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Highlights 2.5D woven composite material inevitably produces void defects in its production process, which will seriously reduce its mechanical properties and reduce its service life. In this paper, the effects of void defects on the mechanical properties of 2.5D woven composites were studied by multi‐scale analysis. An improved Halpin‐Tsai semi‐empirical model is proposed to calculate the elastic properties of yarns with porous defects and verified by finite element method. A microscale representative volume unit (RVE) for predicting the elastic constants of composites with pore defects is established. Theoretical analysis and finite element analysis were used to verify the micro scale, and finite element analysis and experiment were used to verify the micro scale. The effect of porosity on the elastic properties of micro‐scale RVE was studied in detail. The results show that the model is reasonable and accurate in predicting the mechanical properties of yarns and composites. In addition, the effect of porosity on the mechanical properties of 2.5D woven composites is significant. An improved Halpin‐Tsai semi‐empirical model is proposed, which makes the microscale theoretical analysis of 2.5D woven composites better consistent with the finite element analysis. The void position obstructs the stress transfer of the matrix, and the stress concentration phenomenon also occurs. The void content has an effect on the mechanical properties of composites at both micro and micro scales. [ABSTRACT FROM AUTHOR]

The literature presents insufficient data evaluating the displacement and micromotion effects resulting from the combined use of tooth-implant connections in fixed partial dentures. Analyzing the biomechanical behavior of tooth-implant fixed partial denture (FPD) prothesis is vital for achieving an optimum design and successful clinical implementation. The objective of this study was to determine the relative significance of connector design on the displacement and micromotion of tooth-implant-supported fixed dental prostheses under occlusal vertical loading. A unilateral Kennedy class I mandibular model was created using a 3D reconstruction from CT scan data. Eight simulated designs of tooth-implant fixed partial dentures (FPDs) were split into two groups: Group A with rigid connectors and Group B with non-rigid connectors. The models were subjected to a uniform vertical load of 100 N. Displacement, strain, and stress were computed using finite element analysis. The materials were defined as isotropic, homogeneous, and exhibiting linear elastic properties. This study focused on assessing the maximum displacement in various components, including the bridge, mandible, dentin, cementum, periodontal ligament (PDL), and implant. Displacement values were predominantly higher in Group B (non-rigid) compared to Group A (rigid) in all measured components of the tooth-implant FPDs. Accordingly, a statistically significant difference was observed between the two groups at the FPD bridge (p value = 0.021 *), mandible (p value = 0.021 *), dentin (p value = 0.043 *), cementum (p value = 0.043 *), and PDL (p value = 0.043 *). Meanwhile, there was an insignificant increase in displacement values recorded in the distal implant (p value = 0.083). This study highlighted the importance of connector design in the overall stability and performance of the prosthesis. Notably, the 4.7 mm × 10 mm implant in Group B showed a displacement nearly 92 times higher than its rigid counterpart in Group A. Overall, the 5.7 mm × 10 mm combination of implant length and diameter showcased the best performance in both groups. The findings demonstrate that wider implants with a proportional length offer greater resistance to displacement forces. In addition, the use of rigid connection design provides superior biomechanical performance in tooth-implant fixed partial dentures and reduces the risk of micromotion with its associated complications such as ligament overstretching and implant overload, achieving predictable prognosis and enhancing the stability of the protheses. [ABSTRACT FROM AUTHOR]

Underground hydrogen storage could provide buffer capacity to store the excess energy from renewable resources. A lined rock cavern (LRC) is one of the hydrogen geologic storage site options. It offers great flexibility because it does not rely on the existence of salt caverns, aquifer formations or depleted hydrocarbon reservoir fields. However, many important aspects have to be investigated before its full-scale implementation, among them (1) the effect of spatial variation of rock mass properties and (2) hydrogen embrittlement on the steel lining. We present a numerical study on these two aspects by simulating field tests at a pilot LRC project. For the effect of rock heterogeneity, we assign a spatial variation of elastic properties based on the Gaussian covariance model. The results show a good agreement with the field measurements. The spatial correlation length of rock mass elastic properties only has a minor impact on the cavern surface deformation. Regarding hydrogen embrittlement, our simulations predict a significant hydrogen diffusion in the low alloy steel (S355) lining after ∼2 months of operation. The fracture simulations show little fracture propagation even after 10 years of contact with hydrogen gas. However, the product loss may be too high for the low alloy steel (S355). We would recommend the use of stainless steel to inhibit the hydrogen diffusion. We show that advanced numerical models are powerful tools to ensure the safety of hydrogen storage in LRCs. • The finite element simulation results show a good agreement with the field measurements of rock displacement. • The spatial correlation length of rock mass elastic properties only has a minor impact on the cavern surface deformation. • We would recommend the use of stainless steel as the liner material to inhibit the hydrogen diffusion. [ABSTRACT FROM AUTHOR]

Liquid crystal elastomers (LCEs) are elastomeric networks with anisotropic monomers that reorient in response to applied loads, and in particular, thermomechanical loads. LCE complex microstructures translate into complex behaviors, such as soft elasticity, rate‐dependency, and hysteresis. In this work, we develop a three‐dimensional finite element implementation for monodomain LCEs, with the material modeled as a finite deformation viscoelastic network with a viscous director. The formulation is designed so that the director field can be modeled as an internal variable. Unique to this class of materials is that their deformation response function depends on the full deformation gradient and not just the right‐stretch tensor. This results in the material tangent losing its 'usual' symmetry properties. Accordingly, this makes the use of a first Piola–Kirchhoff finite element formulation advantageous. We utilize this framework to examine a number of nuances associated with the simulation and design of LCE based systems. In particular, we investigate in some detail the importance of a careful characterization of an LCE's initial director field. Via simulations of separate tension and compression experiments, we highlight the possibility of incorrect predictions when even small perturbations to initial conditions occur. The simulations are also used to illustrate the goodness of the model in replicating simple and complex experimental results, including the first‐of‐their‐kind buckling‐like column compression and thick‐walled balloon inflation simulations. [ABSTRACT FROM AUTHOR]

Torsional tests were conducted to investigate the influence of service temperature on torsional property of composite/steel hybrid structures. In the experiment, two types of lightweight hybrid composite‐metal shafts were tested at both room temperature and various elevated temperatures up to 150°C, including hybrid shafts with and without a metal core. Consequently, the torsional stiffness of the two hybrid shafts at different temperatures was calculated based on the recorded angular deformation‐torque curves. The experimental results revealed a significant decrease in the torsional stiffness of the hybrid shaft without metal core as the increase of service temperature, while the torsional stiffness of the one with metal core remained almost unchanged, especially at high temperatures. In addition, a finite element model was proposed to predict the torsional behavior of the hybrid shafts at different service temperatures. In the model, an empirical equation was introduced, and micromechanical method was adopted to determine the temperature‐dependant elastic properties of composite material and adhesive layer in the hybrid structure. Then, the predicted torsional property was compared to the experimental results for model verification. Highlights: Two types of hybrid composite‐metal shafts are designed and manufactured.Torsional tests are conducted at both room and elevated temperatures up to 150°C.A finite element model applicable to shaft at various temperatures is proposed.The temperature‐dependant property is characterized by an efficient equation. [ABSTRACT FROM AUTHOR]

Indentation is a versatile method to assess the hardness of different materials along with their elastic properties. Recently, powerful approaches have been developed to determine further material properties, like yield strength, ultimate tensile strength, work-hardening rate, and even cyclic plastic properties, by a combination of indentation testing and computer simulations. The basic idea of these approaches is to simulate the indentation with known process parameters and to iteratively optimize the initially unknown material properties until just a minimum error between numerical and experimental results is achieved. In this work, we have developed a protocol for instrumented indentation tests and a procedure for the inverse analysis of the experimental data to obtain material parameters for time-dependent viscoplastic material behavior and kinematic and isotropic work-hardening. We assume the elastic material properties and the initial yield strength to be known because these values can be determined independently from indentation tests. Two optimization strategies were performed and compared for identification of the material parameters. The new inverse method for spherical indentation has been successfully applied to martensitic steel. [ABSTRACT FROM AUTHOR]

Contact mechanics analysis is crucial because such problems often arise in engineering practice. When examining contact mechanics, the material property of the contacting components is a crucially significant aspect. It is more complex to solve the contact mechanics of systems that are composed of materials that do not have a homogenous structure compared to materials that have homogeneous qualities throughout. While many studies on contact problems with homogeneous materials exist, those involving non-homogeneous materials are scarce in the literature. As material technology improves fast, there will be a greater need to solve such problems. In this respect, analytical and finite element method (FEM) solutions of the continuous and discontinuous contact problems of a functionally graded (FG) layer are carried out in this article. The FG layer in the problem rests on a rigid foundation and is pressed with a rigid punch. From the solutions, the contact length, contact stress, initial separation distance, and beginning and ending points of separation were determined, and the results were compared. It has been concluded that the FEM findings are consistent with the analytical results to a satisfactory degree. This study analyzes contact problem using different approaches and accounts for the influence of body force in a contact geometry that has yet to be reported. [ABSTRACT FROM AUTHOR]

This paper investigates the thermo-elastoplastic sliding frictional contact and wear problem of a functionally graded material (FGM) coated homogeneous half-plane subjected to a rigid cylindrical punch. The coating has arbitrarily varying material properties including elastic modulus, Poisson's ratio, thermal expansion coefficient, wear coefficient, etc. The graded layer is modeled using a thermo-elastoplastic constitutive model of FGM to evaluate the contact pressure, in-plane stress, and temperature field. A modified Archard model is used to characterize the wear behavior of FGM coating, and the influence of wear on the stress and strain behavior is considered. The constitutive model and wear model are implemented in the finite element method (FEM) to study the thermo-elastoplastic sliding frictional contact and wear behavior of FGM coating. After the validation of the numerical approach, the effects of plasticity, wear, cycle number, gradient index, and gradient form are discussed. Simulation results show that changing the gradient form and gradient index can prevent contact damage and reduce frictional wear. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new vectorized MATLAB-based algorithm for efficient serial computation of global matrix/force arising from finite element method (FEM) for meshes of any type and approximation order in linear elasticity. Because for-loops in MATLAB are very slow, we propose a modified process that takes advantage of vectorization and sparse assembly to achieve good performance while using the same memory as the standard algorithm. For this purpose, by using good programming practices, the implementation of this scheme is succinctly described and can be integrated into any MATLAB package dealing with FEM. Specifically, attention is paid to the calculation of the triplet (row index, column index, matrix components) as well as the assembly of the global stiffness matrix, mass matrix and force vector. Additionally, an extension of the proposed approach for Mindlin plate theory and functionally graded materials is outlined. Finally, the accuracy of this strategy is verified on selected numerical tests after comparing the obtained results with those of ABAQUS. In terms of performance, the study conducted on a set of meshes considering the standard algorithm and two other well-known MATLAB vectorized algorithms revealed that: (i) for a 2D beam problem meshed with P 1 -triangle elements, a speedup of about 8 and 15 is achieved with sparse and fsparse, respectively. (ii) for a 3D plate problem meshed with P 1 -tetrahedral elements, a speedup of about 4 and 8 is achieved with sparse and fsparse, respectively. When compared to ABAQUS performance, the proposed scheme results in a computational time that is about five times smaller. [ABSTRACT FROM AUTHOR]

The design of cooling systems is crucial for the thermal management of many energy systems including batteries, microelectro-mechanical systems, photovoltaics and many others. In this study, cooling system for elastic curved conductive panel is developed by using nano-enhanced multiple jet impingement. ALE finite element modeling of the entire coupled fluid-structure conjugate heat transfer system is employed for assessment, which considers both elastic flat and wavy panels. Type of the panel and operating parameters affect the cooling performance and entropy generation. Different effects and contributions of varying parameters such as Cauchy number (Ca), jet-cooling spacing (to the target plate and between the slots), wave amplitude and number of the conducive panel and nanoparticle loading amount in the pure fluid on the cooling performance and entropy generation features are analyzed. Increases in the Cauchy number, waveform amplitude, slot-slot distance, and slot-plate distance reduce the effectiveness of cooling, whereas increases in the nanoparticle loading have the reverse effect. When varying the Ca, there is 12.1% decrease of average Nusselt number (Nu) while average panel temperature rise becomes 3.1°C by using nanofluid. The average Nu deteriorates by 7.7% and 6.6% when amplitude and wave number are varied while the corresponding temperature rises are achieved as 1.4°C and 1°C. When wavy and flat surfaces are used, using nanofluid provides 2.8°C and 2.5°C temperature drops. Lower entropy generation (EG) is obtained with flexible panel while higher amplitude of the wave form and increasing the nanoparticle amount result in EG reduction. The amount of EG reduction by using nanofluid becomes 21% and 27% at the highest loading. [ABSTRACT FROM AUTHOR]

Copyright of Transactions of Nanjing University of Aeronautics & Astronautics is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Transactions of Nanjing University of Aeronautics & Astronautics is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An extended two‐dimensional (2D) elasticity theory based on the weighted residual concept is developed in an attempt to capture thickness effects in vibrating thick plates. Plate theories can only provide approximate solutions due to certain kinematics assumptions. The weighting functions are expressed in terms of Legendre orthogonal polynomials. A formulation in rectangular Cartesian coordinates serves as the basis for an implementation of the finite element method. The applicability of the extended 2D elasticity theory is demonstrated through examples of rectangular, thick plates with different aspect ratios, thickness ratios, and boundary conditions. The accuracy of the extended 2D elasticity theory is assessed through a three‐dimensional finite element analysis. The frequencies and modal stresses show excellent agreement with three‐dimensional finite element calculations. [ABSTRACT FROM AUTHOR]

AbstractThe present article aims at performing a global sensitivity analysis of modal properties of a frequency dependent viscoelastic sandwich plate. The latter are evaluated using a finite element model relying on Kirchhoff theory for the elastic faces and the Mindlin-Reissner approach for the viscoelastic layer. The plate’s characteristics are considered as random variables following log normal laws. Sparse polynomial chaos expansions are employed to evaluate Sobol’s indices. For high damping, the resonant frequencies and loss factors turn to be sensitive to the elastic face properties, while in the weak damping case they are mostly affected by the viscoelastic model parameters. [ABSTRACT FROM AUTHOR]

Purpose: The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil. Design/methodology/approach: First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs. Findings: Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown. Originality/value: This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper. [ABSTRACT FROM AUTHOR]

• An exact matrix-form solution is proposed for analyzing multiple non-circular tunnels in layered media. • Generalized complex variable theory, conformal mapping and fast Fourier transform are used in derivation. • The proposed solution avoids complicated coefficient determinations and iterative algorithm. • Effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels are discussed. This paper presents a matrix-form complex variable method that can predict the stress and displacement field around multiple tunnels in layered media. The proposed matrix-form method avoids complicated coefficient determinations and iterative algorithm, which effectively improves the computation efficiency. Firstly, the expressions for the stress and displacement field are given under the generalized complex variable theory. The conformal mapping technique and fast Fourier transform algorithm are used to formulate the matrix-form expressions of boundary conditions. Considering the boundary conditions of the tunnels and soil interfaces, the global matrix solution for multiple tunnels in layered media are obtained by assembling the matrix solutions of all single layers. The present theory is verified by comparison with the existing literature, finite element analysis and field data in engineering practices, and several numerical examples are given to reveal the effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels. [ABSTRACT FROM AUTHOR]

The anode material Sn used in sodium-ion batteries displays high theoretical capacity, complex phase transformation, and significant volume change during the charging/discharging process. In particular, the effects of small scale on the mechanical behavior of Sn anode at the nanoscale are very active research fields. However, the majority of these results are based on nonlocal gradient formulations. In this study, we proposed and established a model that combines the electrochemical reaction with stress-driven nonlocal integral elasticity for the nanoelectrode to analyze the evolution of diffusion-induced deformation during the sodiation process. Several critical features, such as the small-scale parameter, two-phase reaction, and concentration-dependent elastic modulus, were incorporated into the established model. The model demonstrated that a small scale could significantly affect the deformation behavior. The results obtained using the finite element method showed that the mechanical reliability of the Sn anode could be significantly enhanced when the anode was sodiated with larger nonlocal parameters and smaller slenderness. In addition, the axial action force exhibited a strong size effect and was influenced by the nondimensional thickness parameter of the anode. This work provides a framework for multi-scale research on high-capacity sodium-ion battery electrodes. [ABSTRACT FROM AUTHOR]

The simulation of deformable objects has been the subject of a great deal of work in the field of computer graphics. The constraint-based PBD (Position-Based Dynamics) approach has been proven to be effective in this field for real-time and stable deformable objects simulation. Finite element method with linear tetrahedron discretization is the most widely used in computer graphics despite producing less accurate results than hexahedral or higher-order elements. In this context, our proposal is to integrate higher degree elements within the pbd framework. In addition, we propose a solution to improve convergence of unstable energies (like Neo-Hooke) when used as constraints. We show that our approach improves accuracy compared to linear tetrahedra. We also highlight the time savings, since fewer elements are needed. [ABSTRACT FROM AUTHOR]

The elasticity of bearings as well as their clearance have an essential influence on the total arrow and, therefore, on their own pulsation. In most of the literature, this elasticity is neglected in the calculation of shaft deflections. In some work, the elasticity of the bearings has been taken into account when calculating the deflection of the mixing device shaft, but this has been carried out on the basis of a high degree of customization: the behavior of the bearings has been considered linearly elastic, which does not correspond to reality because according to the elastic response of the bearing, it is a nonlinear function of the radial displacement. When the shaft of a mixing device operates in a pressure vessel, at the outlet of the pressure vessel, the shaft is provided with a sealing device, which can be considered a third bearing. This aspect is also not taken into account in the calculation of the shaft's deflection, which leads to a certain degree of error in its determination. This study aims to highlight the influence of the elasticity of the bearings and the sealing device on the stiffness of the shaft and to propose a method that supports a calculation program for calculating the elastic line of a vertical cantilever shaft, considering the role played by the bearings in the case that they behave nonlinearly and the sealing device as the third bearing. This problem was solved both by applying our own method and with the help of the FEM. [ABSTRACT FROM AUTHOR]

The study aims to bridge this gap by scrutinizing the impact of a specific nonelastic factor, namely the average weight loss, on pipeline weldments and its interaction with elastic properties. To fulfil this objective, a comprehensive experimental inquiry is conducted, encompassing diverse welding methods, materials, and environmental conditions to authentically replicate real-world situations. This investigation unveils the intricate interrelation between elastic and non-elastic facets, underscoring the necessity of encompassing the latter to ensure the dependability of pipeline weldments across various operational contexts. Cutting-edge techniques, such as machine learning algorithms and finite element simulations, are harnessed to accurately predict and optimize these non-elastic factors, thereby enhancing the overall strength and structural integrity of pipeline weldments. The experimental setup adheres to the central composite design, meticulously constructed utilizing design expert software (version 13.0). The response surface methodology analysis yields optimal outcomes, suggesting a gas flow rate of 14.667 liters per minute, a voltage of 21.280 volts, and a current of 160.000 amps. These parameters collectively yield a welded joint with an average weight loss value of 0.236, achieving a desirability value of 0.918. Additionally, the artificial neural network model is employed to predict output parameters and compared against the RSM methodology. The findings underscore the pivotal role of optimizing non-elastic performance factors in pipeline weldments. By accurately anticipating and controlling the period of immersion, engineers and professionals within the pipeline sector can design weldments capable of enduring harsh conditions, thus, prolonging pipeline operational lifespans. [ABSTRACT FROM AUTHOR]

Thin-film electrode arrays (TFEAs) have been developed as an alternative to conventional electrode arrays (CEAs) used in cochlear implants. However, TFEAs produced by microfabrication techniques have not yet been used clinically because their structural and mechanical properties are far from those of CEAs. The aim of this study is to design, fabricate, and investigate the mechanical and tribological behavior and evaluate the performance of different TFEA designs. Finite Element Analysis (FEA) is performed to determine the elastic properties of several designs. A custom-build experimental setup is designed to observe the tribological behavior in different speeds and environments where frictional (lateral) and vertical force (normal force) are measured on a flat surface and within artificial cochlea. According to the FEA results, the maximum stiffness of the CEA is 37.93 mN/mm and 0.363 mN/mm and TFEA-4 has a maximum stiffness of 39.08 mN/mm and 0.306 mN/mm in the longitudinal and transverse axes, respectively. It is shown experimentally that adding a dummy wire to the carrier of the EA enhances both its longitudinal and transverse stiffness, thereby postponing the initiation of dynamic sliding due to the elevated buckling limit. It is also revealed that the type of TFEA support structure affects both normal and frictional forces, as well as the coefficient of friction. [ABSTRACT FROM AUTHOR]

In this paper, a residual-type a posteriori error estimator is proposed and analyzed for a weak Galerkin finite element method for solving linear elasticity problems. The error estimator is proven to be both reliable and efficient, and be used for adaptive refinement. Numerical experiments are presented to illustrate the effectiveness of this error estimator. [ABSTRACT FROM AUTHOR]

A combination of chirality, anti-chirality, and re-entrant lattice pattern is proposed to form a new two-dimensional meta-structure, and a comprehensive parametric study is conducted by using experimental and numerical analysis. The proposed structure can undergo larger deformations without significant stress concentrations. Based on the verified finite element model, the effects of various geometrical parameters on the in-plane mechanical response of the structure are investigated. Results show that the thickness of the structure is the most dominant factor in affecting the Young modulus while other parameters can alter Poisson's ratio. In addition, the proposed structure exhibits tunable negative/near-zero Poisson's ratios. [ABSTRACT FROM AUTHOR]

Currently, the primary factor indicating the necessity of an operation for an abdominal aortic aneurysm (AAA) is the diameter at its widest part. However, in practice, a large number of aneurysm ruptures occur before reaching a critical size. This means that the mechanics of aneurysm growth and remodeling have not been fully elucidated. This study presents a novel method for assessing the elastic properties of an aneurysm using an ultrasound technique based on tracking the oscillations of the vascular wall as well as the inner border of the thrombus. Twenty nine patients with AAA and eighteen healthy volunteers were considered. The study presents the stratification of a group of patients according to the elastic properties of the aneurysm, depending on the relative volume of intraluminal thrombus masses. Additionally, the neural network analysis of CT angiography images of these patients shows direct (r = 0.664271) correlation with thrombus volume according to ultrasound data, the reliability of the Spearman correlation is p = 0.000215. The use of finite element numerical analysis made it possible to reveal the mechanism of the negative impact on the AAA integrity of an asymmetrically located intraluminal thrombus. The aneurysm itself is considered as a complex structure consisting of a wall, intraluminal thrombus masses, and areas of calcification. When the thrombus occupies > 70% of the lumen of the aneurysm, the deformations of the outer and inner surfaces of the thrombus have different rates, leading to tensile stresses in the thrombus. This poses a risk of its detachment and subsequent thromboembolism or the rupture of the aneurysm wall. This study is the first to provide a mechanistic explanation for the effects of an asymmetrical intraluminal thrombus in an abdominal aortic aneurysm. The obtained results will help develop more accurate risk criteria for AAA rupture using non-invasive conventional diagnostic methods. [ABSTRACT FROM AUTHOR]

A novel higher-order multi-scale computational approach for efficient nonlocal gradient elasticity simulation of composite materials is proposed in this paper. Based on the use of decoupling technique, raw fourth-order nonlocal gradient equations with periodically oscillatory coefficients are decoupled as the new second-order multi-scale equations for reducing the continuity requirements when implementing multi-scale simulation. Next, a novel macro-micro coupled multi-scale computational model with higher-order corrected terms is rigorously devised for high-resolution multi-scale and nonlocal analysis of composite materials via multi-scale asymptotic analysis. Then, the local error analysis of higher-order multi-scale solutions in the point-wise sense illustrates that establishing higher-order asymptotic corrected terms plays a vital role in investigating the micromechanical mechanisms. Moreover, a rigorous global error estimation with an explicit rate of higher-order multi-scale solutions is first derived in the energy norm sense. In addition, an efficient multi-scale numerical algorithm is presented to effectively simulate nonlocal gradient elasticity problems of composite materials based on finite element method (FEM). And we also derive the convergence estimation of the proposed numerical algorithm. Finally, numerical experiments are conducted to gauge the efficiency and accuracy of the proposed higher-order multi-scale method. This paper offers a unified higher-order two-scale computational framework for enabling nonlocal gradient elasticity behavior simulation of composite materials. [ABSTRACT FROM AUTHOR]

Based on the three-dimensional elastic-plastic finite element analysis of the 8" (203.2 mm) drill collar joint, this paper studies the mechanical characteristics of the pin and box of NC56 drill collar joints under complex load conditions, as well as the downhole secondary makeup features, and calculates the downhole equivalent impact torque with the relative offset at the shoulder of internal and external threads. On the basis of verifying the correctness of the calculation results by using measured results in Well GT1, the prediction model of the downhole equivalent impact torque is formed and applied in the first extra-deep well with a depth over 10 000 m in China (Well SDTK1). The results indicate that under complex loads, the stress distribution in drill collar joints is uneven, with relatively higher von Mises stress at the shoulder and the threads close to the shoulder. For 203.2 mm drill collar joints pre-tightened according to the make-up torque recommended by American Petroleum Institute standards, when the downhole equivalent impact torque exceeds 65 kN·m, the preload balance of the joint is disrupted, leading to secondary make-up of the joint. As the downhole equivalent impact torque increases, the relative offset at the shoulder of internal and external threads increases. The calculation results reveal that there exists significant downhole impact torque in Well SDTK1 with complex loading environment. It is necessary to use double shoulder collar joints to improve the impact torque resistance of the joint or optimize the operating parameters to reduce the downhole impact torque, and effectively prevent drilling tool failure. [ABSTRACT FROM AUTHOR]

This research aims to investigate the static aeroelastic characteristics of a slender straight 2D wing using aerodynamic strip theory. The finite element method is employed to determine the wing's divergence speed and aileron effectiveness, while Galerkin's method, based on the principle of virtual work is used to obtain the influence coefficient of the straight wing. The application of aerodynamic strip theory and finite span correction is utilized to establish a correlation between elastic twist and lift coefficient. Subsequently, a computational tool in MATLAB is formulated to derive an approximate solution for the static aeroelastic equilibrium equations concerning slender straight wings. An investigation is conducted into the impact of various elastic axis positions on the divergence speed and its implications for structural integrity are analyzed. It was observed in the study that the incorporation of finite span correction into the strip theory led to a 15% augmentation in the divergence speed of the slender wing. Validation of the mathematical model of the slender wing is performed through computational analyses conducted using ANSYS software. The flutter analysis examines parameters such as the distance between the elastic and aerodynamic axes, the sweep position, and the wing span. A MATLAB code is presented in the research article to explore the influence of these parameters on the flutter speed of a slender wing. Through an investigation of the interplay between these parameters and the flutter speed, the study strives to enhance comprehension of the fundamental mechanisms governing flutter occurrence in slender wings. The current research reveals that the flutter speed is notably affected by both the eccentricity and span of the wing. Specifically, a reduction in eccentricity leads to a 1.5% enhancement in flutter speed, while increasing the sweep angle from 15 to 30 degrees for a wing with a 15ft span results in a 2.54% increase in flutter speed. Moreover, wings spanning from 5ft to 15ft exhibit a 5% rise in flutter speed. These findings offer valuable insights for the design of more efficient and stable wings. [ABSTRACT FROM AUTHOR]

The Steklov eigenvalues of the Lamé operator arise from the analysis of surface waves and vibration modes in a linearly elastic structure. In this paper, based on the Lagrange conforming finite element method, we propose and analyze an a posteriori error indicator of the residual type for the Steklov eigenvalue problem of the Lamé operator in linear elasticity. The a posteriori error indicator is computed locally from the approximate eigenpair. We prove the reliability and the efficiency of the error indicator for eigenfunctions as well as the reliability of the error indicator for eigenvalues. Finally, we present numerical experiments to validate our theoretical analysis. [ABSTRACT FROM AUTHOR]

Introduction: Numerical simulations have demonstrated the superior bending flexibility of auxetic stents compared to conventional stent designs for endovascular procedures. However, conventional stent manufacturing techniques struggle to produce complex auxetic stent designs, fueling the adoption of additive manufacturing techniques. Methods: In this study, we employed DMLS additive manufacturing to create Titanium Ti64 alloy stent prototypes based on auxetic stent designs investigated in a previous study. These prototypes were then subjected to experimental three-point bending tests. Result: The experimental results were replicated using a finite element model, which showed remarkable accuracy in predicting the bending flexibility of four auxetic stents and two conventional stents. Discussion: Although this validation study demonstrates the promising potential of DMLS and other additive manufacturing methods for fabricating auxetic stents, further optimization of current stent design limitations and the incorporation of post-processing techniques are essential to enhance the reliability of these additive manufacturing processes. [ABSTRACT FROM AUTHOR]

This article discusses the accuracy and stability of the pressure field in nonlinear mixed displacement‐pressure finite element formulations in solid mechanics. We focus on two‐dimensional mixed polygonal finite element formulations with linear displacement and constant pressure approximations in particular. The inf‐sup stability of these formulations is assessed and compared with classical mixed finite element formulations. An analytical proof is presented, which concludes that the occurrence of spurious pressure modes depends on the chosen meshing strategy. It is shown that these spurious modes are successfully suppressed on any Voronoi mesh in both linear elasticity and nonlinear hyperelasticity without the need for any kind of stabilization. Several linear and nonlinear nearly‐incompressible examples with different discretization strategies and boundary conditions are considered to validate the analytical proof. A mixed polygonal finite element formulation based on the scaled boundary parameterization is used to approximate the field variables, however, the derivations presented herein hold for any lowest‐order mixed polygonal finite element formulation. The nonexistence of checkerboard modes on linear elastic Voronoi discretizations is shown graphically. By evaluating the incremental pressure in each Newton–Raphson iteration, the stabilization effect of the Voronoi discretization is demonstrated for nonlinear problems. In addition, the analytical proof is validated by the numerical (generalized) inf‐sup test. [ABSTRACT FROM AUTHOR]

This study introduces a novel approach to analyze the stress and displacement fields around blunt notches in bi-material media, focusing on mode III loading conditions. The eigenfunction expansion method is used to derive a simplified yet accurate solution, satisfying the boundary conditions for bi-material blunt V-notches. The robustness of the proposed asymptotic solution is validated through several finite element analyses, encompassing a range of notched geometries such as blunt V-notches, VO-notches, and circular holes. Notably, it is demonstrated that when the notch tip radius approaches zero, the solution coincides with the existing sharp V-notch model. [ABSTRACT FROM AUTHOR]

Stretchable inorganic electronics have been of growing interest over the past decades due to their various attractive potential applications. The island-bridge structure is the most widely used structural design, where rigid inorganic devices (islands) and interconnects (bridges) are attached to an elastomer substrate, and large deformations in the structure are accommodated by the large stretchability of the interconnects and the elastomer underneath them. Due to the large modulus mismatch of more than five orders of magnitude between the rigid island and elastomer substrate, there is a severe stress and strain concentration at the interface between the island and the substrate during large deformations, which may cause the interface fracture and delamination. In this work, the analytical solution of the interfacial shear and peel stress between the island and the substrate is derived to reveal the mechanism of interface fracture and agrees well with finite element analysis (FEA) results. A simple porous partition substrate design strategy is proposed to alleviate this stress and strain concentration at the boundary of the interface, where the porous region can undergo larger deformation due to the reduced stiffness of the material. FEA obtains the key parameters affecting the pore layout. The digital image correlation (DIC) experiment verifies the design strategy. The results show that, compared to the solid substrate, the porous partition substrate strategy can significantly reduce the maximum normal strain of the substrate around the island, thus effectively reducing the risk of structural interface failure. [ABSTRACT FROM AUTHOR]

Because dike propagation depends on stress state, the geometry of dikes can be used to make inferences about crustal stress conditions during emplacement. Early work relied on analytical solutions for stress in a two-dimensional elastic medium with a pressurized circular magma chamber and biaxial far-field stress. The principal stress trajectories in this classical model depend on the ratio of deviatoric stress magnitude to chamber pressure. Assuming dikes follow principal stress trajectories and bounding plausible magma chamber excess pressures lead to estimates of deviatoric stress magnitudes from the map pattern of dikes. Mériaux and Lister (2002) pointed out that this approach ignored stresses due to the magma-filled dikes themselves, which significantly alter predicted dike trajectories. They estimated deviatoric stresses 2 to 5 times previous estimates. However, Mériaux and Lister (2002) assumed the pressure distribution within the dike rather than computing it from viscous magma flow. We revisit this simplification using a 2D model which fully couples a linear elastic host rock with a pressurized chamber and a fluid-filled dike, assuming the lubrication approximation for viscous flow. This model is solved using the finite element method (FEM). Ensuring that dike propagation is stable limits the dike-tip cavity pressure for realistic fracture toughness. We find that computed trajectories fall between the classical principal stress and Mériaux and Lister (2002) trajectories for given regional stress and chamber pressure conditions. This leads to deviatoric stress magnitude estimates that are 1 to 2 times the classical estimates, and 1/2 to 1/3 the Mériaux and Lister (2002) estimates. We also explore the consequences of chamber depressurization due to magma outflow during dike propagation. For a given melt compressibility, the resulting trajectories align more closely with those obtained from the classical model, compared to those obtained assuming a constant chamber pressure. At higher ratios of tectonic stress to chamber pressure, the trajectories are nearly identical. In both the constant pressure and depressurizing chamber cases, our results suggest that realistic magma pressure profiles within a dike lead to smaller estimated ratios of deviatoric stress to chamber pressure than found by Mériaux and Lister (2002). Future work should extend dike propagation models to three dimensions, and more thoroughly explore effects of magma compressibility. [ABSTRACT FROM AUTHOR]

The pull-out test is one of the common experiments to determine the bond strength. When the problem is modeled in the context of linear elasticity for a cylindrical reinforced concrete block, the resulting simplified 1-D model yields so-called pull-out paradox Rezaei et al. (Mech Res Commun 126:104015, 2022) due to extreme concentration of energy near the bar. Since the standard linear elasticity is not able to consider this high values of energy, the problem was investigated by strain-gradient elasticity solution in the work of Rezaei et al. (Mech Res Commun 126:104015, 2022). In this study, to resolve the paradoxical solution, classical finite (i.e., St.-Venant–Kirchhoff model) and strain-gradient finite elasticity solutions are presented. Each mathematical model, assuming that the material is isotropic, is derived with the principle of minimum potential energy introducing appropriate strain energy. The numerical simulations are performed by the finite element method, and it is showed that numerical solution of each model converges well. [ABSTRACT FROM AUTHOR]

Composite materials, particularly honeycomb composites, are widely utilized in various industries, including aerospace, due to their high energy absorption against the impact and exceptional strength-to-weight ratio. This study aims to leverage the plastic and elastic properties of these materials to develop a simplified numerical model that incorporates orthotropic properties for core modeling. By doing so, the need for detailed honeycomb structure modeling is eliminated, resulting in reduced computational costs and time. A comprehensive three-dimensional finite element model, accounting for structural intricacies, is presented based on experimental data from a reputable source (isotropic model) and its equivalent finite element model (orthotropic model). The model is validated by the experimental results, demonstrating good agreement. The study also investigates parameters such as energy absorption, the internal energy of the core and faces, maximum displacement, and maximum contact force under low-velocity impact scenarios with spherical and cylindrical projectiles. These findings highlight the effectiveness of the orthotropic model, particularly in showcasing greater energy absorption in the core of the sandwich panel when subjected to a cylindrical impactor. [ABSTRACT FROM AUTHOR]

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The high-speed maglev vehicle/guideway coupled model is an essential simulation tool for investigating vehicle dynamics and mitigating coupled vibration. To improve its accuracy efficiently, this study investigated a hierarchical model updating method integrated with field measurements. First, a high-speed maglev vehicle/guideway coupled model, taking into account the real effect of guideway material properties and elastic restraint of bearings, was developed by integrating the finite element method, multi-body dynamics, and electromagnetic levitation control. Subsequently, simultaneous in-site measurements of the vehicle/guideway were conducted on a high-speed maglev test line to analyze the system response and structural modal parameters. During the hierarchical updating, an Elman neural network with the optimal Latin hypercube sampling method was used to substitute the FE guideway model, thus improving the computational efficiency. The multi-objective particle swarm optimization algorithm with the gray relational projection method was applied to hierarchically update the parameters of the guideway layer and magnetic force layer based on the measured modal parameters and the electromagnet vibration, respectively. Finally, the updated coupled model was compared with the field measurements, and the results demonstrated the model's accuracy in simulating the actual dynamic response, validating the effectiveness of the updating method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a lowest-order locking-free weak Galerkin (WG) finite element scheme for the grad-div formulation of linear elasticity problems. The scheme uses linear functions in the interior of mesh elements and constants on edges (2D) or faces (3D), respectively, to approximate the displacement. An H (d i v) -conforming displacement reconstruction operator is employed to modify test functions in the right-hand side of the discrete form, in order to eliminate the dependence of the L a m e ´ parameter λ in error estimates, i.e., making the scheme locking-free. The method works without requiring λ ‖ ∇ ⋅ u ‖ 1 to be bounded. We prove optimal error estimates, independent of λ , in both the H 1 -norm and the L 2 -norm. Numerical experiments validate that the method is effective and locking-free. [ABSTRACT FROM AUTHOR]

In this study, the frequency and deflection response analysis of basalt, soy, flax and hybrid pineapple and flax hybrid laminated skew plates are done. The conventional hand-layup method is used to fabricate the different bio-composites-based laminated structures. The uniaxial tension test is conducted in the INSTRON 5967 UTM to determine the elastic properties of the bio-composite laminated structure as per ISO 527-5 standards. The hybrid laminate skew plate is modeled using the first-order shear deformation theory (FSDT) and their elastic properties are obtained from the uniaxial tensile test from which the frequency and deflection of the skew laminated plates are calculated. The eight-noded shell elements (S8R5) with each node having five degrees-of-freedom are deputed in the commercial finite element method (FEM) package ABAQUS to beget the numerical solutions. The damping effect is neglected in the analysis. The accuracy of the proposed model is verified with available literature and found to be in good agreement. Later, the effect of different parameters such as boundary conditions, aspect ratio and skew angles on the natural frequency and deflection of the bio-composites hybrid laminated skew plates are investigated. The obtained results inferred the natural frequencies are decreasing with an increasing aspect ratio of skew plates. The skew angles help to increase the natural frequencies of skew plates. The central deflections are lower for high-skew angled laminated plates. [ABSTRACT FROM AUTHOR]

Background: There has been no absolute consensus on the optimal implant for fixation of medial clavicle fracture. The purpose of the present study was to test the biomechanical efficacy of inverted lateral clavicle locking compression plate (LCP-LC) in fixation of this specific fracture location by finite element analysis. Methods: Transverse and comminuted medial clavicle fracture simulated models stabilized by three different devices including inverted LCP-LC, superior clavicle LCP (LCP-SC), and dual reconstruction (LCP-RP) with LCP-SC were investigated biomechanical performance under three loading conditions, i.e., axial compression, inferior bending, and axial torsion. Results: EQV stress exhibited on implant and elastic strain at fracture site under inferior bending was greater than other loading cases. LCP-SC construct represented the greatest EQV stress and elastic strain. The inverted LCP-LC construct demonstrated lower EQV stress than the LCP-SC construct and was comparable to dual plating. Under axial compression and axial torsion, elastic strain produced from the inverted LCP-LC construct was comparable to dual plating, but greater than dual plating when subjected to inferior bending. Conclusion: By the results of FE analysis, inverted LCP-LC could be a potential application for fixation of clavicle fracture with short medial fragment. [ABSTRACT FROM AUTHOR]

A micromechanics procedure performed by the finite element method (FEM) was developed for the sake of examining the synergistic effects of carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) hybrids on the elastic and viscoelastic properties of polymer nanocomposites. The representative volume element (RVE) approach was employed owing to its capability to consider various nano-additives with disparate dimensions and evaluate microstructure-level aspects. Constant-strain minimization method and linear viscoelastic model were utilized to predict components of elastic stiffness and creep compliance tensors. The validity of the proposed model was assessed by comparison with the well-established Halpin–Tsai micromechanical model and available experimental measurements, providing an acceptable agreement. Effects of orientation (random or unidirectional dispersion), volume content, and variation in the length and thickness of the carbonaceous nano-additives on the Young's modulus, Poisson's ratio, and creep compliance of CNT/GNP/epoxy nanocomposites were investigated. The results explicitly revealed that the CNT and GNP contributions to the mechanical reinforcement and the creep resistance in polymer are strongly associated with their distribution and volume content within the hosting matrix. Moreover, the outcomes imply that increasing the length of CNT, reducing the thickness of GNP lead to increasing Young's modulus, and decreasing creep compliance (or increasing creep resistance) of CNT/GNP/epoxy nanocomposites. [ABSTRACT FROM AUTHOR]

In current-generation designs of total primary hip joint replacement, the prostheses are fabricated from alloys. The modulus of elasticity of the alloy is substantially higher than that of the surrounding bone. This discrepancy plays a role in a phenomenon known as stress shielding, in which the bone bears a reduced proportion of the applied load. Stress shielding has been implicated in aseptic loosening of the implant which, in turn, results in reduction in the in vivo life of the implant. Rigid implants shield surrounding bone from mechanical loading, and the reduction in skeletal stress necessary to maintain bone mass and density results in accelerated bone loss, the forerunner to implant loosening. Femoral stems of various geometries and surface modifications, materials and material distributions, and porous structures have been investigated to achieve mechanical properties of stems closer to those of bone to mitigate stress shielding. For improved load transfer from implant to femur, the proposed study investigated a strategic debulking effort to impart controlled flexibility while retaining sufficient strength and endurance properties. Using an iterative design process, debulked configurations based on an internal skeletal truss framework were evaluated using finite element analysis. The implant models analyzed were solid; hollow, with a proximal hollowed stem; FB-2A, with thin, curved trusses extending from the central spine; and FB-3B and FB-3C, with thick, flat trusses extending from the central spine in a balanced-truss and a hemi-truss configuration, respectively. As outlined in the International Organization for Standardization (ISO) 7206 standards, implants were offset in natural femur for evaluation of load distribution or potted in testing cylinders for fatigue testing. The commonality across all debulked designs was the minimization of proximal stress shielding compared to conventional solid implants. Stem topography can influence performance, and the truss implants with or without the calcar collar were evaluated. Load sharing was equally effective irrespective of the collar; however, the collar was critical to reducing the stresses in the implant. Whether bonded directly to bone or cemented in the femur, the truss stem was effective at limiting stress shielding. However, a localized increase in maximum principal stress at the proximal lateral junction could adversely affect cement integrity. The controlled accommodation of deformation of the implant wall contributes to the load sharing capability of the truss implant, and for a superior biomechanical performance, the collared stem should be implanted in interference fit. Considering the results of all implant designs, the truss implant model FB-3C was the best model. [ABSTRACT FROM AUTHOR]

We consider two-scale stress mixed finite element elasticity models using H(div)-conforming tensor approximations for the stress variable, whilst displacement and rotation fields are introduced to impose divergence and symmetry constraints. The variables are searched in composite FE spaces based on polyhedral subdomains, formed by the conglomeration of local shape-regular micro partitions. The two-scale characteristic is expressed in terms of refined discretizations inside the subdomains versus coarser normal components of tensors over their boundaries (traction), with respect to mesh size, polynomial degree, or both. General error estimates are derived and stability is proved for five particular cases, associated with stable single-scale local tetrahedral space settings. Enhanced accuracy rates for displacement and super-convergent divergence of the stress can be obtained. Stress, rotation, and stress symmetry errors keep the same accuracy order determined by the traction discretization. A static condensation procedure is designed for computational implementation. There is a global problem for primary variables at the coarser level, with a drastic reduction in the number of degrees of freedom, solving the traction variable and piecewise polyhedral rigid body motion components of the displacement. The fine details of the solution (secondary variables) are recovered by local Neumann problems in each polyhedron, the traction variable playing the role of boundary data. In this sense, the proposed formulation can be interpreted as an equivalent Multiscale Hybrid Mixed method, derived from a global-local characterization of the exact solution. A numerical example with known smooth solution is simulated to attest convergence properties of the method based on local B D F M divergence-compatible finite element pairs. Application to a problem with highly heterogeneous material is analyzed for robustness verification. • Multiscale method for 3D mixed weak symmetry elasticity approximations. • Theoretical analysis for the convergence of the stress and displacement. • Numerical results confirm theoretical convergence rates. • Method applied to highly heterogeneous 3D model. • Method results in elementwise equilibrated stress field. [ABSTRACT FROM AUTHOR]

We develop randomized neural networks (RNNs) with Petrov–Galerkin (RNN-PG) methods to solve linear elasticity and Navier–Stokes equations. RNN-PGs use the Petrov–Galerkin variational framework, where the solution is approximated by randomized neural networks and the test functions are piecewise polynomials. Unlike conventional neural networks, the parameters of the hidden layers of randomized neural networks are fixed randomly while the parameters of the output layer are determined by the least-squares method, which can effectively approximate the solution. We also develop mixed RNN-PG (M-RNN-PG) methods for linear elasticity problems to ensure symmetry of the stress tensor and avoid locking effects. For the Stokes problem, we present various M-RNN-PG methods that enforce the divergence-free constraint by different techniques. For the Navier–Stokes equations, we propose a space-time M-RNN-PG that uses Picard or Newton iteration to deal with the nonlinear term. Using several examples, we compare RNN-PG methods with the finite-element method, the mixed discontinuous Galerkin method, and the physics-informed neural network. The numerical results demonstrate that RNN-PG methods achieve higher accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Introducing openings or holes into wooden structures is a common practice for providing utility services. However, this practice leads to stress concentration, resulting in a reduction in stiffness and load-carrying capacity. Therefore, understanding the effects of holes on beam properties is important for design considerations. This study investigates the mechanical behavior of a wooden beam made from juvenile Pinus elliottii containing open cylindrical holes with three different diameters: 4, 8, and 12 mm. The mechanical properties were evaluated for compression parallel to the fibers, quasi-static bending, and tension perpendicular to the fibers. Numerical simulations were conducted using a finite element (FE) model, considering the orthotropic elastic properties determined from experimental tests and elastic ratios reported in the literature. The experimental results indicated that the influence of hole diameter was not significant on the compressive properties; however, longitudinal crack failures began to form for holes with diameters of 8–12 mm. Regardless of hole size, the compressive and bending characteristics revealed that hole location did not affect the stiffness, strength, or damage mechanisms. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze the least squares finite element methods for the linear elasticity interface problem in the stress-displacement system on unfitted meshes. We consider the cases that the interface is C2 or polygonal, and the exact solution (σ, u) belongs to Hs(div; Ω0 ∪ Ω1) × H1+s(Ω0 ∪ Ω1) with s > 1/2. Two types of least squares functionals are defined to seek the numerical solutions. The first is defined by simply applying the L2 norm least squares principle, and requires the condition s ≥ 1. The second is defined with a discrete minus norm, which is related to the inner product in H−1/2(Γ). The use of this discrete minus norm results in a method of optimal convergence rates and allows the exact solution has the regularity of any s > 1/2. The stability near the interface for both methods is guaranteed by the ghost penalty bilinear forms and we can derive the robust condition number estimates. The convergence rates under L2 norm and the energy norm are derived for both methods. We illustrate the accuracy and the robustness of the proposed methods by a series of numerical experiments for test problems in two and three dimensions. [ABSTRACT FROM AUTHOR]

We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly valid in the incompressible limit. A posteriori estimates are derived for both the compressible and incompressible cases. The results are verified by numerical examples. [ABSTRACT FROM AUTHOR]