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INTRODUCTION: Although Staphylococcus aureus is the leading cause of biofilm-related infections, the lipidomic distributions within these biofilms is poorly understood. Here, lipidomic mapping of S. aureus biofilm cross-sections was performed to investigate heterogeneity between horizontal biofilm layers. METHODS: S. aureus biofilms were grown statically, embedded in a mixture of carboxymethylcellulose/gelatin, and prepared for downstream matrix-assisted laser desorption/ionization imaging mass spectrometry (MALDI IMS). Trapped ion mobility spectrometry (TIMS) was also applied prior to mass analysis. RESULTS: Implementation of TIMS led to a ∼ threefold increase in the number of lipid species detected. Washing biofilm samples with ammonium formate (150 mM) increased signal intensity for some bacterial lipids by as much as tenfold, with minimal disruption of the biofilm structure. MALDI TIMS IMS revealed that most lipids localize primarily to a single biofilm layer, and species from the same lipid class such as cardiolipins CL(57:0) - CL(66:0) display starkly different localizations, exhibiting between 1.5 and 6.3-fold intensity differences between layers (n = 3, p

Many‐body expansion (MBE) fragment approaches have been applied to accurately compute nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent examples demonstrate that electric field gradient (EFG) tensor parameters can be accurately calculated for 14N and 17O. A key additional development is the simple molecular correction (SMC) approach, which uses two one‐body fragment (i.e., isolated molecule) calculations to adjust NMR parameter values established using 'benchmark' projector augmented‐wave (PAW) density functional theory (DFT) values. Here, we apply a SMC using the hybrid PBE0 exchange‐correlation (XC) functional to see if this can improve the accuracy of calculated 35Cl EFG tensor parameters. We selected eight organic and two inorganic crystal structures and considered 15 chlorine sites. We find that this SMC improves the accuracy of computed values for both the 35Cl quadrupolar coupling constant (CQ) and the asymmetry parameter (ηQ) by approximately 30% compared with benchmark PAW DFT values. We also assessed a SMC that offers local improvements not only in terms of the quality of the XC functional but simultaneously in the quality of the description of relativistic effects via the inclusion of spin–orbit effects. As the inorganic systems considered contain heavy atoms bonded to the chlorine atoms, we find further improvements in the accuracy of calculated 35Cl EFG tensor parameters when both a hybrid functional and spin–orbit effects are included in the SMC. On the contrary, for chlorine‐containing organics, the inclusion of spin–orbit relativistic effects using a SMC does not improve the accuracy of computed 35Cl EFG tensor parameters. [ABSTRACT FROM AUTHOR]

Sulfur‐33(33S) stable‐isotope labeled taurine, 2‐aminoethanesulfonic acid, has been synthesized, and a series of solution and solid‐state 33S nuclear magnetic resonance (NMR) experiments at 14.1 and 18.8 T, respectively, have been carried out at room temperature. The single peak of a solution 33S NMR spectrum in 0.1‐mM [33S]‐taurine in D2O can be observed with the signal‐to‐noise (S/N) ratio of 9 in 40,000 scans, which paves the way toward in vivo analysis of pharmacokinetics and metabolism of 33S‐labeled taurine. Undistorted magic‐angle‐spinning (MAS) and static 33S NMR spectra of polycrystalline [33S]‐taurine are observed with sufficient S/N ratios for analysis, and the magnitudes of 33S EFG and CS tensors can be obtained. [ABSTRACT FROM AUTHOR]

In this study, we explored the effect of an active afterheater on the growth of gallium oxide single crystals using the EFG method. We analyzed the temperature distribution of the crystal under the growing process through multiphysics simulations of the models with and without an active afterheater and investigated the morphology of crystals by applying each model to real experimental growths. The afterheater is a component in the growing furnace that activates radiant heat transfer, and its performance depends on its location, size, material, and shape. The simulation results showed that the afterheater applied in this study was found to be effective in obtaining good temperature distribution in the reactor. Through experimental crystal growth corresponding to the simulation approaches, it was confirmed that an appropriate afterheater reduces thermal stress at the growth front and provides a thermal annealing effect on the post-grown crystals during the growing process to improve crystal quality. [ABSTRACT FROM AUTHOR]

In this study, we explored the effect of an active afterheater on the growth of gallium oxide single crystals using the EFG method. We analyzed the temperature distribution of the crystal under the growing process through multiphysics simulations of the models with and without an active afterheater and investigated the morphology of crystals by applying each model to real experimental growths. The afterheater is a component in the growing furnace that activates radiant heat transfer, and its performance depends on its location, size, material, and shape. The simulation results showed that the afterheater applied in this study was found to be effective in obtaining good temperature distribution in the reactor. Through experimental crystal growth corresponding to the simulation approaches, it was confirmed that an appropriate afterheater reduces thermal stress at the growth front and provides a thermal annealing effect on the post-grown crystals during the growing process to improve crystal quality.

• A new method for discrete crack propagation using visibility criterion in EFG is presented. • Crack can propagate or initiated if a damage criteria are met at the node. • The new method integrates the use of enrichment and the visibility criterion to introduce the discontinuity. • An exact solution was presented for one-dimensional strain softening cracked bar. • The new method gives relatively accurate results with low computational cost. A new approach for modeling cracks in element free Galerkin method is presented in this work, the crack model is assumed to be discrete, therefore, no crack topology is needed. A crack is presented at each node if a certain damage criterion is met, where the node is enriched by discontinuous shape functions and the visibility method is used in which the nodes on one side of the crack are considered opaque to the nodes at the other side. An exact solution is presented for the one-dimensional strain softening bar with a crack and the solution is compared with the proposed method, the results of the displacement field using the visibility based cracking particle method were very accurate, the method was able to capture the behavior of the crack in the one-dimensional bar. The solution of different two-dimensional problems is also presented and validated with experimental results in the literature. The results showed that the method is capable of predicting real life phenomena and mimic the behavior of real-life experiments with reasonable accuracy. The new method is relatively accurate with minimal computational effort compared to other FEM or XFEM. [ABSTRACT FROM AUTHOR]

This paper presents the results of our research regarding the use of a meshless method, namely element-free Galerkin method, in solving an impact problem between a rigid body and a foam plate. Next, the paper gives two answers to two usual questions appearing when modeling foam materials. These questions refer to the choice of a material model and to the extension of the stress–strain curve of the foam material. Solutions start from some experimental data of a foam material and continue by numerical simulations using Ls-Dyna software. The results are very interesting and especially useful in numerical modeling of the foam material. The results are presented in a comparative way, graphically and in tabular form. [ABSTRACT FROM AUTHOR]

This paper combines the numerical mode‐matching (NMM) method with the element‐free Galerkin (EFG) method for the efficient modeling of electromagnetic waves in cylindrically layered media with multiple horizontal beds. In the implementation of the conventional NMM scheme, finite element method (FEM) is commonly used to discretize the radial direction. To improve the efficiency for the discretization along the radial direction, EFG method is utilized instead to construct the element‐free Galerkin NMM (EFG‐NMM) scheme. As a meshless method, EFG scheme avoids the complexity of mesh generation as well as improves the numerical accuracy compared to FEM. The EFG‐NMM scheme is developed for both static and time‐harmonic electromagnetic waves. Excellent agreement between EFG‐NMM and FEM‐NMM is verified by simulating different numerical examples. [ABSTRACT FROM AUTHOR]

We analyze the performance of the linear response elimination of the small component (LRESC) scheme to describe the electric field gradient (EFG), in dihalogen molecular systems, and also to give insight of the relativistic corrections. LRESC shows a good performance, providing results close to four‐component (4c) ones for molecules containing atoms belonging up to the fifth row of the Periodic Table. When heavier nuclei are involved the difference among LRESC and 4c values reaches up to 5%. The main relativistic correction represents 80% of the nonrelativistic part for the heaviest molecule. LRESC can be applied at Hartree–Fock as well as Density Functional Theory levels, therefore we also analyze correlation effects on EFG showing that relativity enhances correlation effects and both effects are not additive. As an application of LRESC method, nuclear quadrupole moment calculations of some halogen nuclei are also carried out and compared with the most recent data. [ABSTRACT FROM AUTHOR]

Multi-plate sapphire crystals were grown by EFG technique. Micro-laser Raman spectrum and ICP-AES were used to identify the chemical composition of the matters in bubbles, showing that these matters may contain sulphur. Growth striations at the surface of the crystal were concerned with fluctuation of growth rate and temperature as well as the working accuracy of the die. Chemical etching test shows that the crystal has a dislocation density of 4.2 ×104 cm-2 and there is no low angle grain boundary defect. X-ray rocking curve measurement shows a single peak with FWHM of 70. 63″. Owing to graphite heat shade, the crystal contains F and F+ centers. The transmittance of the crystal is over 80% at light wavelength from 400 nm to 3 000 nm. Annealing the crystal in air can reduce optical absorption caused by color centers. The results of this paper are useful to theoretical study on formation of defects in sapphire and technical improvement on EFG sapphire industury. [ABSTRACT FROM AUTHOR]

[Cs+(Cryptand[2.2.2])]I− (1; Cryptand[2.2.2] = C222) was characterized via single‐crystal X‐ray diffraction and was shown to crystallize in the monoclinic space group I2/c system with a = 8.9605 (2), b = 23.5073 (5), c = 11.7563 (3) Å, and β = 93.792 (2)°. Stationary and magic angle spinning (MAS) experiments under different magnetic fields allowed for the separation of the chemical shift and quadrupole coupling tensor parameters. Remarkably, MAS spectra showing pure second‐order quadrupole powder patterns at 4.23 T were observed for 133Cs nuclei with small quadrupole moments owing to the large electric field gradients (EFGs) caused by short CsO and CsN bond distances in the [Cs+(C222)] ions. Stationary NMR powder patterns with a combination of the chemical shifts and second‐order quadrupolar interactions were observed. The EFG and chemical shift tensor components calculated using the atomic coordinate files and Gaussian 09 were reasonably consistent with the experimental values. [ABSTRACT FROM AUTHOR]

Efficient implementation of the element-free Galerkin (EFG) method for a phase-field model of linear elastic fracture mechanics is presented, in which the convenience of the meshfree method to construct high order approximation functions and to implement h-adaptivity is fully exploited. A second-order moving-least squares approximation for both displacement and phase field is employed. Domain integration of the weak forms is evaluated by the quadratically consistent 3-point integration scheme. The refinement criterion using maximum residual strain energy history is proposed and the insertion of nodes is based on the background mesh. Numerical results show that the developed method is more efficient than the standard finite element method (3-node triangle element) due to the proposed h-adaptivity. In comparison with the standard EFG method, the proposed consistent EFG method significantly improves the computational efficiency and accuracy. The advantage of the quadratic approximation is also demonstrated. In addition, the feasibility of extending the proposed method to 3D is validated by the modeling of a twisting crack. [ABSTRACT FROM AUTHOR]

Summary: This study aimed to optimize the derivation of trophectoderm from in vitro -produced camel embryos under feeder-free culture conditions using the basement membrane matrix Matrigel. Trophoblastic vesicles were obtained through mechanical microdissection of in vitro -produced camel (Camelus dromedarius) embryos. Supplementing the culture medium with 10 ng/ml of epidermal growth factor and 10 ng/ml fibroblast growth factor improved the attachment and subsequent outgrowths of cultured trophoblastic vesicles when compared with the control group and the groups supplemented individually with each growth factor. The expression levels of pluripotency genes octamer-binding transcription factor 4 (Oct4), sex determining region Y-box 2 (Sox2), myelocytomatosis proto-oncogene (c- Myc) and anti-apoptotic gene B-cell lymphoma 2 (Bcl2) were increased in trophoblastic vesicles supplemented with both growth factors when compared with the control group. Conversely, both growth factors decreased the expression of apoptotic genes tumour protein p53 (p53) and Bcl-2-associated X protein (Bax). To the best of our knowledge, this may be the first report describing the derivation of trophoblast stem cells from in vitro -produced camel embryos. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the element-free Galerkin (EFG) method is applied to the study of vertically integrated two-phase flow of CO 2 and brine in a deep saline aquifer. The methodology comprises of solving two simultaneous partial differential equations (PDEs) involving pressure and saturation terms, which are obtained by combining mass and momentum conservation equations. The obtained pressure and the average CO 2 saturation resulting from the model will help to study the spatial and temporal distribution of the aquifer, bottom pressure buildup and the CO 2 storage capacity of the aquifer respectively. The temporal analysis is solved using an IMplicit Pressure and Explicit Saturation (IMPES) solution strategy. A local refinement zone is introduced to capture the asymptotic pressure solution near the injection wells. Furthermore, the region surrounding the well is modelled as a non-homogeneous interface using Functionally Graded Materials (FGMs) analogy. Various case studies such as the horizontal aquifer, the sloped aquifer, the non-homogenous aquifer and, the horizontal aquifer with multiple wells have been presented to show the efficiency of the proposed model. The performance of the proposed EFG method is compared with that of FEM and XFEM numerical solutions. It is observed that the EFG method can capture average CO 2 saturation (height of CO 2) more effectively than the FEM and as effectively as the XFEM at the injection well. Moreover, it is easier to use the EFG method to solve complex aquifer problems, having non-homogeneity and multiple wells by considering a local nodal refinement around the well with ease. The simplicity of the proposed EFG method is demonstrated in this paper. [ABSTRACT FROM AUTHOR]

Eimeria intestinalis is the most pathogenic species of rabbit coccidiosis, causing weight loss, diarrhea, and even acute death. The currently used anticoccidial drugs against E. intestinalis in rabbits are associated with drug resistance and residues. Immunological control might be a potential alternative. We cloned and expressed the E. intestinalis recombinant EF1α and EFG (r Ei -EF1α and r Ei -EFG, respectively). Rabbits were immunized subcutaneously every 14 days with 100 µg of r Ei -EF1α and r Ei -EFG and followed by 5 × 10 4 E. intestinalis sporulated oocysts orally challenge. Serum samples were collected every 7 days to measure the levels of specific antibodies and cytokines. On post-challenge day 14, rabbits were sacrificed and the anticoccidial index was evaluated. The rabbits of PBS challenged groups exhibited anorexia, diarrhea, marked intestinal wall thickening, and white nodules that formed patches, while rabbits from the r Ei -EFG challenged group exhibited milder symptoms. The r Ei -EFG challenged group exhibited milder symptoms. The r Ei -EFG group had a 60.58% oocyst reduction and 56.04%wt gain. After vaccination, specific IgG levels increased and stayed high ( Ei -EFG group had a 60.58% oocyst reduction and 56.04%wt gain. After vaccination, specific IgG levels increased and stayed high ( P < 0.05). The IL-4 and IL-2 levels of r Ei -EF1α immunized groups showed a significant increase after immunization ( P < 0.05). Both r Ei -EFG could induce humoral and cellular immune responses. In contrast, rabbits immunized with r Ei -EFG could induce humoral and cellular immune responses. In contrast, rabbits immunized with r Ei -EF1α were better protected from challenge by E. intestinalis -EFG.Ei -EFG., Competing Interests: The authors declare no conflict of interest.

The usage of alkyl aluminum compounds and related structures as co‐catalyst finds a broad range of application in homogeneous and heterogeneous catalysis. While understanding the nature of the aluminum species in solution or in solids can be a challenge, 27Al solid state NMR is a powerful tool to understand the structures of Al species, but their assignment remains mostly empirical, typically by comparing chemical shifts with known compounds. In this work, the observed trends in 27Al‐NMR parameters – chemical shift and quadrupolar coupling constant – of chloroalkyl aluminum compounds, a prototypical class of important Lewis activators, are traced back to their frontier orbitals and electron polarization through a natural localized molecular orbital analysis. This study thus provides guidelines to understand the nature of chemical shift and thereby assignment of possible structure. [ABSTRACT FROM AUTHOR]

Reasonable failure paths are crucial in the stability assessment of a highly pressurized gas storage cavern in a rock mass using limit equilibrium analysis. In this study, the fracture patterns in the rock mass around a gas storage cavern are evaluated based on the element-free Galerkin (EFG) method with a cohesive crack model. The proposed analysis method was first validated through scaled-down model testing results before extending to a full-scale problem. Using the current approach, a parametric sensitivity analysis was performed by taking into account the influences of the stress ratio, the depth of the cavern, and the tensile strength of the rock mass. Based on the analysis results obtained, this research showed that the representative failure paths, in which the uplift evaluation is necessary, can be established from the EFG results with careful consideration of crack initiation and the propagation direction. The site having an in situ stress ratio greater than 1.2 is preferred for operation of underground gas storage caverns. By performing the limit equilibrium analyses for stability assessment of the rock mass above the pressurized cavern, we demonstrated that the factor of safety against uplift computed from the failure paths established in this study is higher than or equal to those obtained from analyses with the simplified models in previous studies without considering the influence parameters on the fracture patterns. [ABSTRACT FROM AUTHOR]

The projector-augmented wave (PAW) method is used to calculate electric field gradients (EFG) for various PAW potentials. A variety of crystals containing reactive nonmetal, simple metal, and transition elements, are evaluated in order to determine the predictive ability of the PAW method for the determination of nuclear quadrupole resonance frequencies in previously unstudied materials and their polymorphs. All results were compared to experimental results and, where possible, to previous density functional theory (DFT) calculations. The EFG at the 14N site of NaNO2 is calculated by DFT for the first time. The reactive nonmetal elements were not very sensitive to the variation in PAW potentials, and calculations were quite close to experimental values. For the other elements, the various PAW potentials led to a clear spread in EFG values, with no one universal potential emerging. Within the spread, there was agreement with other ab initio models.

The purpose of this work is to evaluate the use of the Element Free Galerkin (EFG) Method for modeling high speed cutting. EFG is a coupled meshless method, which allows for the easy management of large material distortions that occur in the cutting problem and the “natural” work piece/chip separation. The developed EFG model proves its ability to account for continuous chip formation and provides a more precise estimation of the chip shape then FEM, as illustrated in some orthogonal cutting examples. The chip shape and cutting forces prediction values obtained with the help of this method are compared to conventional FEM. The advantage of the suggested approach is that it allows substituting the classically needed machining tests with numeric experiments. [ABSTRACT FROM AUTHOR]

In the product development process, structural optimization plays vital role because it deals with size, shape and topology of the structures. However, structural performance greatly depends on its geometric shape and hence structural shape optimization has remained one of the most active research areas since early 1970s. Conventional parametric shape optimization technique employs grid-based numerical tools like FEM and BEM for structural analysis, which experiences some innate limitations like mesh distortion and frequent remeshing, element locking and poor approximation while dealing with large shape changes during the optimization process. Meshless Methods (MMs) can alleviate these issues when used as a structural analysis tool in shape optimization. In last two decades, MMs have been explored for structural shape optimization along with various deterministic and stochastic optimization algorithms. The objective of present work is twofold, first is to review advanced parametric shape optimization techniques which are based on MMs like Element Free Galerkin (EFG) method and Reproducing Kernel Particle Method (RKPM) for linear elastic, thermoelastic, hyperelastic, frictional contact and structure dynamics optimization problems and second is to emphasize benefits of meshless techniques in shape optimization. Based on the review, the article presents some critical observations including Design Sensitivity Analysis (DSA) in meshless environment, numerical integration techniques in MMs and benefits of coupled FEM-MM approach in shape optimization. At the end, promising future research directions in shape optimization field based on MMs are presented along with concluding remarks. [ABSTRACT FROM AUTHOR]

For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. A flexible computational procedure for solving 1D linear elastic beam problems is presented that currently uses two forms of approximation function (moving least squares and kernel approximation functions) and two types of formulations, namely the weak form and collocation technique, respectively. The approximations functions constructed in continuous or in discrete way are used as approximations of the strong forms of partial differential equations (PDEs), and those serving as approximations of the weak forms of PDEs to set up a linear system of equations to reproduce Element Free Galerkin (EFG) and Smooth Particle Hydrodynamics (SPH) meshless methods. To approximate the strong form of a PDE, the partial differential equation is usually discretized by specific collocation technique. The SPH is a representative method for the strong form collocation approach. To approximate the weak form of a PDE, Galerkin weak formulation is used.

An equilibrium Element-Free Galerkin (EFG) based formulation for limit analysis of rigid-perfectly plastic plane strain problems is presented. In the formulation pure stress fields are approximated using a moving least squares technique, and a stabilized conforming nodal integration scheme is used in combination with the collocation method, ensuring that the equilibrium equations only need to be fulfilled at the nodes and instability problems can be eliminated. The von Mises yield criterion is enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to a benchmark Prandtl problem.

Electric field gradients (EFG’s) at the In sites and spin magnetic moments at the Ce sites were calculated for the case of solid CeIn3. The calculations were performed by increasing pressure gradually from -5 to +22 GPa within the density functional theory (DFT) using the augmented plane waves plus local orbital (APW+lo) method employing the well-known PBE-GGA+U and WC-GGA+U schemes. The results almost show a linear reduction of spin magnetic moments of Ce by gradually increasing the pressure from -5 GPa to 22 GPa. However, from our results one can see that the calculated electric field gradients at the In site are growing up by increasing the pressure. We have compared the EFG’s at zero pressure with experimental and theoretical results of the others. The comparison shows that at ambient pressure our EFG’s are more consistent with experiment than the results of the other groups. Our result shows that the calculated spin magnetic moments are suppressed in the vicinity of some quantum critical point.

The main idea of meshless methods is to approximate the unknown field by a linear combination of shape functions built without having recourse to a mesh of the domain. The computational domain is discretized using a set of scattered nodes. The shape functions associated with a given node is then built considering the weight functions whose support overlaps the one of the weight function of this node; thus, there is actually no need to establish connectivities between the different nodes as in the finite element method. Monte-Carlo integration techniques are promising schemes in the context of meshless techniques. The purpose of the present paper is to implement in EFG a new body integration technique for the evaluation of the stiffness matrix that does not rely on a partition of the domain into cells, but rather points. Numerical examples based on three-dimensional elasticity problems are presented to examine the accuracy and convergence of the proposed method. In this context, Quasi-Monte Carlo integration techniques are used. The results are compared to traditional EFG. Conclusions are drawn concerning the proposed techniques and its capabilities.

The assumptions underlying the popular projector-augmented wave (PAW) method of computing electronic structure in solids are examined, with primary attention to the computation of NMR observables. In particular, the assumption of non-overlapping PAW spheres is studied, and it is shown that when the spheres do overlap, the errors may be significant and furthermore are of unpredictable sign. Examples are provided by comparing PAW-based calculations with and without overlapping spheres, with the highly accurate all-electron linear augmented wave method. [ABSTRACT FROM AUTHOR]

A combination of two first-principles electronic structure calculation methods in the framework of density-functional theory was applied to investigate the (0 0 1) α-Al 2 O 3 surface reconstruction and its structural, electronic, magnetic, and hyperfine properties when doped with Cd impurities at different depths from the surface. The SIESTA approach was used to obtain the equilibrium positions of all atoms and the Full-Potential Augmented Plane Wave plus local orbital (FP-APW+lo) method was employed in order to obtain the electronic structure at these equilibrium positions and all the other physical properties. For the most stable (0 0 1) α-Al 2 O 3 surface, we have demonstrated that the inclusion of the Cd atom at substitutional Al sites at and near the surface produces a ground state magnetic behavior. The largest principal component V 33 of the electric-field-gradient (EFG) tensor at the Cd atom localized just above the α-Al 2 O 3 terrace showed the same [0 0 1] orientation and a dominating p -character as Cd does when it is localized at bulk α-Al 2 O 3 , but exhibits an anomalous V 33 magnitude four times larger than its value in bulk. Just below the surface, the non symmetric structural relaxation around the Cd impurity is responsible for the strong change in the asymmetry, magnitude, and orientation of the EFG tensor. The changes in the hyperfine properties have been correlated with the modifications observed on the electronic charge density at the different Cd sites and on the p -states of the Cd-projected partial density of states. Accordingly, the significant differences on the hyperfine parameters showed for different depths suggest that 111 Cd probe-atoms used in Perturbed γ–γ Angular Correlation experiments could be used for evaluating geometrical and electronic distortions, particularly for positions quite close to the reconstructed surface, as well as contributing to studies of growth, adsorption, and diffusion of atoms in oxide surfaces and interfaces. [ABSTRACT FROM AUTHOR]

In this manuscript, an extended element-free Galerkin (XEFG) method for dynamic thermo-mechanical fracture is proposed. The crack is considered adiabatic and the discontinuous displacement field and temperature field is modeled by partition-of-unity enrichment of the test and trial functions. The coupled thermo-mechanical formulation is implemented for static and dynamic problems and applied to fracture in composite structures in two dimension. The method is verified through comparison to analytical and experimental results. Where available, the results are also compared to reference solutions. The proposed method models thermo-mechanical efficiently and robustly with few degrees of freedom. Therefore, an h-adaptive refinement procedure is employed that inserts nodes based on the temperature gradient. [ABSTRACT FROM AUTHOR]

A meshless variational multiscale methods for thermo-mechanical material failure is presented. Fracture is modeled by partition of unity enrichment. The displacement field and temperature field is enriched with step-functions and appropriate crack tip enrichment accounting for fine-scale features. The topology of the crack is modeled taking advantage of the level set method. The advantage of using a meshless method instead of finite elements is the ease in treating highly curved cracks with very coarse meshes due to the higher continuity of the meshless method. Moreover, the higher continuity results also in a smoother and more accurate stress field avoiding eratic fracture patterns. The method is applied to several benchmark problems and compared to analytical results, reference solutions and experimental data to demonstrate its robustness and efficiency. [ABSTRACT FROM AUTHOR]

The formulation of three-dimensional element-free Galerkin (EFG) method based on the Hu–Washizu three-field variational principle is described. The orthogonality condition between stress and strain difference is satisfied by correcting the derivatives of the nodal shape functions. This leads to a variationally consistent formulation which has a similar form as the formulation of standard Galerkin weak form. Based on this formulation, an integration scheme which employs only four cubature points in each background tetrahedral element (cell) is rationally developed for three-dimensional EFG with quadratic approximation. The consistency of the corrected nodal derivatives and the satisfaction of patch test conditions for the developed integration scheme are theoretically proved. Extension of the proposed method to small strain elastoplasticity is also presented. The proposed method can exactly pass quadratic patch test, that is, quadratic exactness is achieved, and thus it is named as quadratically consistent 4-point (QC4) integration method. In contrast, EFG with standard tetrahedral cubature and the existing linearly consistent 1-point (LC1) integration fail to exactly pass quadratic patch test. Numerical results of elastic examples demonstrate the superiority of the proposed method in accuracy, convergence, efficiency and stability. The capability of the proposed QC4 scheme in solving elastoplastic problems is also demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

Robust and efficient integration of the Galerkin weak form only at the approximation nodes for second order meshfree Galerkin methods is proposed. The starting point of the method is the Hu-Washizu variational principle. The orthogonality condition between stress and strain difference is satisfied by correcting nodal derivatives. The corrected nodal derivatives are essentially linear functions which can exactly reproduce linear strain fields. With the known area moments, the stiffness matrix resulting from these corrected nodal derivatives can be exactly evaluated using only the nodes as quadrature points. The proposed method can exactly pass the quadratic patch test and therefore is named as quadratically consistent nodal integration. In contrast, the stabilized conforming nodal integration (SCNI) which prevails in the nodal integrations for meshfree Galerkin methods fails to pass the quadratic patch test. Better accuracy, convergence, efficiency and stability than SCNI are demonstrated by several elastostatic and elastodynamic examples. [ABSTRACT FROM AUTHOR]

SUMMARY An element-free Galerkin (EFG) method with linear, quadratic and cubic approximations, which can exactly, in a numerical sense, pass the corresponding patch tests is proposed and is named as consistent EFG (CEFG) method. The development of this method is based on the Hu-Washizu three-field variational principle. Numerical integration schemes with corrected nodal derivatives at quadrature points are proposed according to the satisfaction of the orthogonality condition between stress and strain difference. Thus, the method is variationally consistent. The consistency of the corrected nodal derivatives and the satisfaction of patch test conditions are theoretically proved and also numerically validated. Numerical results show that the proposed CEFG method greatly improves the numerical performance of the EFG method in terms of accuracy, convergence, efficiency and stability, especially the proposed cubic CEFG method, which shows exceptional accuracy and convergence. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled. The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used. Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr–Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. [Copyright &y& Elsevier]

Abstract: Fractures developed around high pressurized gas or air storage tunnels can progressively extend to the ground surface, eventually leading to an uplift failure. A tool reasonably reproducing the failure patterns is necessary for stability assessment. In this study, a numerical method based on the element-free Galerkin (EFG) method with a cohesive crack model is developed to simulate fracture propagation patterns in the rock mass around a tunnel under high internal pressure. A series of physical model tests was also conducted to validate the reliability of the developed method. A qualitative agreement between physical model tests and numerical results can be obtained. The in situ stress ratio, k, has a strong influence on both the position of crack initiation and the propagation direction. The numerical analyses were extended to full-scale problems. Numerical tests were performed to investigate the prime influencing factors on the failure patterns of a high pressurized gas circular tunnel with varying parameters. The results suggest that initial in situ stress conditions with a high k (larger than 1) is favorable for construction of pressurized gas or air storage tunnels. [Copyright &y& Elsevier]

Abstract: The main objective of this work is to reduce the volumetric locking pathology at the Element Free Galerkin (EFG) 3D solid-shell meshless method. For this purpose, a subspace analysis is performed in order to extract the linearly independent incompressible deformation modes that can be reproduced by different background integration cells. Additional deformation modes reproduced by a cell configuration produces more flexibility for the meshless formulation. The Enhanced Assumed Strain (EAS) method is blended with the EFG formulation in such a way that additional (mathematical) variables are included in the formulation increasing its flexibility for nearly incompressible materials. Three numerical examples show the effect of the EAS formulation in alleviating the locking pathology for an almost incompressible material condition. [Copyright &y& Elsevier]