH simulations","authors":"Ting Jiang , Jilin Wang , Mengyao Shen , Wenbing Zhang , Shuyang Yu","doi":"10.1016/j.tafmec.2026.105472","DOIUrl":"10.1016/j.tafmec.2026.105472","url":null,"abstract":"<div><div>To reveal the mechanisms associated with the fracture of grouted and ungrouted double-fissured rock masses, crack propagation of double-fissured rock masses with different dip angles <em>α</em> is studied by combining experiments and numerical simulations. Rock-like samples are produced through sand-based three-dimensional printing technique, and grouted/ungrouted double-fissured models were constructed through cement grouting. Uniaxial compression experimentation and DIC technology are adopted to evaluate the damage modes and stress-strain properties. A modified particle-based model was established by embedding a particle failure treatment method into SPH method, which reproduces the crack evolution process and is validated against experimental results. The research indicates that mechanical responses of specimens are highly consistent with that of natural sandstone, enabling effective simulation of rock mass properties. Modified SPH method is able to precisely capture interface debonding between grout and rock mass as well as the dynamic crack evolution. For ungrouted specimens, with the rise in fracture dipping angle, the crack initiation position shifts from the middle of the fissures to the outer tips, forming “wing cracks”, and the inner tips tend to directly coalesce. After grouting, peak strength significantly enhanced (with the maximum improvement of 126.9% at <em>α</em> = 0°), the concentrated stress effect is diminished, the crack path transitions to passing the grout, the localized tensile stress zone moves from fissure tips to the interior of the grout. The present research offers experimental and numerical fundamentals for elucidating the mechanical response of grouting-reinforced double-fissured rock masses, meanwhile provides important reference value for stability control in rock engineering.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105472"},"PeriodicalIF":5.6,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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