Search Results (29)

This paper presents an experimental and numerical analysis of the mechanical behaviour of orthopaedic implants with crack-type defects, considering the principles and advantages of the modern X-FEM method, which was used due to limitations of traditional FEM in terms of crack growth simulation, especially for complex geometries. In X-FEM, the finite element space is enriched with discontinuity functions and asymptotic functions at the crack tip, which are integrated into the standard finite element approximation using the unity division property. Though rare, femoral component failures are well-documented complications that can occur after hip prosthetic implantation. Most stem fractures happen in the first third of the implant due to the loosening of the proximal stem and fixation of the distal stem, leading to bending and eventual fatigue failure. The main goal of this paper was to obtain accurate and representative models of such failures. Experimental analyses of the mechanical behaviour of implants subjected to physiological loads, according to relevant standards, using a new combined approach, including both experiments and numerical simulations was presented. The goal was to verify the numerical results and obtain a novel, effective methodology for assessing the remaining fatigue life of hip implants. For this purpose, the analysis of the influence of Paris coefficients on the total number of cycles was also considered. Hence, this simulation involved defining loads to closely mimic real-life scenarios, including a combination of activities such as ascending stairs, stumbling, and descending stairs. The tensile properties of the titanium alloy were experimentally determined, along with the Paris law coefficients C and m. The finite element software ANSYS 2022R2 version was used to develop and calculate the three-dimensional model with a crack, and the resulting stresses, stress intensity factors, and the number of cycles presented in the figures, tables, and diagrams. The results for the fatigue life of a partial hip implant subjected to various load cases indicated significant differences in behaviour, and this underscores the importance of analysing each case individually, as these loads are heavily influenced by each patient’s specific activities. It was concluded that the use of numerical methods enabled the preliminary analyses of the mechanical behaviour of implants under fatigue loading for several different load cases, and these findings can be effectively used to predict the possibility of Ti-6Al-4V implant failure under variable cyclic loads. Full article

Underwater gliders are extensively employed in oceanographic observation and detection. The structural characteristics of thin-wall shells are more susceptible to vibrations from internal mechanical components; this noise emission becomes more complex with the presence of water surfaces. The finite element method (FEM) is introduced to discuss the dynamic performance of cylindrical shells with different lengths. The acoustic-structure coupling, together with the effect of the water surface, is validated by comparisons with experimental or analytical solutions under three cases: half-filled, half-submerged, and partially submerged in fluid. Compared to the verification result, the relative error of the eigenfrequency derived from the numerical result is less than 3%, and then the mesh division and boundary conditions are adjusted to calculate the vibroacoustic response of a disc-type glider. During its water entry process, there are six distinct bright curves in frequency–depth spectra of sound pressure radiated from a partially immersed disc-type glider. The first curve is continuous, while the remaining five curves display discontinuities around a region where the geometric curvature changes gradually. As the submerged depth increases, this causes a shift in the resonance frequencies, evidenced by the curves transitioning from higher to lower frequencies. Full article

Unlike traditional base materials such as concrete or masonry, there are no guidelines for rock as a base material for post-installed anchors. The varying rock properties (e.g., rock type, discontinuities) and numerous installation parameters (e.g., embedment depth, anchor diameter) leave engineers with limited information on design resistances, leading to an uncertain basis for anchor applications in rock. To identify the key parameters that determine rock as a base material, an evaluation of rock characteristics was conducted, combined with in situ pull-out tests in different key geologies (granite, limestone, mica schist, dolomite, granulite) and discrete element modeling, which has been found to be suitable for investigating the load-bearing behavior of post-installed anchors in rock. Discontinuities were identified as the main factor influencing the load-bearing capacity of post-installed anchors in rock mass. Based on the in situ investigations, assessment methods for rock as a base material were proposed, along with corresponding resistance partial safety factors for design of 2.5, 2.0, and 1.7 for high, medium, and low levels of uncertainty regarding possible inhomogeneities. A limit value R ≥ 36, associated with rebound hammer assessments, was defined for the low degree of uncertainty, showing limitations for schistose rock. This is concluded by a design approach for determining design resistances of shallow fasteners in rock mass. Full article

The peridotite massifs of New Caledonia are characterised by complex hydrodynamics influenced by intense inherited fracturing, uplift, and erosion. Following the formation of the erosion surfaces and alteration processes, these processes drive chemical redistribution during weathering; particularly lateritisation and saprolitisation. Magnesium, silica, and trace elements such as nickel and cobalt—released as the dissolution front advances—are redistributed through the system. New observations and interpretations reveal how lateritic paleo-land surfaces evolved, and their temporal relationship with alteration processes since the Oligocene. Considering the geometry of discontinuity networks ranging from micro-fractures to faults, the transfers occur in dual-permeability environments. Olivine dissolution rates are heterogeneously due to differential solution renewal caused by erosion and valley deepening. Differential mass transfer occurs between mobile regions of highly transmissive faults, while immobile areas correspond to the rock matrix and the secondary fracture network. The progression of alteration fronts controls the formation of boulders and the distribution of nickel across multiple scales. In the saprolite, nickel reprecipitates mostly in talc-like phases, as well as minor nontronite and goethite with partial diffusion in inherited serpentine. The current nickel distribution results from a complex interplay of climatic, hydrological and structural factors integrated into a model across different scales and times. Full article

Smoothed particle hydrodynamics (SPH) is a state-of-the-art numerical simulation method in fluid mechanics. It is a novel approach for modeling and comprehending complex fluid behaviors. In contrast to traditional grid-dependent techniques like finite element and finite difference methods, SPH utilizes a meshless, purely Lagrangian approach, offering significant advantages in fluid simulations. By leveraging a set of arbitrarily distributed particles to represent the continuous fluid medium, SPH enables the precise estimation of partial differential equations. This grid-free methodology effectively addresses many challenges associated with conventional methods, providing a more adaptable and efficient solution framework. SPH’s versatility is evident across a broad spectrum of applications, ranging from advanced computational fluid dynamics (CFD) to complex computational solid mechanics (CSM), and proves effective across various scales—from micro to macro and even astronomical phenomena. Although SPH excels in tackling problems involving multiple degrees of freedom, complex boundaries, and large discontinuous deformations, it is still in its developmental phase and has not yet been widely adopted. As such, a thorough understanding and systematic analysis of SPH’s foundational theories are critical. This paper offers a comprehensive review of the defining characteristics and theoretical foundations of the SPH method, supported by practical examples derived from the Navier–Stokes (N-S) equations. It also provides a critical examination of successful SPH applications across various fields. Additionally, the paper presents case studies of SPH’s application in tunnel and underground engineering based on practical engineering experiences and long-term on-site monitoring, highlighting SPH’s alignment with real-world conditions. The theory and application of SPH have thus emerged as highly dynamic and rapidly evolving research areas. The detailed theoretical analysis and case studies presented in this paper offer valuable insights and practical guidance for scholars and practitioners alike. Full article

The use of synthetic materials with high corrosion resistance in a concrete matrix yields structures that are more durable and suitable for use in aggressive environments, eliminating the need for frequent maintenance. Examples of such materials include glass (GFRP) and basalt (BFRP) fiber-reinforced polymer bars (FRP). Due to the low modulus of elasticity of these bars, concrete elements reinforced with FRP longitudinal rebars tend to exhibit cracks with wider openings and greater depths compared to those reinforced with steel rebars, which diminishes the element’s shear resistance. The addition of discontinuous fibers into the concrete aims to maintain stress transfer across the cracks, thereby enhancing the shear capacity and ductility of FRP-reinforced structures. This study evaluates the impact of fiber addition on the shear resistance of concrete beams reinforced with FRP rebars. An experimental investigation was conducted, focusing on the partial and complete substitution of stirrups with polypropylene macro fibers in concrete beams reinforced with FRP longitudinal rebars and stirrups. This research examined beams reinforced with glass (GFRP) and basalt (BFRP) fiber-reinforced polymer bars. For the initial set of beams, all stirrups were replaced with synthetic macro fibers. In the subsequent set, macro fibers were added to beams with insufficient stirrups. Although the complete replacement of GFRP and BFRP stirrups with polypropylene macro fibers did not alter the brittle shear failure mode, it did enhance the shear resistance capacity by 78.5% for GFRP-reinforced beams and 60.4% for BFRP-reinforced beams. Furthermore, the addition of macro fibers to beams with insufficient stirrups, characterized by excessive spacing, changed the failure mode from brittle shear to pseudo-ductile flexural failure due to concrete crushing. In such instances, the failure load increased by 18.8% for beams with GFRP bars and 22.8% for beams with BFRP bars. Full article

Pressure–temperature estimates of a xenolith found within a post-obduction granodiorite in southern New Caledonia provide evidence for subcrustal, granulite facies, peak crystallisation conditions (ca. 850 °C—8.5 ± 1.0 kbar), followed by isobaric cooling to 700 °C, and final decompression with partial rehydration at ca. 650 °C—3.5 kbar. The xenolith, dated at 24.7 Ma (U-Pb zircon), i.e., the same age as the granodiorite host rock, has low SiO₂ (35.5 wt%) and high Al₂O₃ (33.2 wt%) contents, suggesting that it is the restite of a previous melting episode, while the elevated Ca (Ba and Sr) contents suggest mantle metasomatism. Although the concentrations of Rb, K, Ca, Ba, and Sr have been strongly modified, some geochemical (REE patterns and some “immobile” trace element ratios) and isotopic (Sr and Nd isotopic ratios, U-Pb zircon age) characteristics of the granulite facies xenolith are similar to those of the xenoliths found in other Late Oligocene intrusions in southern New Caledonia; therefore, this rock is interpreted to be related to an early magmatic episode. The rock protolith was emplaced and equilibrated at the base of the crust where it underwent ductile deformation. Younger ascending magma picked it up and they eventually crystallised together at a shallow crustal level, near the tectonic sole of the ophiolite. The recrystallisation and ductile deformation at ~8.5 kbar suggest that a rheological discontinuity existed at about 25–28 km, probably representing the Moho. It is concluded that a continental crust of normal thickness must have existed beneath New Caledonia at about 24 Ma, i.e., 10 Ma after obduction. Full article

In this paper, we present an innovative approach to solve a system of boundary value problems (BVPs), using the newly developed discontinuous Galerkin (DG) method, which eliminates the need for auxiliary variables. This work is the first in a series of papers on DG methods applied to partial differential equations (PDEs). By consecutively applying the DG method to each space variable of the PDE using the method of lines, we transform the problem into a system of ordinary differential equations (ODEs). We investigate the convergence criteria of the DG method on systems of ODEs and generalize the error analysis to PDEs. Our analysis demonstrates that the DG error’s leading term is determined by a combination of specific Jacobi polynomials in each element. Thus, we prove that DG solutions are superconvergent at the roots of these polynomials, with an order of convergence of $O\left(h^{p+2}\right)$. Full article

This work presents an original 3D code in FreeFem++ to recreate the behavior of anaerobic microorganisms in non-stirred anaerobic reactors with an intermittent feed. The physical and biochemical phenomena have been considered using a mathematical model based on a set of partial differential equations: Stokes, advection–diffusion, and diffusion–reaction. The description of the anaerobic metabolism was carried out by implementing the structured AMD1 model. The Galerkin finite element method has been used to solve the partial differential equations defined in the model. Finally, the methodology and procedures are presented by means of a concrete example. Thanks to the inclusion of this e-learning tool for use in virtual laboratories, it is possible to improve the understanding of engineering students on the functioning of the metabolism that takes place inside non-stirred anaerobic reactors that are fed discontinuously. This proposal reinforces to students, in a transversal way, both environmental sensitivity and awareness of the circular economy focused on the implementation of natural wastewater treatment systems in rural areas. Full article

Carbon nanotubes (CNTs) exhibit high strength, Young’s modulus, and flexibility and serve as an ideal reinforcement for composite materials. Owing to their toughness against bending and/or twisting, they are typically used as fabric composites. The conventional multiaxial braiding method lacks tension and resultant strength in the thickness direction. Some braiding patterns are proposed; however, they may have shortcomings in flexibility. Thus, this study proposed three types of braiding pattern for fabrics based on natural products such as spider net and honeycomb, in accordance with thickness-direction strength. The spider-net-based structure included wefts with spaces in the center with overlapping warps. At both sides, the warps crossed and contacted the wefts to impart solidness to the structure and enhance its strength as well as flexural stability. In addition, box-type wefts were proposed by unifying the weft and warps into boxes, which enhanced the stability and flexibility of the framework. Finally, we proposed a structure based on rectangular and hexagonal shapes mimicking the honeycomb. Moreover, finite element calculations were performed to investigate the mechanisms through which the proposed structures garnered strength and deformation ability. The average stress in fabrics becomes smaller than half (43%) when four edges are restrained and sliding is inserted. Under three-dimensional forces, our proposed structures underwent mechanisms of wrapping, warping, sliding and doubling, and partial locking to demonstrate their enhanced mechanical properties. Furthermore, we proposed a hierarchical structure specialized for CNTs, which could facilitate applications in structural components of satellites, wind turbines, and ships. The hierarchical structure utilizing discontinuity and sliding benefits the usage for practical mechanical systems. Full article

This study aimed to investigate how the depth-to-width (D/W) ratio of the welding area affects the welding quality of the SSM6061 aluminum alloy via the friction-stir spot welding (FSSW) process. The results showed that a higher D/W ratio directly results in better mechanical properties. If the D/W ratio value is high (at 1.494), then this leads to higher tensile shear strength at 2.25 kN. On the other hand, if the D/W ratio values are low (at 1.144), then this reduces tensile shear strength to 1.17 kN. The fracture surface behavior on the ring zone also affects the characteristics of ductile fracture. During Vickers hardness analysis, the hardness profiles are in the shape of a W; the maximum hardness was 71.97 HV, resulting from the rotation speed of 3500 rpm and the dwell time of 28 s, where the hardness of the base metal was at 67.18 HV. Finite element (FEM) analysis indicated that the maximum temperature during simulation was 467 °C in the region near the edge shoulder tool, which is 72.96% of the melting point. According to FEM simulation, the temperature under the tool pin region was 369 °C. The generated heat was sufficient to induce changes in the microstructure. For microstructure changes, the globular grain took on a rosette-like form, and coarse grains were observed in the thermal mechanical affect zone (TMAZ) and in the nugget zone (NZ), transforming in the mix zone. Hooks, kissing bonds, voids, and porosity are the defects found in this experiment. These defects indicate a discontinuity in the NZ that leads to worse mechanical properties. During examination via SEM and energy dispersive X-ray (EDX) analysis, the recrystallization structure from β-Mg₂Si IMCs to Al₃Mg₂ and Al₁₂Mg₁₇ IMCs was observed. The size was reduced to an average width of 1–2 µm and an average length of 2–17 µm. Simultaneously, the oxides from the ambient atmosphere present during welding showed dominant partial elements from SiO₂, MgO, and Al₂O₃. Full article

This study was devoted to an investigation on the dynamics of double-walled carbon nanotubes (DWCNTs) under the influence of Winkler–Pasternak foundation near the primary resonance. Two Euler–Bernoulli beams embedded on nonlinear foundation, interacting through van der Waals forces, subjected to mechanical impact are considered. By means of Hamilton’s principle, Eringen’s nonlocal elastic theory, and taking into account the moving nanoparticles, the Galerkin–Bubnov method is applied and accordingly, governing partial differential equations are reduced to two differential equations with variable coefficients. The nonlinear damped and forced vibration is studied using the optimal auxiliary functions method (OAFM). An explicit and very accurate analytical solution is obtained by means of OAFM without considering simplifying hypotheses. An accurate analysis is for the first time reported considering the cumulated effects of nonlinearities simultaneously induced by the Winkler–Pasternak foundation, the curvature of beams and van der Waals force, and also the effect of discontinuities marked by the presence of the Dirac function. Finally, a stability analysis of the considered model is developed by means of the homotopy perturbation method (HPM) using the condition of existence of the two frequencies. It was shown that an increasing of some constitutive parameters substantially reduces the area of stability, all these being of much help in guiding the design of advanced nanoelectromechanical devices, in which nanotubes act as basic elements. Full article

Physics-informed neural network (PINN) models are developed in this work for solving highly anisotropic diffusion equations. Compared to traditional numerical discretization schemes such as the finite volume method and finite element method, PINN models are meshless and, therefore, have the advantage of imposing no constraint on the orientations of the diffusion tensors or the grid orthogonality conditions. To impose solution positivity, we tested PINN models with positivity-preserving activation functions for the last layer and found that the accuracy of the corresponding PINN solutions is quite poor compared to the vanilla PINN model. Therefore, to improve the monotonicity properties of PINN models, we propose a new loss function that incorporates additional terms which penalize negative solutions, in addition to the usual partial differential equation (PDE) residuals and boundary mismatch. Various numerical experiments show that the PINN models can accurately capture the tensorial effect of the diffusion tensor, and the PINN model utilizing the new loss function can reduce the degree of violations of monotonicity and improve the accuracy of solutions compared to the vanilla PINN model, while the computational expenses remain comparable. Moreover, we further developed PINN models that are composed of multiple neural networks to deal with discontinuous diffusion tensors. Pressure and flux continuity conditions on the discontinuity line are used to stitch the multiple networks into a single model by adding another loss term in the loss function. The resulting PINN models were shown to successfully solve the diffusion equation when the principal directions of the diffusion tensor change abruptly across the discontinuity line. The results demonstrate that the PINN models represent an attractive option for solving difficult anisotropic diffusion problems compared to traditional numerical discretization methods. Full article

In the present study, Mo was added to Cu–15Ni–8Sn alloy as the fourth element to solve the limitation of service performance of the alloy by composition design. The phase composition, microstructure transformation and mechanical properties of Cu–15Ni–8Sn–xMo (x = 0.3, 0.9, 1.5 wt.%) alloy were systematically studied by simulation calculation and experimental characterization. The results show that the addition of Mo can improve the as-cast structure of Cu–15Ni–8Sn alloy and reduce segregation and Cu–Mo phase precipitates on the surface with the increase in Mo contents. During solution treatment, Mo can partially dissolve into the matrix, which may be the key to improving the properties of the alloy. Furthermore, the discontinuous precipitation of Sn can be effectively inhibited by adding the appropriate amount of Mo to Cu–15Ni–8Sn alloy, and the hardness of alloy does not decrease greatly after a long-time aging treatment. When Mo content is 0.9 wt.%, the alloy reaches the peak hardness of 384 HV at 4 h of aging. These results provide new ideas for composition optimization of Cu–15Ni–8Sn alloy. Full article

Laminated composite structures suffer from failure because of concentrations of gradient fields on interfaces due to discontinuity of material properties. The rapid development of material science enables designers to replace classical laminated plate elements in aerospace structures with more advanced ones made of functionally graded materials (FGM), which are microscopic composite materials with continuous variation of material coefficients according to the contents of their micro-constituents. Utilization of FGM eliminates the inconvenience of laminated structures but gives rise to substantial changes in structural design This paper deals with the presentation of a strong formulation meshless method for the solution of FGM composite plates. Recall that the fourth-order derivatives of deflections are involved in the governing equations for plate structures. However, the high-order derivatives of field variables in partial differential equations (PDE) lead to increasing inaccuracy of approximations. For that reason, the decomposition of the high-order governing equations into the second-order PDE is proposed. For the spatial approximation of field variables, the meshless moving least square (MLS) approximation technique is employed. The reliability (numerical stability, convergence, and accuracy) as well as computational efficiency of the developed method is illustrated by several numerical investigations of the response of FGM plates with the transversal gradation of material coefficients under stationary and/or transient mechanical and thermal loadings. Full article