{"title":"A novel analytical approach for simulating the mechanical behavior of multi-cracked nanobeams","authors":"Daniela Scorza , Raimondo Luciano , Andrea Carpinteri , Sabrina Vantadori","doi":"10.1016/j.engfracmech.2025.111353","DOIUrl":"10.1016/j.engfracmech.2025.111353","url":null,"abstract":"<div><div>This paper presents a novel nonlocal analytical model for simulating the mechanical behaviour of a nanobeam with multiple cracks under bending. The proposed model incorporates the Stress-Driven Nonlocal Model within the framework of the Euler-Bernoulli beam theory, dividing the nanobeam into <em>n + 1</em> beam segments at each of the <em>n</em> crack locations. These segments are connected by massless elastic rotational springs, whose stiffness is determined using both the Griffith’s energy criterion and Linear Elastic Fracture Mechanics. Firstly, the study focuses on asymmetric double cracks, characterised by different lengths and relative distances, for which Stress Intensity Factors are computed using finite element simulations. Then, the proposed model is validated against experimental data from the literature, specifically data on edge-cracked microbeams composed of NiAl single crystals subjected to bending. Finally, a parametric study is conducted varying crack lengths and distances to evaluate their influence on the mechanical response of the microbeam. The main objective of this research work is to provide valuable insights for the design and analysis of nanoscale structures with multiple cracks, contributing to various engineering applications.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"326 ","pages":"Article 111353"},"PeriodicalIF":4.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517556","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}
Duo Yi , Liangping Yi , Zhaozhong Yang , Jianping Liu , Liangjie Gou , Changxin Yang , Dan Zhang , Nanxin Zheng
{"title":"A consistent fatigue phase-field model for dynamic pulsed fracture propagation in poroelastic media","authors":"Duo Yi , Liangping Yi , Zhaozhong Yang , Jianping Liu , Liangjie Gou , Changxin Yang , Dan Zhang , Nanxin Zheng","doi":"10.1016/j.engfracmech.2025.111336","DOIUrl":"10.1016/j.engfracmech.2025.111336","url":null,"abstract":"<div><div>This paper presents a thermodynamically consistent dynamic hydraulic-mechanical coupled mixed-mode fatigue phase-field model for simulating fracture propagation in poroelastic rocks under cyclic fluid load. A fatigue degradation function is introduced that significantly reduces fracture toughness as the number of cycles increases and history variables accumulate. Damage is driven by both elastic strain energy density and fluid energy. The model uses the Newmark integration method within a finite element framework and solves the nonlinear system of equations using the Newton-Raphson iterative algorithm. The model is validated through several two-dimensional problems, including a dynamic shear test, a single-edged fracture fatigue test, a Khristianovic-Geertsma-de Klerk model, and a pulse fracturing experiment. The effects of critical energy release rate, injection rate, and injection method on pulse fracture propagation are investigated under single-fracture conditions. Additionally, the effects of different injection rates on fracture propagation are examined for tri-cluster fractures in homogeneous and layered reservoirs. The results demonstrate that the model accurately predicts complex fracture morphology.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"325 ","pages":"Article 111336"},"PeriodicalIF":4.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470025","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}
{"title":"A new formulation of SBFEM and its application to SIF computation of 3D crack","authors":"Yu Fu , Xin Xu , Zhiqiang Hu , Gao Lin","doi":"10.1016/j.engfracmech.2025.111355","DOIUrl":"10.1016/j.engfracmech.2025.111355","url":null,"abstract":"<div><div>This paper presents a novel scaling line center based scaled boundary finite element method for accurately computing stress intensity factors in three-dimensional fracture problems. Traditional methods, such as the finite element method and the boundary element method, often necessitate mesh refinement near crack fronts, which can result in computational inefficiencies and potential inaccuracies. Although scaled boundary finite element method provides advantages in addressing crack tip singularities, its existing formulations depend on a single scaling center point, which imposes geometric constraints and reduces accuracy in complex crack geometries. The proposed scaling line center based scaled boundary finite element overcomes these limitations by taking the crack front as a scaling line center, characterizing the singularity of stress field and improving accuracy of the computation of the stress intensity factor. The proposed methodology is theoretically formulated within a Hamiltonian framework and rigorously validated through a series of benchmark problems, including: (1) a cantilever beam subjected to concentrated loading, (2) single-edge crack specimens under both uniaxial tension and shear loading conditions, and (3) a lens-shaped crack embedded in a cubic domain under hydrostatic tension. Its ability to efficiently model complex three-dimensional cracks make it a valuable method for structural integrity assessment and failure analysis in fracture mechanics.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"325 ","pages":"Article 111355"},"PeriodicalIF":4.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144335748","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}
{"title":"XFEM fracture parameters are not unique for consistent global behavior in tensile, CT, and SENB specimen","authors":"Kishan Dwivedi , Saher Attia , Himanshu Pathak , Samer Adeeb","doi":"10.1016/j.engfracmech.2025.111351","DOIUrl":"10.1016/j.engfracmech.2025.111351","url":null,"abstract":"<div><div>This study investigates multiple sets of fracture parameters that yield the same global behavior for tensile, Compact Tension (CT) and Single Edge Notch Bending (SENB), using a cohesive zone model within the framework of the Extended Finite Element Method (XFEM) in Abaqus software. The cohesive zone model uses fracture energy and maximum principal strain as input parameters to determine damage initiation and crack propagation. By carefully balancing these two fracture parameters across different materials, it is possible to achieve comparable global responses in terms of fracture toughness. Crack Tip Opening Displacement (CTOD) and Crack Mouth Opening Displacement (CMOD) are used to evaluate fracture toughness for tensile, CT, and SENB specimens. Fracture behavior of specimens is presented through Force-CMOD and Force-CTOD curves for various sets of fracture parameters and compared for those sets, showing similar behaviors. The comparison includes an analysis of total crack length, cohesive damage area, and longitudinal strain (LE22) at different locations along the Force-CMOD curves where the CMOD values are identical. Additionally, this study examines the damage initiation location during crack propagation through maximum longitudinal strain perpendicular to the crack surface within region of interest. While the results show that multiple sets of XFEM fracture parameters can produce similar global Force-CMOD/CTOD responses, the local behavior around the crack tip differs significantly. For instance, the crack length varied by 10.46 % (tensile), 6.89 % (CT), and 4.96 % (SENB), and the maximum longitudinal strain near the crack surface changed by 20.80 %, 27.53 %, and 39.69 %, respectively. These findings reveal that global behavior alone is insufficient for selecting accurate XFEM fracture parameters and emphasize the need to also consider local behavior near the crack tip.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"325 ","pages":"Article 111351"},"PeriodicalIF":4.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307871","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}
{"title":"Fracture characteristic of Mg-Gd-Y alloy in wide stress state: Experiment and modeling","authors":"Pengfei Wu , Yanshan Lou","doi":"10.1016/j.engfracmech.2025.111354","DOIUrl":"10.1016/j.engfracmech.2025.111354","url":null,"abstract":"<div><div>The stress state with the complex loading path substantially impacts the hardening and fracture behaviors of the magnesium-rare earth alloys, creating considerable difficulties for practical engineering implementation. To uncover the complicated deformation behavior from yield to fracture, this research carried out the mechanical experiments of an Mg-Gd-Y alloy under various loading conditions. A constitutive model is established, including the analytical Yoon2014 (A-Yoon2014) yield function, the modified Voce (M-Voce) hardening law and the two-component ductile fracture stress-based (2DFs) fracture criterion. Experimental results indicate that the mechanical strength is with the strain-dependent coupling effect of the anisotropic and strength-differential hardening. The A-Yoon2014+M-Voce model accurately captures the non-proportional evolution characteristic of the anisotropic-asymmetric hardening behavior, and simulates the deformation behavior of all fracture specimens to determine the fracture-related variables. The fracture stress is with a strong sensitivity to the loading path. The loading path-related fracture behavior at wide stress triaxiality is modeled by the 2DFs fracture criterion with a lower prediction error (0.212) than that (0.251) of the DF2016 stress-based fracture criterion. This work proposes a constitutive model from yield to fracture to provide the numerical guidance for the forming and application of magnesium-rare earth alloys.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"325 ","pages":"Article 111354"},"PeriodicalIF":4.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322037","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}
{"title":"Application of advanced numerical material models for the simulation of a thermal shock on a ladle shroud","authors":"Zain Ali , Dietmar Gruber","doi":"10.1016/j.engfracmech.2025.111338","DOIUrl":"10.1016/j.engfracmech.2025.111338","url":null,"abstract":"<div><div>This study investigates three different numerical models (Localizing Gradient-Enhanced Damage (LGED), Phase-Field Cohesive Zone Model (PF-CZM), and Concrete Damage Plasticity (CDP)) for the simulation of the thermo-mechanical behaviour of ladle shroud. Ladle shrouds are essential in steelmaking, ensuring molten steel purity during transfer under extreme conditions. Because creep is a decisive factor, the Norton-Bailey creep model is applied to capture time-dependent high-temperature inelastic deformation. Results reveal that PF-CZM and CDP models excel in localized damage prediction, while LGED produces unphysically wide fracture zones. Creep reduces elastic energy in the system, delaying fracture. These insights enhance understanding of refractory behaviour, guiding optimized ladle shroud design to improve performance and reduce steelmaking costs.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"325 ","pages":"Article 111338"},"PeriodicalIF":4.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322038","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}
{"title":"Stress, strain, or displacement? A novel machine learning based framework to predict mixed mode I/II fracture load and initiation angle","authors":"Amir Mohammad Mirzaei","doi":"10.1016/j.engfracmech.2025.111349","DOIUrl":"10.1016/j.engfracmech.2025.111349","url":null,"abstract":"<div><div>Accurate prediction of fracture load and initiation angle under complex loading conditions, like mixed mode I/II, is essential for reliable failure assessment. This paper aims to develop a machine learning framework for predicting fracture load and crack initiation angles by directly utilizing stress, strain, or displacement distributions represented by selected nodes as input features. Validation is conducted using experimental data across various mode mixities and specimen geometries for brittle materials. Among stress, strain, and displacement fields, it is shown that the stress-based features, when paired with Multilayer Perceptron models, achieve high predictive accuracy with R<sup>2</sup> scores exceeding 0.86 for fracture load predictions and 0.94 for angle predictions. A comparison with the Theory of Critical Distances (Generalized Maximum Tangential Stress) demonstrates the high accuracy of the framework. Furthermore, the impact of input parameter selections is studied, and it is demonstrated that advanced feature selection algorithms enable the framework to handle different ranges and densities of the representative field. The framework’s performance was further validated for datasets with a limited number of data points and restricted mode mixities, where it maintained high accuracy. The proposed framework is computationally efficient and practical, and it operates without any supplementary post-processing steps, such as stress intensity factor calculations.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"325 ","pages":"Article 111349"},"PeriodicalIF":4.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322039","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}
Mohammad A. Ansari , Rujing Zha , Rui Huang , Kenneth M. Liechti
{"title":"Rotation control with dual actuators: A new device to extract mixed-mode traction–separation relations","authors":"Mohammad A. Ansari , Rujing Zha , Rui Huang , Kenneth M. Liechti","doi":"10.1016/j.engfracmech.2025.111318","DOIUrl":"10.1016/j.engfracmech.2025.111318","url":null,"abstract":"<div><div>This paper addresses the extraction of traction-separation relations associated with the mixed-mode interactions at the interfaces between two materials in the context of cohesive zone modeling for large scale bridging during delamination. A direct approach that provides the normal and shear components of the traction-separation relation at any mode-mix is pursued using a novel rotation-controlled loading device. In the past, multiple laminated beam specimen geometries have been used to vary the mode-mix. However, when using the same specimen geometry is desirable, dual actuation provides the most general solution to mixed-mode loading path control. Based on our previous work, rotation control of laminated beams has been proposed as being optimal from crack growth stability and mode-mix control standpoints. This paper describes the implementation of this concept using laminated beams consisting of an epoxy sandwiched between aluminum strips. Digital image correlation was used to determine the location of the crack front and measure the normal and shear components of the crack tip separations. The specimen geometry allows the normal and shear components of the J-integral to be determined separately via measurements of the reactive torques. The normal and shear components of the traction–separation relations for five different mode-mixes are then presented. The results challenge some of the commonly accepted trends regarding the initiation and evolution of damage. The change of mode-mix as the damage evolves is also discussed as it relies heavily on the definition of the mode-mix.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"326 ","pages":"Article 111318"},"PeriodicalIF":4.7,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517290","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}
Shijie Deng , Liangping Yi , Xiaogang Li , Zhaozhong Yang , Nanqiao Zhang
{"title":"A diagnostic model for hydraulic fracture in naturally fractured reservoir utilising water-hammer signal","authors":"Shijie Deng , Liangping Yi , Xiaogang Li , Zhaozhong Yang , Nanqiao Zhang","doi":"10.1016/j.engfracmech.2025.111347","DOIUrl":"10.1016/j.engfracmech.2025.111347","url":null,"abstract":"<div><div>The diagnostic of hydraulic fractures is vital to the exploitation of subsurface resource. Diagnostic technique for hydraulic fracture based on the water-hammer pressure have been gradually highlighted owing to their cost effectiveness and simplicity. The present diagnostic models overlook the effects of fluid leak-off and natural fracture in hydraulic fractures, and it is limited for application in naturally fractured reservoirs. In this study, the location and number of hydraulic fractures are first obtained through the enhancement and cepstrum processing of a water-hammer signal. Subsequently, the water-hammer pressure within the wellbore is calculated by solving the continuity and momentum equations for the fluid. Wellbore and hydraulic fractures are considered as a hydraulic system. To estimate the fracture dimension, flow boundary conditions are imposed to the fluid leak-off, interactions between natural and hydraulic fractures, and multifracture stress shadows. The results show that the fracturing shut-in method can be appropriately adjusted to avoid large pressure pulsations, which damage well integrity, and to obtain a clear water-hammer signal for fracture diagnosis. Natural fractures reduce the hydraulic fracture dimensions but facilitate the creation of complex fracture networks, while this complexity cannot be increased indefinitely. The minimum horizontal stress decreases the fracture dimension and a greater difference in the horizontal stress renders it easier for hydraulic fractures to cross natural fractures to create larger dimensions. The field study shows the optimisation measures can be recommended based on the diagnostic results.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"325 ","pages":"Article 111347"},"PeriodicalIF":4.7,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307869","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}
{"title":"Effects of temperature gradient and curing time on shear properties of concrete-rock interfaces in geothermal tunnels: experimental investigations","authors":"Chaojun Jia, Liang Wang, Sheng Zhang, Yanni Zheng, Chenghua Shi, Zhu Peng","doi":"10.1016/j.engfracmech.2025.111323","DOIUrl":"10.1016/j.engfracmech.2025.111323","url":null,"abstract":"<div><div>Understanding the evolution of concrete-rock interface properties under gradient thermal conditions is critically significant for ensuring the durability of support structures in high geothermal tunnels, where extreme thermal gradients threaten structural integrity. This study aims to investigate the shear behavior and failure mechanisms at this interface under simulated one-sided heating conditions (50 °C, 95 °C) representing tunnel environments. Our innovative methodology employs a custom experimental system, integrating direct shear tests at 3-day and 28-day curing ages with multi-scale characterization (SEM, XRD, CT) to link microstructure to performance. The main conclusions are that curing age dictates temperature effects; at 3 days, moderate heat (50 °C) enhances density/P-wave velocity via accelerated hydration, while 95 °C causes degradation. By 28 days, both temperatures reduce these properties. SEM/XRD/CT identify high-temperature-induced porosity, cracks, and disordered hydration products. Shear strength exhibits four-stage behavior, increasing with normal stress but critically degrading under high temperature/long curing. Two failure modes emerge: Type I (bonding surface failure) and Type II (mixed failure in adjacent concrete). The transition between modes depends on temperature and curing age. Mechanistically, thermal gradients cause uneven hydration and severe drying shrinkage, concentrating stress, initiating micro-cracks, and weakening the interface. Moderate curing temperatures enhance early performance, but strong gradients and high temperatures drastically impair long-term shear strength and structural resilience. The study establishes a novel temperature-dependent failure criterion, providing a theoretical basis for optimizing concrete in geothermal tunnels. Limitations include the simulation of one-dimensional heating and omission of cyclic thermal effects.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"325 ","pages":"Article 111323"},"PeriodicalIF":4.7,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144299002","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}