Fracture toughness is a key engineering design parameter. Fracture of engineering materials and components may occur under 3 basic deformations or modes namely pure mode I (opening), pure mode II (shearing) and pure mode III (tearing). However, in practice the possibility of fracturing under mixed mode I/II, I/III and general mixed mode I/II/III case are more than the pure modes. Several experimental methods and testing specimens have been employed by the fracture mechanics researcher to determine the fracture toughness of engineering materials under different mode mixities. Among them, a recently designed and proposed test configuration named Edge-Notched-Disc-Bend (ENDB) is a suitable and favorite testing method for conducting general mixed-mode I/II/III fracture toughness experiments. In this research following a brief description of the ENDB specimen, a review of some recently published papers for investigating the mixed mode fracture problem is presented. According to such a review, it can be concluded that the ENDB method is a suitable candidate specimen for studying general mixed-mode I/II/III fracture problems in materials with brittle or quasi-brittle nature.

Several waste materials are often used in the mixt-design of asphalt concrete materials to manufacture green construction materials and among them recycled asphalt pavement (RAP) is a favorite material that can be utilized as partial replacement of natural stone aggregates. Addition of such waste and recycled materials may have a negative influence on the mechanical properties and strength or performance of asphalt pavements. In particular, resistance of asphaltic overlays made by some amounts of RAP material against cracking and crack propagation can be reduced and it is necessary to investigate possible effects of RAP addition on cracking resistance of asphalt mixtures. Passage of traffic loads from the cracked overlays and asphaltic pavements can activate all basic tensile and shear mode crack deformations (i.e., pure mode I, pure mode II and pure mode III). In addition, due to the visco-elastic nature of bitumen used in the asphalt mixture, the risk of crack propagation and failure at low temperature conditions is higher than the intermediate and high temperatures. Therefore, in this research, the influence of adding RAP material on the fracture toughness of all three basic fracture modes (namely, K_Ic, K_IIc and K_IIIc) is investigated using edge-notched disc bend (ENDB) specimens. Fracture toughness tests are conducted on hot mix asphalt (HMA) mixtures containing 0, 20 and 40 % RAP material (as replacement of natural aggregates) at five low temperatures of 0, -6, -12, -18, -24 oC. Based on the results, all fracture toughness data were decreased by increasing the temperature from -24oC to zero and increasing the RAP content from 0 to 40%. Depending on the test temperature and mixture type (HMA with or without RAP content) the K_Ic and K^IIc values were varied from 0.5 to 1.1 MPa.m^0.5. This range for KIIIc value was in the lower limit of 0.35 MPa.m^0.5 and 0.75 MPa.m^0.5. Some fracture indexes such as fracture toughness ratios (K_IIc/K_Ic, K_IIIc/K_Ic, K_IIc/K_IIIc, and Kopening/Kshearing-eff) and effective fracture toughness were determined and discussed for the investigated HMA mixtures at different temperatures.

This paper investigates experimentally and numerically the influence of geometry and loading conditions on the fracture response of rock materials. Seven different test samples namely “Edge-Notched-Disc-Bend (ENDB), Semi-Circular-Bend (SCB), Three-Point-Bend-Inclined-Crack (TPB-IC), Single-Edge-Notched-Bending (SENB), Asymmetric-Three-Point-Bend (ATPB), Edge-Notched-Disc-Compression (ENDC) and Double-Notched-Disc-Compression (DNDC)” made of a marble rock were manufactured and tested under bending and compressive loading conditions. The results showed that the failure loads of all samples increase with the change of pure mode I to pure mode III. However, the corresponding fracture toughness values of ENDB, SCB, TPB-IC, SENB and ATPB specimens decreased, while the ENDC and DNDC samples experienced an increase in the fracture toughness. Among the studied specimens, only the ENDB, ENDC and DNDC samples presented pure mode III with KIIIc/KIc ratio ranging from 0.735 for the ENDB specimen to 2.076 for the DNDC sample. The highest mode-I fracture toughness among all the studied specimens was obtained for the SENB and TPB-IC samples, with a value of 1.54 MPa m0.5, while the lowest value was obtained for the DNDC specimen with a value of 1.21 MPa m0.5. The sign and the magnitude of T-stress considerably depended on the loading condition and geometry of the specimens. The crack trajectories of all specimens under study were also investigated.

Fracture parameters of a bi-material plate containing a cener crack and subjected to biaxial tensile loading was calculated numerically. Based on the crack tip stress field obtained numerically in a bi-material joint and using the finite element over deterministic (FEOD) method, the stress intensity factors (KI and KII) and also non-singular T-stress terms, were determined for different material properties and biaxial loading cases. Due to asymmetry of loading and material properties in the investigated dissimilar plate, the center crack experinces mixed mode I/II fracture in general. By increasing the bi-material constant value, which shows the difference between the mechanical properties of two materials, the amplitude of stress intensity factor decreases. The obtained results from this method were in good agreement with the displacment field method prevousiuly reported by other researchers.

Over the past decades, high entropy alloys (HEAs) have attracted continuously increasing research efforts because of their technological promise for structural applications and their scientific interest as a multi-component alloy exhibiting an overall random solid solution structure with high mixing entropy at high temperature. In this summary, we briefly review the recent studies focused on the structure and mechanical behavior of HEAs, covering the important issues from phase stability to elastic modulus, mechanical strength, hardness and fatigue resistance. Finally, we highlight a few key findings recently reported for HEAs and discuss the outstanding issues yet to be resolved.

This study evaluates the relative efficiency of digital health adoption across ten major German cities and regions. In a landscape where digital transformation is critical, this research moves beyond mere technological assessment to determine which locales most effectively convert inputs into outputs. A multi-criteria decision-making framework is employed, integrating Data Envelopment Analysis (DEA) under both constant and variable returns-to-scale assumptions and the TOPSIS method. Key metrics include Infrastructure, Healthcare System Integration, Service Breadth, Regulatory Environment, and a critical cost factor, Accessibility & Equity. Results from DEA models highlight a system-wide scale inefficiency, yet identify specific efficient units under variable returns, including Berlin, Rhineland-Pfalz, Leipzig, and Aachen. The TOPSIS analysis, particularly when prioritizing cost-equity, reveals a distinct ranking: Rhineland-Pfalz, Leipzig, and Aachen emerge as top performers, while major economic hubs like Munich, Frankfurt, and Stuttgart demonstrate lower efficiency due to high costs and systemic fragmentation. The findings challenge the presumption that economic scale guarantees digital health efficiency, instead underscoring the superior performance of strategically coordinated and equity-focused models. This study provides policymakers with a robust framework for benchmarking and highlights governance and integration, not just investment, as the key levers for enhancing digital health system performance.

The amount of damage induced by brittle fracture of cracked bodies depends considerably on the path of fractures. Therefore, prediction of the trajectory of fracture using suitable theoretical fracture criteria is very important for cracked structures. In this paper, using higher-order terms of Williams’s series expansion and the maximum tangential stress criterion, the mixed mode I/II crack growth path of an angled crack plate subjected to biaxial far field loading is investigated theoretically. To evaluate the accuracy of the theoretical results, they are compared with the experimentally reported trajectories for the angled crack plate specimen. It is shown that by taking into account the higher order terms of the Williams series expansion a very good agreement is observed between the experimental and theoretical mixed mode fracture paths in the angled crack problem. It was also observed that the theoretically determined initial angle of crack growth is consistent with the experimental results.

Hospital departments are continuously challenged to allocate their limited resources—beds, nursing staff, and operating room (OR) time—among patients with different clinical priorities on the waiting list. This paper presents a solution to this intricate planning problem by constructing a novel Integer Linear Programming (ILP) model to schedule elective patient admissions optimally. The goal is to increase the total priority score of the patients admitted, where the score indicates clinical urgency and waiting time, while at the same time honoring the restrictions on bed capacity, nursing hours, and OR availability through a multi-day planning horizon. The model uses binary decision variables for patient admission as well as pre-processed parameters to map the individual patient resource consumption over the time they are expected to stay in the hospital. We showcase the model's application through a realistic scenario with synthetic data. The outcomes reveal that the suggested framework not only effectively creates an optimum admission timetable but also considerably enhances the use of vital resources when compared to a first-come-first-served standard. The ILP model is not only potent but also clear and just decision-support tool for hospital management, according to the study's findings. By assigning priority to clinical criteria and making patient access more equitable, it provides a data-guided way to improve operational productivity, as well as to decide the trade-offs that come with the limitations of healthcare facilities in terms of resources. Besides, the model is computationally capable of meeting the needs for the inclusion of extra real-world constraints and adjustments.

The aim of the present work was to develop a guideline for approving the railway axles made of C35 steel and containing surface and/or in-body defects after manufacturing. First, several through and part-through circular cracks were modeled on the surface and in the body of the axle at its critical cross-section. Then, the permissible size of such cracks was determined by using the fracture mechanics. To verify the validity of the guideline, the theoretical result for the semi-circular surface crack was compared with the allowable size prescribed by the international railway standard. A very good agreement was found to exist between the predicted and the standard values.

Facility Layout Planning (FLP) is one of the most important strategic decisions that have a very big effect on the operational efficiency and therefore also the productivity and cost-effectiveness of manufacturing and service systems. The uncertainty which is inherent to the parameters like product demand, material flow, and processing times makes the FLP problem very complicated and dynamic. This paper exhibits a detailed review of the works done so far on FLP under uncertainty which has been based on an analysis of 163 articles from the Scopus database. The review organizes and evaluates systematically the main methodologies used, among them mathematical programming, heuristics and metaheuristics, simulation, and Multi-Criteria Decision-Making (MCDM) methods. The different types of uncertainty—fuzzy, stochastic, robust, and fuzzy-random—being modeled and integrated into solution approaches is one of the main areas of focus. It turned out from the analysis that hybrid metaheuristics, especially when combined with fuzzy MCDM techniques, are the most common and effective means of dealing with fluoroscope FLP issues today. Moreover, the paper contains a bibliometric analysis that underlines the main contributors, geographical patterns, and the trend of shifting research emphasis toward topics like construction site layout, sustainable logistics, and digital twin-supported planning. The review not only presents the gaps in the current literature but also points to further research implications including more integrated use of AI and dealing with the problem of real-time dynamic layout reconfiguration.