High-velocity fragments from building glass pose severe safety hazards during gas explosions. This study investigated the failure mechanisms and fragmentation dynamics of architectural glass under liquefied petroleum gas (LPG) and natural gas (NG) explosions using integrated full-scale experiments and numerical simulations. The results demonstrate that gas type is the dominant factor influencing blast load and glass response. Owing to its higher energy density and burning velocity, LPG produced a far-field overpressure peak of 78.2 kPa, approximately 8 times greater than that of NG, which was 10.4 kPa. Additionally, LPG generated a faster blast wave (arrival time: 0.62 versus 1.75 s, respectively) and 78% higher initial fragment velocities (15.1 m/s compared to 8.3 m/s, respectively). Gas stratification further affected fracture patterns, with floor-deposited LPG causing top-initiated fracture and ceiling-accumulated NG leading to bottom-initiated failure. Fragment dispersal follows a two-stage acceleration process: initial blast-induced fracture within 1 m, followed by gas-venting-driven acceleration propelling fragments beyond 30 m/s. Mass recovery analysis indicated that only 16.5% of glass was recovered after LPG explosions, compared with 25.54% for NG explosions, indicating significantly farther fragment projection and an expanded hazard zone. Numerical simulations using LS-DYNA with the Johnson–Holmquist ceramic (JH-2) constitutive model accurately captured fracture and fragmentation processes, confirming that thinner glass produces sharper, high-aspect-ratio fragments with elevated penetration risk despite lower velocities. These findings provide valuable insights for safety assessments and structural design in explosion-prone environments.

All-solid-state batteries promise improved safety and higher energy density by replacing flammable liquid electrolytes and graphite anodes with solid electrolytes and lithium metal1-4. However, the penetration of soft lithium dendrites into hard ceramic electrolytes remains a substantial obstacle to realizing all-solid-state lithium metal batteries5-7. The mechanism by which mechanically soft lithium dendrites fracture hard ceramic electrolytes remains under debate7-10 owing to the challenges of characterizing nanoscale lithium distribution and its microstructure at the dendrite tip11. Here we investigate the fracture process driven by lithium dendrites in garnet electrolytes using multiscale cryogenic electron microscopy and micromechanical fracture models. We directly visualize lithium dendrites fully filling nanoscale crack tips and extending into micrometre-scale cracks. Limited crystal lattice rotation and plasticity in lithium dendrites indicate that the plated lithium generates substantial hydrostatic stress, which induces tensile stress in the solid electrolyte and drives both intergranular and transgranular fracture. By contrast, the region ahead of the lithium dendrite tip shows no measurable enrichment of lithium or lithium metal nuclei. The mechanically driven lithium penetration in garnet solid electrolyte can be redirected by geometrically engineered voids in the electrolyte, thus mitigating short-circuiting. Our findings suggest that grain boundary toughening and defect engineering are effective strategies for designing dendrite-resistant solid electrolytes.

Liquid nitrogen (LN2) fracturing is a highly promising stimulation technology for unconventional reservoirs. Understanding its in situ fracture network formation mechanism is essential for engineering practice. This study investigates coal rock fracturing driven by the synergistic effect of thermal stress and fluid pressure during LN2 injection. A coupled thermal–hydraulic–mechanical–damage (THMD) numerical model is developed, incorporating in situ stress conditions and LN2 phase change behavior. Through true triaxial LN2 fracturing simulations validated against physical experiments, the multi-field dynamic coupling behavior is systematically analyzed, revealing the synergistic mechanism of fracture propagation and permeability enhancement under cryogenic conditions. The results show the following: (1) The proposed model effectively reproduces the true triaxial LN2 fracturing process, with simulation results in good agreement with physical experiments. (2) LN2 fracturing exhibits distinct stage-wise characteristics: cryogenic temperatures induce thermal stress that triggers micro-crack initiation; the self-enhancing effects of damage and permeability significantly promote fracture propagation; fluid pressure then becomes the dominant driving force. (3) Coal rock damage follows a four-stage evolution—wellbore crack initiation, stable propagation, unstable propagation, and through-going failure—ultimately forming a complex spatial fracture network. (4) The horizontal stress ratio is a key factor controlling fracture morphology: a single dominant fracture forms under a high stress difference, whereas a multi-directional complex network develops under equal confining pressure. Fractal analysis reveals significant anisotropy and a non-monotonic stress response in the fracture complexity, reflecting structural evolution from multi-directional propagation to main channel connection. This study provides theoretical support for understanding LN2 fracturing mechanisms and optimizing field treatment parameters.

Abstract The incorporation of fibers can effectively mitigate the degradation of static mechanical properties in rubberized concrete and further improve its toughness. However, the internal structural damage evolution and failure mechanisms pre‐ and post‐elevated temperatures remain unclear. Therefore, this study uses acoustic emission (AE) technology to monitor the fracture process of fiber‐reinforced rubberized concrete pre‐ and post‐elevated temperatures in real time, and applies avalanche dynamics theory to statistically analyze the AE signals generated during the loading process. The study discusses the influence of rubber powder (0%, 5%, 10%, 15%) content and ambient temperature (25°C, 100°C, 200°C, 400°C, and 600°C) on the probability distribution of AE characteristic signals and their corresponding distribution indices. Results show that enhancing rubber powder content significantly raises the percentage of low‐energy events in the fracture process, indicating improved ductility. The AE characteristic index also increases with higher rubber powder dosage, reaching ε , τ , and α values of 1.55, 2.35, and 2.80 at 15% rubber powder. Under elevated temperatures, high‐energy events decrease while low‐energy events increase, reducing the monitorable AE signal. The characteristic index increases with rising temperature, with ε , τ , and α being 1.65, 2.62, and 3.80 at 600°C. The avalanche index correlates with peak load variations and is sensitive to microstructure changes.

ABSTRACT The Theory of Critical Distances comprises several methodologies that allow fracture, fatigue, and stress corrosion cracking phenomena to be analyzed. Such methodologies are usually referred to as the Point Method (PM), the Line Method (LM), the Area Method (AM), and the Volume Method (VM). All of them provide analyses where the corresponding material resistance (e.g., fracture toughness, fatigue threshold, and stress corrosion cracking threshold) is used together with an additional material parameter with length units (the critical distance, L). Moreover, the accuracy of these four approaches is very similar, but the PM and the LM have a much simpler application. When dealing with fracture processes, the TCD allows fracture conditions for structural materials in the presence of notch‐type defects to be established, and simple formulas for estimating the apparent fracture toughness (i.e., the fracture resistance in the presence of notches) to be obtained. This paper provides a number basic reasonings related to both the PM and/or the LM formulations that allow different straightforward conclusions to be derived, with significant theoretical and practical implications. Real cases with experimental results are also included, exemplifying what is discussed in the theoretical analysis.

Fluid-driven fracture processes are central to the development of subsurface energy systems such as geothermal and hydrocarbon reservoirs. Although phase-field formulations have become a widely used tool for describing fracture initiation and growth, the diffuse representation of cracks makes it difficult to resolve flow behavior accurately inside discrete fracture networks (DFNs) and to represent hydro-mechanical coupling in a sharp-interface sense. This study develops a hybrid-dimensional iterative framework for lubrication-flow simulation in deformable fractured geomaterials. By leveraging phase-field point clouds together with non-conforming discretization schemes for both the solid matrix and fracture domains, the proposed framework enables the dynamic reconstruction of evolving fracture networks. The theoretical formulation and numerical implementation of the coupling strategy are presented in detail. Hydraulic benchmark examples verify the performance of the fluid flow solver under various physical conditions. The classical Sneddon problem and Khristianovic-Geertsma-de Klerk (KGD) model are employed to validate the solid deformation solver, confirming accurate predictions of crack opening displacement and mesh independence in fracture width calculation. Additional simulations with complex pre-existing fracture patterns further demonstrate the applicability of the framework to coupled hydro-mechanical analysis in fractured media.

ABSTRACT In this study, a generalized peridynamic model incorporating Seth–Hill bond‐strain measures is proposed to capture mixed‐mode fracture behaviors. We begin with the reformulation of the model introduced by Tupek and Radovitzky within the ordinary state‐based peridynamic (OSB‐PD) framework, where we demonstrate that the three‐dimensional shape tensor state satisfies an integral identity equivalent to the fourth‐order symmetric identity tensor. Based on this identity, the shape tensor state tailored for two‐dimensional problems is constructed, enabling the derivation of the corresponding scalar force state based on Seth–Hill bond‐strain measures for linear elastic materials. This generalized model avoids unphysical material interpenetration and enables the decomposition of the scalar force state over the classic model. Moreover, a nonlocal work‐conjugate stress tensor is developed for the first time by employing the reformulated scalar force state based on the principle of work conjugacy and the integral identity of the shape tensor state. Finally, the maximum principal stress and Drucker–Prager failure criteria are incorporated into the generalized OSB‐PD framework to enable the simulation of mixed‐mode brittle fracture. The accuracy and robustness of the proposed model are validated through several benchmark cases, demonstrating accurate stress evaluation and failure prediction. Notably, the model successfully captures complex crack coalescence patterns in rock subjected to uniaxial compression, underscoring its effectiveness in depicting mixed‐mode fracture processes.

Abstract The Extended Finite Element Method (XFEM) has recently emerged as a highly effective tool for analyzing crack propagation in complex structures, but its use in pipeline fracture studies, particularly with cohesive zone models (CZM), is still developing. Current XFEM fracture criteria are not calibrated for pipeline steels, relying on fixed fracture stress or strain to initiate crack propagation. While the stress-based criterion works for brittle fractures, it fails for ductile ones, either accelerating cracks or preventing them altogether. The strain-based criterion better predicts both fracture types, but its numerical accuracy remains inadequate, highlighting a need for further research. This numerical study explores the use of XFEM to predict crack propagation in standard fracture specimens of single edge notch bending (SENB) made of X52 pipe steels. First, an XFEM-based cohesive zone model was developed to simulate the specimens. The maximum principal strain (MAXPE) and fracture energy (Gc) were selected as key damage parameters to characterize the fracture process, controlling crack initiation and resistance to crack propagation, respectively. These damage parameters were adjusted until the model closely matched experimental results (Load-crack tip opening displacement (CTOD)) for different initial notch sizes in (SENB) specimens. Subsequently, experimental results for (CTOD-R) and the strain distribution around the crack tip, both at crack initiation and during unstable crack propagation, were compared with the numerical model's predictions to validate the chosen XFEM input damage parameters. The research confirms the effectiveness of XFEM in predicting fracture characteristics.

This paper focuses on trans-laminar fracture process under varying environmental conditions which is crucial for the design and certification of many modern engineering applications. High-fidelity Finite Element (FE) models are developed for predicting trans-laminar fracture of a quasi-isotropic carbon/epoxy laminate under room temperature dry, and for the first time hot temperature wet conditions. Such FE modelling of ASTM E1922 specimens has not been done before. The FE models in ABAQUS Explicit employ a Weibull failure criterion for fibre fracture and cohesive surfaces for sub-critical damage to explain the complex trans-laminar fracture process. It successfully captures the toughening mechanisms, which are further enhanced by increased sub-critical damage under hot temperature wet conditions. This can finally be confirmed by the current models which addresses some limitations of ASTM E1922 e.g. a limited ligament length and the tendency of having premature compressive failure at the specimen rear end.

Mineral Information-Driven 3D Simulation of Meso-Mechanical Behavior and Fracture Process in Granite

To address the application limitations of traditional weakening techniques under complex geological conditions such as hard coal mine roofs, directional hydraulic fracturing (DHF) technology has become a key technical measure to ensure safety production by virtue of its core advantages of directional rock breaking. This paper systematically reviews the research status and development trends of underground DHF technology in underground coal mines, focusing on an analysis of the three key dimensions: directional fracturing methods, processes, and equipment. Regarding fracturing methods, three mainstream technologies based on manual slotting, linear arrangement drilling, and high-pressure water jet slotting have been sorted out. The paper compares their principles, advantages, and applicable scenarios, pointing out that a linear synergistic fracturing method using multiple fracturing holes with high-pressure water jet slotting demonstrates both precision and scalability, making it the most promising technological path at present. For fracturing processes, it elaborates on the standardized progress of the four core procedures: drilling construction, pre-treatment, high-pressure water injection, and effect verification, and analyzes the key bottlenecks in process optimization under complex geological conditions. In terms of fracturing equipment, technical characteristics and existing issues of drilling, slotting, high-pressure water injection, and monitoring devices are summarized. Aligning the development trends of mining engineering technology, the paper proposes that future directional hydraulic technology will evolve towards intelligent directional fracturing, multi-field coupled fracturing, and miniaturized precision fracturing. At the process level, it will develop towards integrated efficiency, adaptive dynamics, and green low-carbonization, while equipment will focus on breakthroughs in intelligent automation, high efficiency and reliability, and miniaturization and integration. These research results provide a reference for theoretical study, equipment development, and engineering applications of underground DHF technology, contributing to safe, efficient, and sustainable coal mining practices.

The bottom water of the Shizhouji Formation tight sandstone reservoir in the Tazhong Shun 9 well area is developed. General fracturing faces the problem of excessive extension of hydraulic fractures and easy communication with water layers. A true triaxial fracturing physical simulation experiment was conducted on the sandstone and mudstone outcrops of the same layer to explore the expansion laws of hydraulic fractures in the tight sandstone reservoir and consider the influence of mudstone interlayers, horizontal stress difference, fracturing fluid flow rate, and viscosity. The mechanism of multi-cluster fractures/artificial fractures penetrating through the layers was revealed. The research results show that the existence of mudstone interlayers greatly increases the complexity of fractures, from 1.88 to 2.96, an increase of 57%. When there is a mudstone interlayer in the rock, the fracturing process is prone to open weak planes, hindering the expansion of hydraulic fractures. The hydraulic fractures of Sample No. 4 were cut off four times and penetrated through the layers once. The larger the flow rate, the greater the complexity of hydraulic fractures, and the easier the fractures penetrate through the layers. The fractures with a large flow rate (200 mL/min) were cut off three times, and the stress difference was larger, the hydraulic fractures tended to be simple, and the penetration through the layers was zero times at a high-level stress difference (18 MPa); the greater the viscosity, the greater the fracture pressure, and the complexity of fractures first increased and then decreased; the greater the viscosity, the more easily the hydraulic fractures penetrate through the layers, with low viscosity cutting off three times, medium viscosity cutting off four times, and high viscosity cutting off five times. Therefore, considering the limitation requirements of the on-site fracturing on the extension of fracture height, it is recommended that the on-site fracturing construction flow rate be 6 m3/min, and the fracturing fluid viscosity be 10 mPa·s.

Ice shocks associated with the springtime thermal expansion of ice represent a manifestation of fracture processes in a complex nonlinear medium. In this study, we investigate temporal changes in statistical characteristics derived from ice deformation measurements preceding such events. The analysis demonstrates that the approach of ice shocks is accompanied by the formation of ordered linear features that constrain the evolution of a statistical functional constructed from deformation data. These features indicate a transition from predominantly stochastic behavior to the emergence of deterministic patterns in the system dynamics. A detailed examination of the temporal evolution of the statistical dependencies reveals several distinct groups of short-term precursors. The earliest indicators appear approximately one hour before an ice shock, followed by a second group emerging on the order of tens of minutes prior to the event. A further concentration of precursor signatures is observed within the final minutes preceding ice failure. Particular attention is given to the increasing topological similarity of the statistical patterns observed during these intervals, suggesting a progressive synchronization of deformation processes prior to fracture. The results support the applicability of statistical and topological analysis for identifying short-term precursors of ice shocks and highlight the potential of this approach for studying explosive-like processes in other complex natural systems.

ABSTRACT Mixed-mode I−II crack growth in a bio-based wood adhesive bondline was investigated using a three-dimensional finite-element model with a cohesive zone formulation. Cohesive parameters – including strengths, onset displacements and fracture energies – were obtained directly from double cantilever beam experiments with uneven bending moments. These experimentally derived parameters were then implemented in the finite element model without any calibration to fit the global response, as the aim was to validate the modelling approach rather than to identify material parameters. The model reproduced stable delamination, captured the expected variation in fracture-process-zone size, provided insight into the distribution and magnitude of normal and shear stresses along the bondline from crack initiation through propagation, and showed good agreement with the global experimental response in opening-dominated (nominal Mode I) loading (phase angles ψ = 0° and 41°). In shear-dominated mixed-mode loading (ψ = 69°, 85° and 89°), fracture resistance was overpredicted, attributed to large fracture process zones and model simplifications. Overall, the results demonstrate that a relatively simple cohesive zone model, when driven by experimentally derived cohesive laws, can capture the key trends in mixed-mode fracture response of wood-adhesive bonds.

The low-frequency distributed acoustic sensing (LF-DAS) data acquired through fiber-optic cables cemented behind the fracturing well casing can dynamically capture the hydraulic fracturing process. After removing the thermal effect, the LF-DAS data can reveal the strain evolution induced by the initiation of hydraulic fractures. This paper presented an improved strain-temperature decoupling method for LF-DAS measurements based on joint LF-DAS/distributed temperature sensing (DTS) monitoring. The decoupling method was based on strain change and temperature change pre-processed from the raw DAS and DTS data to avoid the enhancement of DTS data noise. The moving window function method and the image processing parameter cosine similarity was introduced to cope with the differences in temporal and spatial resolution between LF-DAS and DTS data. The region significantly affected by temperature change could be identified automatically and the mechanical strain change could be extracted. The tensile strain response generally reached a local peak at perforation clusters and increased significantly at those with dominant fracture fluid inflow. By analyzing the evolution of strain profile during fracturing, the effectiveness of multi-cluster fracture initiation and fracture temporary plugging could be evaluated.

Polypropylene fibers provide an innovative solution for enhancing the crack resistance of tunnel lining segments. However, existing macro-models obscure the distinct effects of fibers on the mortar and ITZ, while explicit meso-modeling remains computationally prohibitive. This study develops a multi-scale modeling framework to investigate PFRC segment fracture under bending. The framework integrates a 3D meso-scale module for calibrating fracture-related material properties, a 3D macro-scale module for predicting global displacements, and a 2D meso-scale module for resolving local fracture processes. A full-scale bending test was performed to validate the framework and to examine the effects of fiber content at both scales. Both the full-scale test and numerical simulations show that the segment response exhibits three stages: elastic, damage development, and cracking at the design load. Numerical simulations further reveal that an optimal fiber content of 0.4% reduces the vertical displacement at the load point by 9.8% and the horizontal displacement at the edge point by 2.9% relative to the fiber-free case. Meso-scale simulations show that 0.4% fibers decrease the bottom crack width from 0.0868 to 0.0770 mm (−11.29%) and limit internal crack connectivity. Although fibers may locally promote ITZ cracking due to reduced mortar–aggregate bonding, a strengthened mortar matrix suppresses crack penetration and connected crack networks. A pronounced high-damage peak in the ITZ near the failure threshold confirms the ITZ as the governing weak link; therefore, further improvements may require ITZ-strengthening strategies.

Prediction of fatigue failure in concrete structures remains a major challenge due to progressive material degradation. Reliable prediction, therefore, requires modeling the 3D heterogeneous microstructure of concrete to explain the underlying mechanisms governing fatigue failure. While such mesoscale models can reliably predict the fatigue-induced fracture mechanisms, the identification of the associated material parameters remains a significant challenge due to the high-dimensional parameter space introduced by the model. The key challenge addressed in this study is to capture microcrack initiation and coalescence under fatigue loading, using a model capable of representing fracture process: crack initiation, crack propagation, and final failure. Firstly, concrete domain is discretized into Voronoi cells, enabling explicit representation of aggregates and mortar by randomly assigning cohesive links connecting Voronoi cells as aggregates and mortar. After this, mortar links are modeled as coupled damage–plasticity 3D Timoshenko beam elements with nonlinear kinematic hardening and isotropic softening introduced using embedded discontinuity formulation, enabling fracture Modes I–III, whereas aggregate links are modeled as elastic 3D Timoshenko beam elements. The model efficiency is additionally reinforced by using surrogate model approach, with corresponding material parameter identification carried out by multi-objective Bayesian optimization framework to reproduce experimental results. The performance of the proposed model is illustrated by reproducing experimental results obtained from concrete cube compression test and three-point bending test under low-cycle fatigue loading, where the errors between experimental and numerical results are reduced by 82% (stress) and 88% (energy) for the cube test and by 86% (force) and 93% (energy) for the bending test, relative to the initial dataset error.

Characteristics of microwave-induced borehole fracturing in hard rock with different heating rates and temperatures under true triaxial stress

Optimal design and field test of volume fracturing for shale oil well A in Sichuan Basin

In this study, an in-house combined finite-discrete element method (FDEM) code is further developed and applied to investigate the fracture, fragmentation and collapse process of rock mass induced by smooth blasting during the excavation of a deep-buried tunnel with the presence of high in-situ stresses and complex pre-existing joints. The simulation approach in this study enables the modeling of the transition from continuous to discontinuous behavior of rock, the explosive-rock interaction via gas pressure variation and simplified gas flow model, and the incorporation of pre-existing joints with various lengths, dip angles, spacings and connectivity rates. The blasting-induced stress redistribution and the corresponding rock fracture, fragmentation and collapse process on site are simulated, which vividly replicate the formation of smooth tunnel sidewalls and the occurrence of rock collapse at the tunnel crown area incorporating pre-existing joints. The simulated rock collapse extent at the tunnel roof corresponds well with that from field observations. Furthermore, with the setup of various modeling cases, the effects of in-situ stresses, joint distributions and initiation time delay errors on the fracture propagation behavior in the excavation damaged zone (EDZ) are investigated in detail. The complex mechanisms regarding the critical roles of these three factors in the fracture propagation and EDZ development process are highlighted. The FDEM code in this study is expected to serve for the prevention or mitigation of the potential rock collapse induced by blasting excavation under the combined effects of in-situ stresses, blasting operation and geological structures.