Search Results (28)

In this paper, we introduce a generalised formulation of the logistic map extended to the complex plane and correspondingly redefine the classical Mandelbrot and Julia sets within this broader framework. Central to our approach is the development of an escape criterion based on the Picard orbit, which underpins the escape-time algorithms employed for graphical approximations of these sets. We analyse the structural and dynamical properties of the resulting Mandelbrot and Julia sets, emphasising their inherent symmetries through detailed visualisations. Furthermore, we examine how variations in a key parameter of the generalised map affect two critical numerical metrics: the average escape time and the non-escaping area index. Our computational study reveals that, particularly for Julia sets, these dependencies are characterised by intricate, highly non-linear behaviour—highlighting the profound complexity and sensitivity of the system under this generalised mapping. Full article

The accuracy of numerical predictions in sheet metal processes involving multiaxial stress–strain states (e.g., blanking, riveting, and incremental forming) heavily depends on the characterisation of plastic anisotropy under multiaxial loading conditions. A fully calibrated 3D plastic anisotropy model is essential for this purpose. While in-plane material behaviour can be conventionally characterised through uniaxial and equi-biaxial tensile tests, calibrating out-of-plane material behaviour remains a significant challenge. This behaviour, governed by out-of-plane shear stress and associated material parameters, is typically described by out-of-plane shear yielding. These parameters are notoriously difficult to determine, leading researchers to frequently assume isotropic behaviour or identical shear parameters for in-plane and out-of-plane responses. Although advanced calibrations may utilise crystal plasticity modelling, there remains a critical need for macro-mechanical characterisation methods. This paper presents an out-of-plane shear testing and material characterisation procedure based on full-field strain measurements using digital image correlation (DIC). Strains within the shear zone are measured via DIC and employed in the Finite Element Model Updating (FEMU) to identify out-of-plane shear parameters of a 2.42 mm thick, cold-rolled AW5754-H22 aluminium alloy sheet, using the Yld2004-18p yield criterion. Given that the characteristic strain response at this scale may be influenced by local crystal structure behaviour on the surface, this paper evaluates the feasibility of such measurements. Finally, to test the validity of the full-field-based approach, the FEMU-identified parameters are compared against results obtained through a classical optimisation procedure based on force-elongation measurements from the shear zone. Full article

The inherent mineralogical alignment in stratified rock formations engenders pronounced mechanical anisotropy, presenting persistent challenges across geological, geotechnical, and petroleum engineering disciplines. While substantial progress has been made in modeling transversely isotropic media, current methodologies exhibit limitations in reconciling theoretical predictions with complex failure mechanisms. This investigation examines the anisotropic response of diverse lithologies through triaxial testing across bedding orientations (0–90°) and confinement levels (0–60 MPa), revealing a pressure-dependent attenuation of directional strength variations. Experimental evidence identifies three dominant failure modes: cross-bedding shear fracturing, bedding-parallel sliding, and hybrid mechanisms combining both, with transition thresholds governed by confinement intensity and bedding angle. Analytical comparisons demonstrate that conventional single weakness plane models produce characteristic shoulder-shaped strength curves with overpredictions, particularly in hybrid failure regimes. Conversely, the modified patchy weakness plane formulation achieves superior predictive accuracy through parametric representation of anisotropy gradation, effectively capturing strength transitions between end-member failure modes. The Pariseau criterion, though marginally less precise in absolute terms, provides critical insights into directional strength contrasts through its explicit differentiation of vertical versus parallel bedding responses. These findings advance the fundamental understanding of anisotropic rock behavior while establishing practical frameworks for optimizing stability assessments in bedded formations, particularly in high-confinement environments characteristic of deep reservoirs and engineered underground structures. Full article

Tensile strength perpendicular to the plane of the board (also known as the Internal Bond—IB), determined in accordance with standard EN 319, is one of the most critical properties in particleboard quality control. Given the need for efficient, rapid methods to assess the IB in industrial contexts, artificial neural networks (ANN) have been used as a predictive modelling tool. However, one of the main limitations of these techniques is the absence of estimates associated with the uncertainty of their predictions. The present study addresses this shortfall by applying bootstrap techniques to obtain confidence intervals using estimates generated by ANN. To achieve this, multiple models were trained and validated using experimental data taken from real production processes. The results show that the methodology proposed can be used to obtain a high level of accuracy (determination coefficient R² = 0.96) and a coverage probability of 93%. It also provides a robust criterion to assess conformity with standard specifications. This study concludes that adding bootstrap to ANN modelling is a very useful tool for application in industrial quality control systems, as it allows decision making based on confidence intervals rather than individual values. Full article

To investigate the influence of weakly structured formations on wellbore stability in deep coal seams within the Lufeng Block, this study establishes an innovative predictive model for coal seam wellbore collapse pressure. The model integrates mechanical parameter variations along weak structural planes with the Mohr–Coulomb criterion, leveraging experimental correlations between mechanical properties and bedding angle. Key findings reveal that the coal sample demonstrates enhanced compressive strength and elastic modulus under elevated confining pressures. A distinctive asymmetric “V” pattern emerges in mechanical parameter evolution: compressive strength, elastic modulus, cohesion, and internal friction angle initially decrease before recovering with increasing bedding angle, reaching minimum values at a 60° bedding angle. Comparative analysis demonstrates that the proposed model predicts a higher collapse pressure equivalent density than conventional Mohr–Coulomb approaches, particularly when accounting for mechanical parameter alterations along weak structural planes. Field validation through coal seam data from the operational well confirms the model’s effectiveness for stability analysis in weakly structured coal formations within the Lufeng Block. These findings provide critical theoretical support for wellbore stability management in deep coal seam engineering applications. Full article

An accurate understanding of the tensile mechanical behavior of shale rock is essential for optimizing shale gas drilling and hydraulic fracturing operations. However, the mechanical behavior of shale is significantly influenced by its anisotropy. Therefore, this study investigated the tensile mechanical behavior of layered shale by combining acoustic emission (AE) monitoring with two testing methods: the Brazilian splitting test (BST) and a novel direct tensile test (DTT). The impact of anisotropy on the tensile mechanical behavior and failure modes of layered shale under different test methods was evaluated. Additionally, seven anisotropic tensile strength criteria were compared and validated using the experimental results. The results show that: (1) As the loading angle (β) increased, the tensile strength measured by both BST and DTT increased. Both methods exhibited maximum tensile strength at β = 90° and minimum tensile strength at β = 0°. The anisotropy ratios for BST and DTT were 1.52 and 2.36, respectively, indicating the significant influence of the loading angle on tensile strength. (2) The AE results indicated that both DTT and BST specimens exhibited brittle failure characteristics. However, the DTT specimens demonstrated more pronounced progressive failure behavior, with failure modes categorized into four types: tensile failure across the bedding plane, shear failure along the bedding plane, and two types of tensile–shear mixed failure. In contrast, the BST specimens primarily exhibited tensile–shear mixed failure, except for tensile failure along the bedding plane at β = 0° and tensile failure across the bedding plane at β = 90°. (3) Neither of the two test methods could fully eliminate the influence of anisotropy, but three anisotropic tensile criteria, the Lee–Pietruszczak criterion, the critical plane approach criterion, and the anisotropic mode I fracture toughness criterion based on the stress–strain transformation rule demonstrated high accuracy in predicting tensile strength. Furthermore, in alignment with previous studies, the indirect tensile strength of various rock types was found to range between one and three times the direct tensile strength, and a linear correlation between the two variables was established, with a coefficient of approximately 1.11. Full article

This study investigates the scale effects on the experimental shear strength of earthen walls, a critical parameter influencing the seismic performance of adobe and rammed-earth (RE) buildings. Recognized for their historical significance and sustainable construction practices, earthen structures require a comprehensive understanding of their mechanical behavior under shear loads to ensure effective design and preservation. This research compiles data from over 120 in-plane shear wall tests (adobe and RE), nearly 20 direct shear tests from the scientific and technical literature, and new cyclic direct shear tests performed on large cubic specimens (300 mm side length) made from the same material as a previously tested two-story RE wall. Based on the findings, this study recommends a minimum specimen cross-sectional area of 0.5 m² for reliable shear strength testing of earthen walls in structural laboratories. This recommendation aims to prevent the unconservative overestimation of shear strength commonly observed in smaller specimens, including direct shear tests. Furthermore, the Mohr–Coulomb failure criterion outlined in the AIS-610 Colombian standard is validated as a conservative lower bound for all compiled shear strength data. Cyclic direct shear tests on nine 300 mm cubic specimens produced a Mohr–Coulomb envelope with an apparent cohesion of 0.0715 MPa and a slope of 0.66, whereas the full-scale two-story wall (5.95 × 6.20 × 0.65 m) constructed with the same material exhibited a much lower cohesion of 0.0139 MPa and a slope of 0.26. The analysis reveals significant scale effects, as small-scale specimens consistently overestimate shear strength due to their inability to capture macro-structural behaviors such as compaction layer interactions, construction joint weaknesses, and stress redistributions. Based on the analysis of the compiled data, the novelty of this study lies in defining a strength reduction factor for direct shear tests (3.4–3.8 for rammed earth, ~3.0 for adobe) to align with full-scale wall behavior, as well as establishing a minimum specimen size (≥0.5 m²) for reliable in-plane shear testing of earthen walls, ensuring accurate structural assessments of shear strength. This study provides a first approach to the shear behavior of unstabilized earth. To expand its application, future research should explore how the scale of specimens with different stabilizers affects their shear strength. Full article

This work studies numerically the development of adiabatic shear banding (ASB) during high strain-rate compression of AISI 1045 steel. Plane strain and cylindrical axisymmetric compressions are simulated in LS-DYNA, considering rectangular and cylindrical steel samples, respectively. Also, a parametric analysis in height-to-base ratio is conducted in order to evaluate the effect of geometry and dimensional ratio of the sample on ASB formation. Doubly structural-thermal-damage coupled finite element models are developed for the numerical simulations, implementing the thermo-viscoplastic Modified Johnson–Cook constitutive relation and damage criterion, while further damage-equivalent stress and strain fields are introduced for the damage coupling. The simulations revealed that plane strain compression promotes more ASB formation, providing lower critical strain for ASB initiation and wider and stronger ASBs compared with axisymmetric compression. Further, X-shaped ASBs initially form during plane strain compression, while as deformation increases, they transform into S-shaped ASBs in contrast to axisymmetric compression, where parabolic ASBs are developed. Also, a lower height-to-base ratio leads to greater ASB propensity, reducing critical strain in axisymmetric compression. Finally, thermal softening is found to precede damage softening and dominate the ASB genesis and its early evolution, while in contrast damage softening drives later ASB evolution and its transition to fracture. Full article

The mean stress effect remains a critical aspect in multiaxial fatigue analysis. This work presents a new criterion that, based on the classical Findley criterion, applies a material-dependent exponent to the mean normal stress term and includes the ultimate tensile stress as a fitting parameter. This way of considering the non-linear effect of the mean stress, with a material-dependent rather than a fixed exponent, is totally innovative among the multiaxial fatigue criteria found in the literature. In order to verify its accuracy, the new criterion has been checked against an extended version of the Papuga database of multiaxial experimental tests with 485 results, and compared with the criteria by Findley, Robert, and Papuga. The new criterion provides outstanding results for pure uniaxial cases, with multiaxial performance similar to the Robert criterion with a smaller range of error and a conservative trend, even surpassing the popular Papuga method in several relevant loading scenarios. These features enhance the applicability and versatility of the criterion for its use in the fatigue design of structural components. Full article

Fretting fatigue is a specific fatigue phenomenon. Due to the complex mechanisms and multitude of influencing factors, it is still hard to predict fretting fatigue life accurately, despite there being many works on this topic. This paper developed a particle-swarm-optimized back propagation neural network to predict the fretting fatigue life of aluminum alloys using the test data gathered from the published literature. A commonly used critical plane model, the Smith, Watson, and Topper criterion, was used as a contrast. The analysis result shows that the proposed fretting fatigue life prediction neural network model achieves a higher prediction accuracy compared to the traditional SWT model. Experimental validation demonstrates the effectiveness of the model in improving the accuracy of fretting fatigue life prediction. This research provides a new data-driven methodology for fretting fatigue life prediction. Full article

A unified critical state model has been developed for both clean sand and silty sand using the modified Cam-clay model (MCC). The main feature of the proposed model is a new critical state line equation in the e-ln(p) plane that is capable of handling both straight and curved test results. With this feature, the error in calculating plastic volumetric strain is, in theory, eliminated. Another crucial feature of the model is the transformed stress tensor based on the SMP (spatially mobilized plane) criterion, which takes into account the proper shear yield and failure of soil under three-dimensional stresses. Additionally, the proposed model applies the intergranular void ratio with the fines influence factor for silty sand. Only eight soil parameters are required for clean sand, and a total number of twelve soil parameters are needed for silty sand. This model not only enhances the predictive accuracy for granular soils but also broadens the applicability of the model to encompass silty sand in both drained and undrained analyses. Full article

As is well-known, non-proportional fatigue loading, such as asynchronous one, can have significant detrimental effects on the fatigue behavior of metallic materials by reducing the fatigue strength/fatigue limit and by leading to a fatigue damage accumulation increased with respect to that under proportional loading. In the present paper, the novel refined equivalent deformation (RED) criterion is applied for the first time to estimate the fatigue lifetime of materials, sensitive to non-proportionality, subjected to asynchronous loading under low-cycle fatigue regime. The present criterion is complete since it considers: (i) the strain path orientation, (ii) the degree of non-proportionality, and (iii) the changing of material cyclic properties under non-proportional loading. To evaluate its accuracy, this criterion is applied to examine two different metals (a 304 stainless steel and a 355 structural steel) whose experimental data under multiaxial asynchronous loading are available in the literature. More precisely, the parameters of the criterion are firstly determined by using experimental strain paths, and then the computed refined equivalent deformation amplitude is used to represent the experimental data with a satisfactory accuracy. Finally, a comparison with the results obtained through two other criteria available in the literature is performed, highlighting the good prediction of the present RED criterion. Full article

Gears are one of the the most widespread mechanical components and their design is supported by standard calculation methods. Among all the possible failure modes of gears, tooth root bending is the most critical and could lead to catastrophic failures. In this regard, different surface treatments could be exploited to improve the gear strength. Among them, shot peening is the most common. The aim of this study is to evaluate the effectiveness of shot peening on improving the tooth root bending resistance. This is achieved by exploiting the Finite Element Method (FEM) in combination with advanced multiaxial fatigue criterion based on the critical plane concept. A standard Single Tooth Bending Fatigue test was reproduced numerically via FEM. Beside the wrought gears, shot peened ones were also simulated. The state of stress induced by the shot peening was obtained numerically by simulating the surface treatment itself with non-linear dynamic analyses. The results have shown quantitatively how the residual stresses promote an improvement in the resistance and how the local hardening could lead to different early paths of nucleation and propagation of cracks on the tooth fillet. Full article

Borehole instability problems are commonly encountered while drilling highly deviated and horizontal shale gas wells within the shale formations associated with high-dip bedding planes. An integrated rock mechanical study is described in this paper to evaluate the risk of the borehole instability problems in this area. First, a set of uniaxial compressive tests are carried out to measure the strength of the bedding shales on cores with different angles between the load direction and the bedding planes. A critical strength criterion is then proposed based on the test results. Next, the stress state of the borehole with arbitrary inclination and azimuth is determined through coordinate transformations. Finally, through combining the strength criterion and the stress state of the borehole, the risk of borehole instability is investigated for deviated and horizontal wells in shale formations with different bedding dips (0–90°) and dip directions (45° and 90° to the direction of minimum horizontal stress ${\sigma }_h$). The results show the dependence of borehole instability on the orientation of bedding planes of the formation as well as inclination and azimuth of the well. The most desirable borehole trajectory from the viewpoint of borehole stability is at the direction normal to the bedding planes. For a horizontal well specifically, if the bedding direction is perpendicular to the direction of ${\sigma }_h$, the risk of instability is relatively high for most drilling directions except drilling along the dip direction of the bedding planes. However, if there is a moderate acute angle (e.g., 45°) between the dip direction and the direction of ${\sigma }_h$, the risk of instability is relatively low for most drilling directions unless drilling along the direction of ${\sigma }_h$. Full article

The characterization of new materials for enabling gear design is definitely a fundamental objective in the gear industry and research. Single Tooth Bending Fatigue (STBF) tests can be performed to speed up this process. However, it is well known that STBF tests tend to overestimate material strength compared to tests performed directly on meshing gears (MG) which, in turn, require an excessively long test time. Therefore, it is common practice to use a constant correction factor $f_{korr}$ of 0.9 to translate STBF results for designing actual MG (e.g., via ISO 6336). Recent works involving a combination of Finite Element Models (FEM) and multiaxial (non-proportional) fatigue criteria based on the critical plane concept have highlighted that the assumption of considering $f_{korr}$ as a constant independent of the gear design parameters leads to inaccurate results. However, in previous studies, no correlation between $f_{korr}$ and gear design parameters has emerged. In the present paper, the influence of the normal pressure angle (${\alpha }_n$), the profile shift coefficient ($x^{*}$), and the normal module ($m_n$) on $f_{korr}$ was investigated by analyzing FEM simulations with the Findley fatigue criterion. 27 gear geometries were studied by varying the above 3 parameters in 3 levels (full factorial DOE). These geometries were simulated in both MG and STBF configurations. The results of the 54 FEM simulations were analyzed by applying the Findley fatigue criterion and the corresponding $f_{korr}$ were calculated. The correlation between $f_{korr}$ and ${\alpha }_n$, $x^{*}$ and $m_n$ was investigated using the Analysis of Variance (ANOVA) technique. The results show that the only gear design parameter influencing $f_{korr}$ is $x^{*}$ hence, a regression model for $f_{korr}$ including $x^{*}$ has been developed. This latter has been then adopted for calculating and comparing $f_{korr}$ values from other combination of the parameters found in literature, giving good correspondence. Full article