Pub Date : 2026-01-01DOI: 10.1016/j.engfracmech.2025.111838
Yaohui Deng , Peisheng Liu , Zhao Zhang , Jiajie Jin , Feiyu Qiang
A unified energy-based framework is developed to predict fatigue life and interpret damage evolution in viscoplastic joints under combined thermal cycling and broadband random vibration. The methodology integrates the Anand constitutive model for nonlinear time-dependent deformation, Darveaux’s strain energy density method for low-cycle thermal fatigue, and a Basquin-type strain life relation for vibration-induced high-cycle fatigue. Using strain energy density as a physically grounded surrogate for the fracture driving force, we propose a coupling law with an explicit interaction term that links thermal and vibrational damage channels. We further derive an analytical lifetime bound showing that the coupled lifetime is upper-bounded by the harmonic mean of the single-mode lives. Dimensionless similarity groups are introduced to generalize the predictions across materials and geometries and to support rapid design screening. Finite-element case studies on micro-interconnects demonstrate nonlinear degradation under coupled loading. The predicted hot-spot locations qualitatively follow experimentally reported corner-joint and upper-interface initiation trends. The proposed framework provides quantitative life estimation, spatial localization of fracture-prone regions without explicit crack tracking, and mechanism-informed design guidance for layered structures containing viscoplastic interfaces in thermo-vibrational environments.
{"title":"Energy-based coupling law and lifetime bounds for nonlinear fatigue of viscoplastic joints under thermo-vibrational loading","authors":"Yaohui Deng , Peisheng Liu , Zhao Zhang , Jiajie Jin , Feiyu Qiang","doi":"10.1016/j.engfracmech.2025.111838","DOIUrl":"10.1016/j.engfracmech.2025.111838","url":null,"abstract":"<div><div>A unified energy-based framework is developed to predict fatigue life and interpret damage evolution in viscoplastic joints under combined thermal cycling and broadband random vibration. The methodology integrates the Anand constitutive model for nonlinear time-dependent deformation, Darveaux’s strain energy density method for low-cycle thermal fatigue, and a Basquin-type strain life relation for vibration-induced high-cycle fatigue. Using strain energy density as a physically grounded surrogate for the fracture driving force, we propose a coupling law with an explicit interaction term that links thermal and vibrational damage channels. We further derive an analytical lifetime bound showing that the coupled lifetime is upper-bounded by the harmonic mean of the single-mode lives. Dimensionless similarity groups are introduced to generalize the predictions across materials and geometries and to support rapid design screening. Finite-element case studies on micro-interconnects demonstrate nonlinear degradation under coupled loading. The predicted hot-spot locations qualitatively follow experimentally reported corner-joint and upper-interface initiation trends. The proposed framework provides quantitative life estimation, spatial localization of fracture-prone regions without explicit crack tracking, and mechanism-informed design guidance for layered structures containing viscoplastic interfaces in thermo-vibrational environments.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111838"},"PeriodicalIF":5.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881613","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 : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111836
Tong Cui, Xiaofang Zhang, Yanan Yuan
The variable wing requires a flexible skin composite that combines high strength, high toughness, and flexibility. Inspired by the layered arrangements found in biological structures such as fish scales, a novel gradient overlapped structural design strategy based on the span direction using thin ply has been proposed. Under three-point bending tests, experimental results demonstrate that the gradient overlapped laminates with thin ply can effectively mitigates the inherent brittle fracture of continuous fiber composite. Compared to continuous fiber designs, the bio-inspired overlapped design exhibits superior structural performance in terms of flexibility and damage tolerance. Particularly, the four-gradient overlap structure achieves an excellent balance between strength and toughness by integrating the advantages of continuous and short overlap configurations. Finite element simulations further reveal the significant advantages of “S-C type” special joints designs in enhancing the comprehensive mechanical performance of composites. The optimized special joint configurations demonstrate exceptional superiority in terms of toughness and flexibility. This study provides new insights and methodologies for the structural design of composite laminates, offering important guidance for engineering applications such as aircraft skin structures that require a balance between high strength and high toughness.
{"title":"Design strategy of overlapped composite joint integrating strength, flexibility and toughness","authors":"Tong Cui, Xiaofang Zhang, Yanan Yuan","doi":"10.1016/j.engfracmech.2025.111836","DOIUrl":"10.1016/j.engfracmech.2025.111836","url":null,"abstract":"<div><div>The variable wing requires a flexible skin composite that combines high strength, high toughness, and flexibility. Inspired by the layered arrangements found in biological structures such as fish scales, a novel gradient overlapped structural design strategy based on the span direction using thin ply has been proposed. Under three-point bending tests, experimental results demonstrate that the gradient overlapped laminates with thin ply can effectively mitigates the inherent brittle fracture of continuous fiber composite. Compared to continuous fiber designs, the bio-inspired overlapped design exhibits superior structural performance in terms of flexibility and damage tolerance. Particularly, the four-gradient overlap structure achieves an excellent balance between strength and toughness by integrating the advantages of continuous and short overlap configurations. Finite element simulations further reveal the significant advantages of “S-C type” special joints designs in enhancing the comprehensive mechanical performance of composites. The optimized special joint configurations demonstrate exceptional superiority in terms of toughness and flexibility. This study provides new insights and methodologies for the structural design of composite laminates, offering important guidance for engineering applications such as aircraft skin structures that require a balance between high strength and high toughness.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111836"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882175","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 : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111833
Tom De Vuyst , Rade Vignjevic , Nenad Djordjevic , Marius Gintalas , Kevin Hughes
<div><div>The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic–plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics.</div><div>Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, as appropriately normalised kernel function, which inherently satisfies all the specific requirements on <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>: The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic–plastic fracture mechanics, including the combination with elastic–plastic constitutive models is
{"title":"Fracture Mechanics in Smoothed Particle Hydrodynamics: An algorithm to calculate the J-Integral","authors":"Tom De Vuyst , Rade Vignjevic , Nenad Djordjevic , Marius Gintalas , Kevin Hughes","doi":"10.1016/j.engfracmech.2025.111833","DOIUrl":"10.1016/j.engfracmech.2025.111833","url":null,"abstract":"<div><div>The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic–plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics.</div><div>Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, as appropriately normalised kernel function, which inherently satisfies all the specific requirements on <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>: The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic–plastic fracture mechanics, including the combination with elastic–plastic constitutive models is ","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111833"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922181","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 : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111821
Zhen Yue , Chi Zhan , Hanming Yang , Yifang Qin , Ningge Fan , Shunhua Chen
Fiber-reinforced thermoplastic laminated composites are highly sensitive to low-velocity impacts, which induces barely visible damage and accelerates fatigue failure under cyclic loading, thereby reducing structural service life. Conventional approaches for predicting post-impact fatigue behavior rely heavily on experimental testing and numerical simulations, which are often time-consuming and costly. Moreover, existing machine learning studies pay limited attention to the effects of initial impact-induced damage. To address these limitations, this study combines experimental and machine learning-based approaches for accurate fatigue life prediction of laminated composites after low-velocity impacts. Low-velocity impact tests are performed on composite specimens, and their impact responses are recorded. The induced damage is characterized using non-destructive techniques. The impacted specimens are then subjected to tensile–tensile fatigue tests to determine residual fatigue life and construct the corresponding S–N curves. The experimental results show that higher energy impacts significantly reduce the fatigue life of laminated composites. To improve model robustness, a fatigue knowledge-based data augmentation strategy via S–N curves is presented to expand the fatigue life dataset. Multiple machine learning algorithms, including Support Vector Machines (SVM), Random Forests (RF), Back-Propagation Neural Networks (BPNN), and Bayesian Neural Networks (BNNs), are introduced, trained, and optimized through hyperparameter tuning. The predictive results indicate that all employed models estimate post-impact fatigue life with reasonable accuracy, with BPNN and BNNs achieving the best overall performance.
{"title":"Experimental study and machine learning-based fatigue life prediction of thermoplastic laminated composites after low-velocity impact","authors":"Zhen Yue , Chi Zhan , Hanming Yang , Yifang Qin , Ningge Fan , Shunhua Chen","doi":"10.1016/j.engfracmech.2025.111821","DOIUrl":"10.1016/j.engfracmech.2025.111821","url":null,"abstract":"<div><div>Fiber-reinforced thermoplastic laminated composites are highly sensitive to low-velocity impacts, which induces barely visible damage and accelerates fatigue failure under cyclic loading, thereby reducing structural service life. Conventional approaches for predicting post-impact fatigue behavior rely heavily on experimental testing and numerical simulations, which are often time-consuming and costly. Moreover, existing machine learning studies pay limited attention to the effects of initial impact-induced damage. To address these limitations, this study combines experimental and machine learning-based approaches for accurate fatigue life prediction of laminated composites after low-velocity impacts. Low-velocity impact tests are performed on composite specimens, and their impact responses are recorded. The induced damage is characterized using non-destructive techniques. The impacted specimens are then subjected to tensile–tensile fatigue tests to determine residual fatigue life and construct the corresponding S–N curves. The experimental results show that higher energy impacts significantly reduce the fatigue life of laminated composites. To improve model robustness, a fatigue knowledge-based data augmentation strategy via S–N curves is presented to expand the fatigue life dataset. Multiple machine learning algorithms, including Support Vector Machines (SVM), Random Forests (RF), Back-Propagation Neural Networks (BPNN), and Bayesian Neural Networks (BNNs), are introduced, trained, and optimized through hyperparameter tuning. The predictive results indicate that all employed models estimate post-impact fatigue life with reasonable accuracy, with BPNN and BNNs achieving the best overall performance.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111821"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881615","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 : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111829
Zhongpan Li , Yan Li , Boumediene Nedjar , Ling Tao , Huijian Chen , Zhiqiang Feng
This paper presents a semi-explicit algorithm for modeling dynamic damage and fracture in ductile materials under finite deformation. The algorithm combines the efficiency of explicit methods with the stability of implicit schemes, enabling robust simulations in large deformation and contact scenarios. To further enhance numerical stability, a rotational stress update scheme based on Kirchhoff stress is implemented, which effectively handles rigid-body rotations and mitigates artificial stress artifacts. Frictional contact is addressed using an implicit algorithm based on the bi-potential method, ensuring stable and efficient contact resolution. The damage model is formulated within the continuum damage mechanics (CDM) framework, following the damage evolution theory of Chaboche and Lemaitre. Material nonlinearity is captured using an isotropic von Mises yield criterion. The proposed method is implemented in the plastic finite element program CCMPF and verified through a series of numerical examples. Two quasi-static simulations are first conducted to evaluate the mesh sensitivity of the local damage model and to verify the accuracy of the constitutive integration scheme. A dynamic Taylor impact, including both 2D and 3D cases, is performed to validate the algorithm under high strain-rate conditions. The results demonstrate the method’s accuracy, efficiency, and robustness in simulating dynamic failure in ductile materials.
{"title":"Dynamic damage evolution and fracture initiation in finite deformation ductile materials","authors":"Zhongpan Li , Yan Li , Boumediene Nedjar , Ling Tao , Huijian Chen , Zhiqiang Feng","doi":"10.1016/j.engfracmech.2025.111829","DOIUrl":"10.1016/j.engfracmech.2025.111829","url":null,"abstract":"<div><div>This paper presents a semi-explicit algorithm for modeling dynamic damage and fracture in ductile materials under finite deformation. The algorithm combines the efficiency of explicit methods with the stability of implicit schemes, enabling robust simulations in large deformation and contact scenarios. To further enhance numerical stability, a rotational stress update scheme based on Kirchhoff stress is implemented, which effectively handles rigid-body rotations and mitigates artificial stress artifacts. Frictional contact is addressed using an implicit algorithm based on the bi-potential method, ensuring stable and efficient contact resolution. The damage model is formulated within the continuum damage mechanics (CDM) framework, following the damage evolution theory of Chaboche and Lemaitre. Material nonlinearity is captured using an isotropic von Mises yield criterion. The proposed method is implemented in the plastic finite element program CCMPF and verified through a series of numerical examples. Two quasi-static simulations are first conducted to evaluate the mesh sensitivity of the local damage model and to verify the accuracy of the constitutive integration scheme. A dynamic Taylor impact, including both 2D and 3D cases, is performed to validate the algorithm under high strain-rate conditions. The results demonstrate the method’s accuracy, efficiency, and robustness in simulating dynamic failure in ductile materials.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111829"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922262","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 : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111834
Tianchi Hui , Yu Tan , Zirong Guo , Xuejun Gao , Jianjun Zhao , Xiangyu Li
Magneto-electro-elastic (MEE) solids are renowned for their excellent coupling effect among electric, magnetic and elastic fields. Nevertheless, MEE solids are susceptible to failure owing to their weak fracture toughness and inherent brittleness. Fracture analyses of MEE materials are therefore of great academic importance. In this paper, a length scale insensitive phase-field fracture model for MEE materials is proposed. The corresponding analytical solutions, including the critical stress upon crack nucleation and global responses of the specimen, are derived for the first time in 1D cases. Analytical and numerical examples are carried out to verify the insensitivity of the length scale parameter and analyse the influences of the external magnetic and electric fields on the fracture behaviors of MEE solids. The fracture load may be increased under a negative magnetic or electric field, which provides strategies for enhancing the fracture resistance performance of MEE specimens. This work is of significance in assessing the reliability of MEE-based structures and devices.
{"title":"A phase-field fracture model for magneto-electro-elastic materials: Analytical and numerical results","authors":"Tianchi Hui , Yu Tan , Zirong Guo , Xuejun Gao , Jianjun Zhao , Xiangyu Li","doi":"10.1016/j.engfracmech.2025.111834","DOIUrl":"10.1016/j.engfracmech.2025.111834","url":null,"abstract":"<div><div>Magneto-electro-elastic (MEE) solids are renowned for their excellent coupling effect among electric, magnetic and elastic fields. Nevertheless, MEE solids are susceptible to failure owing to their weak fracture toughness and inherent brittleness. Fracture analyses of MEE materials are therefore of great academic importance. In this paper, a length scale insensitive phase-field fracture model for MEE materials is proposed. The corresponding analytical solutions, including the critical stress upon crack nucleation and global responses of the specimen, are derived for the first time in 1D cases. Analytical and numerical examples are carried out to verify the insensitivity of the length scale parameter and analyse the influences of the external magnetic and electric fields on the fracture behaviors of MEE solids. The fracture load may be increased under a negative magnetic or electric field, which provides strategies for enhancing the fracture resistance performance of MEE specimens. This work is of significance in assessing the reliability of MEE-based structures and devices.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111834"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922263","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 : 2025-12-30DOI: 10.1016/j.engfracmech.2025.111820
Johannes Jonasson , Johan Lindström , Henrik Danielsson , Erik Serrano
The characterisation of wood’s fracture behaviour is a challenging task due to its inherently complex microstructure and natural variability. Consequently, to accurately model wood for engineering applications, deterministic input parameters are rarely sufficient in, for example, finite element models; the stochastic nature of the material must be considered. In the present work, we aim to quantify the variability in the fracture behaviour of two wood species: Norway spruce, which is commonly used for structural purposes in Europe, and birch, which could be an advantageous complement to Norway spruce, mainly thanks to its stiffer and stronger mechanical properties. The fracture behaviour is characterised through the three parameters that govern a material’s brittleness: the stiffness, the strength and the specific fracture energy. By formulating a parameter estimation problem based in probability theory, we use Bayesian optimisation to estimate statistical distributions of the fracture parameters of interest. These distributions are multi-variate distributions and thus contain information about the mean values, variability and dependence among the parameters. It is shown that by using random samples from the acquired distributions as input parameters to finite element models, variability observed in experimental testing is recovered well.
{"title":"Probabilistic parameter estimation and uncertainty quantification of mode I fracture in wood","authors":"Johannes Jonasson , Johan Lindström , Henrik Danielsson , Erik Serrano","doi":"10.1016/j.engfracmech.2025.111820","DOIUrl":"10.1016/j.engfracmech.2025.111820","url":null,"abstract":"<div><div>The characterisation of wood’s fracture behaviour is a challenging task due to its inherently complex microstructure and natural variability. Consequently, to accurately model wood for engineering applications, deterministic input parameters are rarely sufficient in, for example, finite element models; the stochastic nature of the material must be considered. In the present work, we aim to quantify the variability in the fracture behaviour of two wood species: Norway spruce, which is commonly used for structural purposes in Europe, and birch, which could be an advantageous complement to Norway spruce, mainly thanks to its stiffer and stronger mechanical properties. The fracture behaviour is characterised through the three parameters that govern a material’s brittleness: the stiffness, the strength and the specific fracture energy. By formulating a parameter estimation problem based in probability theory, we use Bayesian optimisation to estimate statistical distributions of the fracture parameters of interest. These distributions are multi-variate distributions and thus contain information about the mean values, variability and dependence among the parameters. It is shown that by using random samples from the acquired distributions as input parameters to finite element models, variability observed in experimental testing is recovered well.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111820"},"PeriodicalIF":5.3,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922250","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 : 2025-12-30DOI: 10.1016/j.engfracmech.2025.111830
Hong Zhao , Lei Peng , Guangcheng Long , Gang Ma , Wei Hou , Fan Wang
The mechanical responses of concrete are vital for the long-term stability of CRTS III slab track structure. This study employs laboratory tests and discrete element method (DEM) simulations to investigate the fracture behavior and crack propagation of steam-cured concrete (SC) and self-compacting concrete (SCC) used in CRTS III slab tracks. Results reveal that SC primarily fails due to aggregate penetration, while SCC is characterized by aggregate pullout. SC exhibits approximately 28% higher initial fracture toughness, about 30% greater unstable fracture toughness, and nearly 16% higher fracture energy than SCC, along with a modest 3% increase in ductility index. In contrast, SCC shows larger ultimate deformation, a more uniform crack-opening displacement distribution, and a slower evolution of the fracture process zone (FPZ), indicating better deformation capacity and crack dispersion. DEM simulations show that SC has a straighter crack propagation path, denser force-chain networks, and higher load-bearing capacity due to continuous stress transmission through the mortar matrix. Conversely, SCC demonstrates significant stress localization within aggregates, resulting in a more tortuous load-transfer path and a complex fracture process.
{"title":"Fracture behaviors of steam-cured concrete and self-compacting concrete under three-point bending:laboratory testing and DEM simulation","authors":"Hong Zhao , Lei Peng , Guangcheng Long , Gang Ma , Wei Hou , Fan Wang","doi":"10.1016/j.engfracmech.2025.111830","DOIUrl":"10.1016/j.engfracmech.2025.111830","url":null,"abstract":"<div><div>The mechanical responses of concrete are vital for the long-term stability of CRTS III slab track structure. This study employs laboratory tests and discrete element method (DEM) simulations to investigate the fracture behavior and crack propagation of steam-cured concrete (SC) and self-compacting concrete (SCC) used in CRTS III slab tracks. Results reveal that SC primarily fails due to aggregate penetration, while SCC is characterized by aggregate pullout. SC exhibits approximately 28% higher initial fracture toughness, about 30% greater unstable fracture toughness, and nearly 16% higher fracture energy than SCC, along with a modest 3% increase in ductility index. In contrast, SCC shows larger ultimate deformation, a more uniform crack-opening displacement distribution, and a slower evolution of the fracture process zone (FPZ), indicating better deformation capacity and crack dispersion. DEM simulations show that SC has a straighter crack propagation path, denser force-chain networks, and higher load-bearing capacity due to continuous stress transmission through the mortar matrix. Conversely, SCC demonstrates significant stress localization within aggregates, resulting in a more tortuous load-transfer path and a complex fracture process.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111830"},"PeriodicalIF":5.3,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881667","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 : 2025-12-29DOI: 10.1016/j.engfracmech.2025.111818
Peichen Chang , Yujun Xie , Lu Wang
The natural flaws in geotechnical, mining and civil engineering structures are primarily subjected to Mode II loading and confining pressure. Studying the fracture mechanisms of pre-cracked rock subjected to both Mode II loading and confining pressure holds great academic and practical significance. A double-ended cracked cylindrical specimen can be employed to generate a reliable quasi-Mode II singular stress field, as recommended by ISRM for determining the Mode II fracture toughness KIIC. Based on conservation law and elementary strength theory, a condition for iso-stress intensity factor (SIF) has been found for double-ended cracked cylinders subjected to punch-through shear (PTS) loading. The effective SIFs have been determined. Using the multiple-crack initiation model, the potential fracture behaviors, including notch tip coplanar growth, kinking, and branching, along with the corresponding fracture toughness KIIC, have been predicted for the PTS specimen. The notch effect on potential fracture behaviors has been investigated. The practical application of the present method has been demonstrated through the experimental investigation.
{"title":"A condition of iso-stress intensity factor and the potential fracture behaviors for double-ended cracked cylinder in punch-through shear test","authors":"Peichen Chang , Yujun Xie , Lu Wang","doi":"10.1016/j.engfracmech.2025.111818","DOIUrl":"10.1016/j.engfracmech.2025.111818","url":null,"abstract":"<div><div>The natural flaws in geotechnical, mining and civil engineering structures are primarily subjected to Mode II loading and confining pressure. Studying the fracture mechanisms of pre-cracked rock subjected to both Mode II loading and confining pressure holds great academic and practical significance. A double-ended cracked cylindrical specimen can be employed to generate a reliable quasi-Mode II singular stress field, as recommended by ISRM for determining the Mode II fracture toughness <em>K<sub>IIC</sub></em>. Based on conservation law and elementary strength theory, a condition for <em>iso</em>-stress intensity factor (SIF) has been found for double-ended cracked cylinders subjected to punch-through shear (PTS) loading. The effective SIFs have been determined. Using the multiple-crack initiation model, the potential fracture behaviors, including notch tip coplanar growth, kinking, and branching, along with the corresponding fracture toughness <em>K<sub>IIC</sub></em>, have been predicted for the PTS specimen. The notch effect on potential fracture behaviors has been investigated. The practical application of the present method has been demonstrated through the experimental investigation.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111818"},"PeriodicalIF":5.3,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034506","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 : 2025-12-27DOI: 10.1016/j.engfracmech.2025.111826
Yannan Lu , Yongjia Song , Deyou Yu , Wei Guan , Hengshan Hu
This paper analyzes the Mode-I stress intensity factor (SIF) of parallel cracks in a poroelastic medium. In particular, we investigate the influences of crack shielding on fluid flow which in turn can further change the frequency-dependent behaviors of SIF. Numerical results reveal that the frequency-dependent behaviors of SIF are jointly controlled by fluid flow and the shielding effect which is characterized by a spacing ratio , the ratio of crack spacing to crack length. The SIF of permeable cracks decreases with frequency, implying that in short-term responses the fluid has insufficient time to flow between cracks and surrounding micropores so that the crack deformation is inhibited. In the case of , the shielding effect is negligible so that our results reduce to that of a single crack for which the SIF decays the fastest when the wavelength of fluid diffusion roughly equals the crack length. For , the shielding effect can remarkably reduce the magnitude of the SIF over a broader frequency range and thereby enhance the effective material strength. In this case, the SIF decays the fastest at a higher characteristic frequency where the wavelength of fluid diffusion equals the crack spacing. For an intermediate value of , the characteristic frequency is influenced by both crack length and crack spacing. In contrast, the effect of fluid flow on the SIF of impermeable cracks is much weaker. Our findings show that both the crack shielding and permeability of crack surfaces strongly affect the magnitudes and frequency-dependent behaviors of the SIF.
{"title":"Effect of fluid flow on Mode-I dynamic stress intensity factor in the presence of crack shielding in a poroelastic medium","authors":"Yannan Lu , Yongjia Song , Deyou Yu , Wei Guan , Hengshan Hu","doi":"10.1016/j.engfracmech.2025.111826","DOIUrl":"10.1016/j.engfracmech.2025.111826","url":null,"abstract":"<div><div>This paper analyzes the Mode-I stress intensity factor (SIF) of parallel cracks in a poroelastic medium. In particular, we investigate the influences of crack shielding on fluid flow which in turn can further change the frequency-dependent behaviors of SIF. Numerical results reveal that the frequency-dependent behaviors of SIF are jointly controlled by fluid flow and the shielding effect which is characterized by a spacing ratio <span><math><mi>γ</mi></math></span>, the ratio of crack spacing to crack length. The SIF of permeable cracks decreases with frequency, implying that in short-term responses the fluid has insufficient time to flow between cracks and surrounding micropores so that the crack deformation is inhibited. In the case of <span><math><mrow><mi>γ</mi><mo>≥</mo><mn>10</mn></mrow></math></span>, the shielding effect is negligible so that our results reduce to that of a single crack for which the SIF decays the fastest when the wavelength of fluid diffusion roughly equals the crack length. For <span><math><mrow><mi>γ</mi><mo><</mo><mn>1</mn></mrow></math></span>, the shielding effect can remarkably reduce the magnitude of the SIF over a broader frequency range and thereby enhance the effective material strength. In this case, the SIF decays the fastest at a higher characteristic frequency where the wavelength of fluid diffusion equals the crack spacing. For an intermediate value of <span><math><mrow><mn>1</mn><mo><</mo><mi>γ</mi><mo><</mo><mn>10</mn></mrow></math></span>, the characteristic frequency is influenced by both crack length and crack spacing. In contrast, the effect of fluid flow on the SIF of impermeable cracks is much weaker. Our findings show that both the crack shielding and permeability of crack surfaces strongly affect the magnitudes and frequency-dependent behaviors of the SIF.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111826"},"PeriodicalIF":5.3,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882176","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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