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The restoration of endodontically treated teeth is one of the main challenges of restorative dentistry. The structure of the tooth is a complex assembly in which the materials that make it up, enamel and dentin, have very different mechanical behaviors. Therefore, finding alternative replacement materials for dental crowns in the area of restorative care isa highly significant challenge, since materials such as ceramic and zirconia have very different stress load resistance values. The aim of this study is to assess which material, either ceramic or zirconia, optimizes the behavior of a restored tooth under various typical clinical conditions and the masticatory load. A finite element analysis (FEA) framework is developed for this purpose. The 3D model of the restored tooth is input into the FEA software (Ansys Workbench R23)and meshed into tetrahedral elements. The presence of masticatory forces is considered: in particular, vertical, 45° inclined, and horizontal resultant forces of 280 N are applied on five contact points of the occlusal surface. The numerical results show that the maximum stress developed in the restored tooth including a ceramic crown and subject to axial load is about 39.381 MPa, which is rather close to the 62.32 MPa stress computed for the natural tooth; stresses of about 18 MPa are localized at the roots of both crown materials. In the case of the zirconia crown, the stresses are much higher than those in the ceramic crown, except for the 45° load direction, while, for the horizontal loads, the stress peak in the zirconia crown is almost three times as large as its counterpart in the ceramic crown (i.e., 163.24 MPa vs. 56.114 MPa, respectively). Therefore, the zirconia crown exhibits higher stresses than enamel and ceramic that could increase in the case of parafunctions, such as bruxism. The clinician's choice between the two materials should be evaluated based on the patient's medical condition. [ABSTRACT FROM AUTHOR]

Consider the quadratic finite element method over a regular family of uniform tetrahedral partitions for the three-dimensional Poisson equation. Utilizing properties of the bubble function and estimates for discrete Green's function, we derive a pointwise superconvergent estimate for the finite element approximation in the sense of L ∞ -norm. Furthermore, the L 2 -norm superconvergent estimate is also provided. A numerical example is presented to demonstrate the accuracy of the theoretical results. [ABSTRACT FROM AUTHOR]

Geomagnetic depth sounding (GDS) is a geophysical electromagnetic (EM) method that studies the deep structure and composition of the Earth by using long-period EM signals from geomagnetic observatories and satellites. In this paper, a 3-D anisotropic GDS modelling algorithm is developed. The curl–curl equation is discretized using the edge-based finite-element method on unstructured tetrahedral grids. In order to solve the computationally demanding problem of EM modelling on a global scale, the complex linear system is first separated into the equivalent real linear systems and then the real system is iteratively solved by the flexible generalized minimum residual method with a block diagonal pre-conditioner. This will greatly reduce the condition number of the linear system and thus speed up the solution process. We verify the accuracy of the proposed algorithm by comparing our results with the existing methods. After that, we design a subduction zone model to simulate the EM responses under isotropic and anisotropic environments, respectively. The numerical results show the high efficiency of the proposed algorithm and the response differences between isotropic and anisotropic models. This research can provide theoretical and technical support for the high-accuracy and efficient inversion of GDS data for the geo-dynamic study. [ABSTRACT FROM AUTHOR]

Airborne electromagnetic (AEM) surveys using airborne mobile platforms enable rapid and efficient exploration of areas where groundwork is difficult. They have been widely used in fields such as shallow resource exploration and environmental engineering. Three-dimensional AEM inversion is the main technique used in fine structural interpretation. However, most current methods focus on separate component data inversions, which limit the kinds of structures that can be recovered in the inversion results. To address this issue, a method for the robust 3D joint inversion of multicomponent frequency-domain AEM data was developed in this study. First, a finite element method based on unstructured tetrahedral grids was used to solve the forward problem of frequency-domain AEM data for both isotropic and anisotropic media. During inversion, a limited-memory quasi-Newton (L-BFGS) method was used to reduce the memory requirements and enable the joint inversion of large-scale multicomponent AEM data. The effectiveness of our algorithm was demonstrated using synthetic models for both isotropic and anisotropic cases, with 5% Gaussian noise added to the modeling data to simulate the measured data for separate and joint inversions. The results of the synthetic models show that joint inversion has advantages over separate inversion in that it enables the recovery of finer underground structures and provides a novel approach for the fine interpretation of frequency-domain AEM data. [ABSTRACT FROM AUTHOR]

Topologically interlocked materials (TIMs) are an emerging class of architectured materials that each of block is supported by their neighboring blocks without any connector, which is inspired by microstructures observed in nature. Therefore, they showed alluring attributes such as resistance to impact, toughness, high flexibility even when using brittle materials, and high crack propagation resistance. In these structures, the presence of lateral compressive force, applied on peripheral blocks, ensures the integrity and identified properties. Lateral load, however, can adversely affect TIM plates and cause instability, and initiate buckling. In the present study, to focus on the buckling behavior of TIM plates due to the lateral force, a finite element model of TIM plates, made of tetrahedral blocks, was first validated using numerical results available in the literature and then analyzed. In this regard, an appropriate procedure has been presented to simulate the possible instability of these structures. Unlike monolithic plates, geometric parameters of TIM plates are dependent and this makes their parametric study more challenging. Therefore, some case studies have been accomplished to illustrate the effect of diverse parameters. The current study indicates that increasing the assembly plate length and decreasing its thickness causes a reduction of buckling load; nevertheless, it is necessary to mention that the thickness variation is a more impressive factor. [ABSTRACT FROM AUTHOR]

This paper presents a finite element method to search for equilibrium points around a heterogeneous small body, which degenerates from the full two-body problem in finite element form. The gravitational potential, acceleration, gravitational gradient matrix, and the linearized perturbation equation, which are key formulas for solving the equilibrium points and discriminating their stabilities, are interpolated by the tetrahedral model nodes of the small body. The finite element method could capture the complex internal structures of small bodies and provide a uniform and simple formula for various configurations. The method is applied to the Kuiper Belt Object (486958) Arrokoth, which is a contact binary asteroid. Three types of heterogeneous structures are hypothesized to investigate the evolutions of equilibrium points, namely density disparity of two sub-lobes, hardcore structure, and cavity structure. Under the condition of constant Arrokoth mass, the density disparity of the two sub-lobes greatly influences the local gravitational field. It thus has a significant influence on the positions of equilibrium points. The hardcore and cavity structures have less impact on the equilibrium points. These three simulation groups verified that the equilibrium points of a heterogeneous small body are quite different from those of a homogeneous small body. Such investigation of the equilibrium points may give an in-depth understanding of the dynamical environment around the heterogeneous small body, which is significant for future deep-space missions. [ABSTRACT FROM AUTHOR]

We apply here a class of substructuring method to improve the performance of linear tetrahedral element used in finite element analysis (FEA). The method is novel and relied on the construction of mesh inside a tetrahedron volume which behaves as an assembly of substructures. The corresponding stiffness matrix of the mesh is assembled using a static condensation procedure which is used further to obtain strain energy from a set of particular displacement vectors. This energy is the key to obtain a so-called energy ratio that will modify the stiffness matrix of a linear tetrahedral element. In the numerical tests, we show that the method can improve the performance of the tetrahedral element to approximate displacement and stress fields from the analytical solutions for cantilever and stress concentration problems, respectively. [ABSTRACT FROM AUTHOR]

Fracture produces new mesh fragments that introduce additional degrees of freedom in the system dynamics. Existing finite element method (FEM) based solutions suffer from increasing computational cost as the system matrix size increases. We solve this problem by presenting a graph‐based FEM model for fracture simulation that is remeshing‐free and easily scales to high‐resolution meshes. Our algorithm models fracture on the graph induced in a volumetric mesh with tetrahedral elements. We relabel the edges of the graph using a computed damage variable to initialize and propagate fracture. We prove that non‐linear, hyper‐elastic strain energy density is expressible entirely in terms of the edge lengths of the induced graph. This allows us to reformulate the system dynamics for the relabelled graph without changing the size of the system dynamics matrix and thus prevents the computational cost from blowing up. The fractured surface has to be reconstructed explicitly only for visualization purposes. We simulate standard laboratory experiments from structural mechanics and compare the results with corresponding real‐world experiments. We fracture objects made of a variety of brittle and ductile materials, and show that our technique offers stability and speed that is unmatched in current literature. [ABSTRACT FROM AUTHOR]

Edge‐based and face‐based smoothed finite element methods (ES‐FEM and FS‐FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element‐based formulation of ES‐FEM and FS‐FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element‐based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS‐FEM applications found in the literature. Shape functions for non‐simplex 3D elements are proposed in order to apply FS‐FEM to any standard finite element. [ABSTRACT FROM AUTHOR]

Unstructured tetrahedral grids have been applied in magnetotelluric (MT) forward modeling using the finite element (FE) method because of their adaptability to complex anomalies. However, high-quality results require an extreme refinement of the near-surface area, which leads to excessive meshes and an increased degree of freedom (DoF) of the governing equation of the finite element system. To reduce the computational cost, we have developed a hybrid mesh based on triangular prisms and tetrahedrons. The required elements in the near-surface area are reduced because the quality of the triangular prism is not limited by the element aspect ratio. The deep area is discretized by tetrahedral elements to ensure the flexibility of the unstructured grids. The superiority of this hybrid mesh has been tested on a layered model, the DTM1 model and terrain relief models. The results show that the modeling efficiency has been improved, especially for high-frequency data. The accuracy of the modeling using the hybrid mesh is significantly higher than that of the tetrahedral mesh with a similar DoF. Usage of the hybrid mesh can be easily adapted to complex geoelectric models with strong terrain fluctuations, which requires less computational cost than using conventional unstructured elements. [ABSTRACT FROM AUTHOR]

The semi‐airborne transient electromagnetic method is characterized by a large detection depth, high signal‐to‐noise ratio, fast acquisition rate, low cost, and ability to be used for exploration in scenarios with complex geological conditions. As a result, the semi‐airborne transient electromagnetic method has a great potential in the fields of mineral exploration, hydrological study and geohazard detection. However, most of the existing semi‐airborne transient electromagnetic data interpretation methods still rely on one‐dimensional forward modelling and inversion, which could lead to an incorrect geological interpretation. In this paper, we develop a three‐dimensional inversion for semi‐airborne transient electromagnetic data to recover a reliable subsurface conductivity distribution. The forward modelling is based on the effective vector finite element method with an unstructured tetrahedral mesh, which is capable of simulating complex geo‐electric structures and the topography. Through the numerical experiments of several three‐dimensional synthetic models, we study the influence of the number of excitation sources, flight mode and complex topography on the inversion results. The synthetic model studies reveal that: (1) by increasing the number of excitation sources, we can obtain a higher resolution conductivity image with less artefacts; (2) the detectability can be increased by flying along the terrain when the topography is complex; (3) the topography should be considered in the forward modelling and inversion to obtain a reasonable conductivity model using the semi‐airborne transient electromagnetic method; and (4) the three‐dimensional inversion still works when the inhomogeneity is present nearby the transmitter. [ABSTRACT FROM AUTHOR]

The interpretation of three-dimensional (3-D) magnetotelluric (MT) data is usually based on the isotropic assumption of the subsurface structures, and this assumption could lead to erroneous interpretation in the area with considerable electrical anisotropy. Although arbitrary anisotropy is much closer to the ground truth, it is generally more challenging to recover full anisotropy parameters from 3-D inversion. In this paper, we present a 3-D triaxial anisotropic inversion framework using the edge-based finite element method with a tetrahedral mesh. The 3-D inverse problem is solved by the Gauss-Newton (GN) method which shows fast convergence behavior. The computation cost of the data-space method depends on the size of data, which is usually smaller than the size of model; therefore, we transform the inversion algorithm from the model space to the data space for memory efficiency. We validate the effectiveness and applicability of the developed algorithm using several synthetic model studies. [ABSTRACT FROM AUTHOR]

In reality, the spatial distribution of geological anomalies is extremely complex. In the process of numerical simulation of transient electromagnetic method, limited to the modeling level, regular sphere, cylinder, cuboid and other simple models are often used to replace the complex actual geological model. As a result, there is a large deviation between the numerical simulation results and the real transient electromagnetic response of the actual geological model, which affects the reliability of the data interpretation. In order to solve the problem of transient electromagnetic numerical simulation of complex geoelectric model, we established complex geological anomalies model based on a variety of modeling platforms, and integrated the spatial combination information of nodes, lines and surfaces of the model with the spatial information of the observation system. Then gained the unstructured mesh discrete space of the integrated model according to the Delaunay tetrahedral subdivision principle. Finally, we realized the simulation of the transient electromagnetic responses of ultra-complex models by using vector finite element method. [ABSTRACT FROM AUTHOR]

In recent years, Hybrid Cellular Automata Method (HCAM) has been successfully applied to solve structural topology optimization problems. However, there was no report on HCAM research of three-dimensional composite structure composed of multiple materials and multiple bodies. Therefore, in this paper, three-dimensional non-cube cells of irregular size (such as tetrahedral cells with adaptive changes inside length) and Finite Element Method (FEM) are introduced to extend HCAM, which is better and more flexibly to fit complex geometric shapes. Furthermore, a better structure configuration of multi-material and multi-body structure is obtained. The typical example study showed that the proposed topology optimization method could effectively remove the redundant materials of multi-material and multi-body structure, and the optimized structure configuration could still meet the requirements of the original condition after geometric reconstructed. Thus it provided a reference for the intelligent design of other products. [ABSTRACT FROM AUTHOR]

Predicting thermal gradient of engineered structures with uncertain parameters is crucial for the safety. Many numerical computation methods have been developed in literatre; however, a practical approach is still pursued. To bridge this research gap, a data-driven approach is proposed to realize real-time prediction of thermal gradient in engineered structures with uncertain parameters. First, tetrahedral elements are used to build structures with complex geometry, and the face-based smoothed finite element method (FS-FEM) is employed to calculate the thermal response of the structures. By doing so, a good trade-off between the efficiency and accuracy for modelling the structures can be achieved. Then, the generated datasets are used for training a back propagation neural network (BPNN) model, and real-time prediction of thermal gradient in engineered structures can be performed without knowing the exact distribution functions of stochastic parameters. Lastly, two case studies were investigated to evaluate the performance of the proposed approach. The analysis results demonstrate that the proposed data-driven approach is able to offer accurate predictions of the thermal gradient for the engineered structures with uncertain parameters. [ABSTRACT FROM AUTHOR]

$Z$ -axis tipper electromagnetic (ZTEM) technique is an airborne electromagnetic method that detects anomalies in the deep earth that are induced by natural sources. Conventional ZTEM forward modeling is generally conducted using structured grids that have limited accuracy and cannot be used to invert complex underground structures and topography. However, unstructured grids can accurately model complex underground structures with fewer cells. Therefore, to effectively model and recover the complex underground structures, we developed a 3-D framework with unstructured tetrahedral grids for ZTEM forward modeling and inversions. The forward problem was formulated using the finite-element method with unstructured tetrahedral grids. To solve the inverse problem, we used a limited-memory quasi-Newton algorithm (L-BFGS) with a parallel direct solver for optimization in order to avoid the explicit calculation of the Hessian matrix and save the memory and computational time. To validate our forward and inversion algorithms, we conducted numerical experiments on three synthetic models and inverted a survey dataset acquired for a tunnel project in Tibet, China. The experimental results demonstrate the effectiveness of our unstructured finite-element and L-BFGS method for modeling and inverting ZTEM data. [ABSTRACT FROM AUTHOR]

The Material Point Method is a relative newcomer to the world of solid mechanics modelling. Its key advantage is the ability to model problems having large deformations while being relatively close to standard finite element methods, however its use for realistic engineering applications will happen only if the material point can be shown to be both efficient and accurate (compared to standard finite element methods), when modelling complex geometries with a range of material models. In this paper we present developments of the standard material point method aimed at realizing these goals. The key contribution provided here is the development of a material point method that avoids volumetric locking (arising from elastic or elasto‐plastic material behavior) while using low‐order tetrahedral finite elements for the background computational mesh, hence allowing unstructured background grids to be used for complex geometries. We also show that these developments can be effectively parallelized to improve computational efficiency. [ABSTRACT FROM AUTHOR]

In the discontinuous Galerkin time-domain (DGTD) method, tetrahedral meshes are typically used to discretize the computational domain. However, due to their different topological structures, when tetrahedrons or hexahedrons of the same discrete scale are used to divide the same computational domain, there are more tetrahedral mesh units, resulting in higher temporal and spatial complexity. In this article, a hybrid mesh DGTD algorithm based on virtual elements for tetrahedra and hexahedra is proposed to improve the computational efficiency compared with the traditional DGTD method. The fine-structured computational domain and the outer region are computed using tetrahedral and hexahedral meshes, respectively. During calculation, the numerical flux of each interface element requires data from the other subdomain. In this article, virtual elements are established at each subdomain interface to enable the exchange of field values for ease of processing. Edge assignment or field interpolation is applied to sample points to create corresponding virtual units to calculate fringe fields. Finally, the field value of each virtual element is assigned to the corresponding real element for the numerical flux calculation. Numerical results verify the correctness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, we propose a three-dimensional (3D) forward modeling algorithm of surface-to-borehole transient electromagnetic (SBTEM) fields based on an unstructured vector finite-element method to analyze the characteristics of SBTEM responses for complex geoelectrical models. To solve the double-curl diffusion equation for the electric field, we use an unstructured tetrahedral mesh to discretize the model domain and select the unconditionally stable backward Euler scheme to discretize the time derivative. In our numerical experiments, we use a grounded wire as a transmitting source. After validating the algorithm's effectiveness, we first analyze the diffusion characteristics and detectability of the electromagnetic field. After that, we focus our attention on the distribution and the cause of zero bands for Ex and dBy/dt components with the hope of guiding future field surveys. Finally, by simulating different models, we analyze the capability of the SBTEM method in detecting typical mineral veins so that we can provide a reference for mineral resource exploration in the deep earth. [ABSTRACT FROM AUTHOR]

Linear tetrahedral elements with four nodes (Te4) are currently the simplest and most widely used ones in the finite element (FE) developed for solving three-dimensional (3D) mechanics problems. However, the standard Te4 element cannot be used to simulate accurately the 3D problems with curved boundaries because of the flat surfaces. In this paper, we develop a set of new elements having curved surfaces to properly simulate the curved boundaries. At the same time, additional nodes are put on the curved boundaries to improve the accuracy of the approximation. These novel elements are defined as five-noded, six-noded, and seven-noded tetrahedron elements (Te5, Te6, and Te7) according to the number of the nodes in one element. Based on the Te4 FE mesh, a hybrid mesh can be conveniently built for 3D problems with curved boundaries, in which the standard Te4 elements are used for the interior elements, and Te5, Te6, and Te7 elements are used for the curved boundary elements. Compared with the standard FEM using Te4 elements, our hybrid mesh can significantly improve the accuracy of the solutions at the curved boundaries. Several solid mechanics problems are studied using the hybrid meshes to validate the effectiveness of the present new elements. [ABSTRACT FROM AUTHOR]

A new concept of smoothed finite element method (S-FEM) using 10-node tetrahedral (T10) elements, CS-FEM-T10, is proposed. CS-FEM-T10 is a kind of cell-based S-FEM (CS-FEM) and thus it smooths the strain only within each T10 element. Unlike the other types of S-FEMs [node-based S-FEM (NS-FEM), edge-based S-FEM (ES-FEM), and face-based S-FEM (FS-FEM)], CS-FEM can be implemented in general finite element (FE) codes as a piece of the element library. Therefore, CS-FEM-T10 is also compatible with general FE codes as a T10 element. A concrete example of CS-FEM-T10 named SelectiveCS-FEM-T10 is introduced for large deformation problems of nearly incompressible solids. SelectiveCS-FEM-T10 subdivides each T10 element into 12 four-node tetrahedral (T4) subelements with an additional dummy node at the element center. Two types of strain smoothing are conducted for the deviatoric and hydrostatic stress evaluations and the selective reduced integration (SRI) technique is utilized for the stress integration. As a result, SelectiveCS-FEM-T10 avoids the shear/volumetric locking, pressure checkerboarding, and reaction force oscillation in nearly incompressible solids. In addition, SelectiveCS-FEM-T10 has a relatively long-lasting property in large deformation problems. A few examples of large deformation analyses of a hyperelastic material confirm the good accuracy and robustness of SelectiveCS-FEM-T10. Moreover, an implementation of SelectiveCS-FEM-T10 in the FE code ABAQUS as a user-defined element (UEL) is conducted and its capability is discussed. [ABSTRACT FROM AUTHOR]

A state-of-the-art tetrahedral smoothed finite element method, F-barES-FEM-T4, is demonstrated on viscoelastic large deformation problems. The stress relaxation of viscoelastic materials brings near incompressibility when the long-term Poisson's ratio is close to 0.5. The conventional hybrid 4-node tetrahedral (T4) elements cannot avoid the shear locking and pressure checkerboarding issues, meanwhile F-barES-FEM-T4 can suppress these issues successfully by adopting the edge-based smoothed finite element method (ES-FEM) with the aid of the F-bar method and the cyclic smoothing procedure. A few examples of analyses verify that F-barES-FEM-T4 is locking-free and pressure oscillation-free in viscoelastic analyses as well as in nearly incompressible hyperelastic or elastoplastic analyses. [ABSTRACT FROM AUTHOR]

A stabilization method of the F-bar aided edge-based smoothed finite element method with four-node tetrahedral elements (F-barES-FEM-T4), which is named SymF-barES-FEM-T4, is proposed. The proposed formulation aims to remove the instability associated with energy divergence of F-barES-FEM-T4 in dynamic analysis. The stiffness matrix of F-barES-FEM-T4 is asymmetric due to the adoption of F-bar method, meanwhile that of SymF-barES-FEM-T4 is symmetrized so that the dynamics system of the formulation is stabilized. The differences between F-barES-FEM-T4 and SymF-barES-FEM-T4 in their formulations are only the definition of the B -matrix and the corresponding volume in the internal force calculation. Therefore, SymF-barES-FEM-T4 is applicable in dynamic explicit schemes as is the case with F-barES-FEM-T4. A few demonstrations of dynamic explicit analysis for nearly incompressible materials reveal that SymF-barES-FEM-T4 conserves the total energy and does not cause energy divergence in the free vibration problems. They also reveal that SymF-barES-FEM-T4 has a moderate capability in the suppression of pressure checkerboarding: worse than F-barES-FEM-T4 but better than Selective ES/NS-FEM-T4. [ABSTRACT FROM AUTHOR]

Featured Application: The amount of heat transferred by conduction is given by Fourier's law. For the study of these phenomena, the application of computational techniques that allow the design of machines and devices used in engineering becomes crucial. In this paper, a new constitutive matrix [ M τ ] for thermal conduction, for tetrahedral meshes, in a steady state thermal regime is developed through a new algebraic methodology, using the Cell Method as a computational method, which is included in the finite formulation. The constitutive matrix defines the behavior of solids when they are under a thermal potential. The results are compared with those obtained for the same problem by means of the constitutive matrix [ M λ ] developed previously, taking in both cases with a 2D axisymmetric model as reference, calculated with the finite element method. The errors obtained with the new matrix [ M τ ] are of the order of 0.0025%, much lower than those obtained with the matrix [ M λ ] . [ABSTRACT FROM AUTHOR]

• A new enrichment of the standard simplicial linear finite element. • A new nonconforming finite element. • Many examples for admissible enrichment functions. • Explicit expression of the basis function. Low-order elements are widely used and preferred for finite element analysis, specifically the three-node triangular and four-node tetrahedral elements, both based on linear polynomials in barycentric coordinates. They are known, however, to under-perform when nearly incompressible materials are involved. The problem may be circumvented by the use of higher degree polynomial elements, but their application become both more complex an computationally expensive. For this reason, non-polynomial enriched finite element methods have been proposed for solving engineering problems. In line with previous researches, the main contribution of this paper is to present a general strategy for enriching the standard simplicial linear finite element by non-polynomial functions. A key role is played by a characterization result, given in terms of the non-vanishing of a certain determinant, which provides necessary and sufficient conditions, on the enrichment functions and functionals, that guarantee the existence of families of such enriched elements. We show that the enriched basis functions admit a closed form representation in terms of enrichment functions and functionals. Finally, we provide concrete examples of admissible enrichment functions and perform some numerical tests. [ABSTRACT FROM AUTHOR]

In order to solve the problem of multi-domain adjacency in the modeling of complex orebodies, we implemented an adaptive meshing method for complex orebodies based on the Delaunay refinement method, which could generate multi-domain surface models and volume models for the finite element simulation in the later stage. The method relies on the constraint Delaunay triangulation to approximate the domain and the surface, and the Delaunay refinement to ensure the approximate accuracy of the domain and the grid quality of the cell. On the basis of constraint Delaunay triangulation, the multi-domain polyhedron method of prediction was constructed by separating the intermediate domain or fitting the intermediate domain by distance field. The method of adaptive meshing of multi-domain was implemented. Experimental tests of Beiminghe Iron Mine show that the method can generate a seamless and continuous multi-domain model with high-quality tetrahedral and triangular meshes by mesh optimization. And it can avoid many degraded and singular triangles by contour-matching. It is significant to apply this method in the reverse engineering, finite element analysis, scientific computing visualization and other fields. [ABSTRACT FROM AUTHOR]

In this note we present a generalization of the maximum angle condition, proposed by J.L. Synge in 1957 and M. Křížek in 1992 for triangular and tetrahedral elements, respectively, for the case of higher-dimensional simplicial finite elements. Its relations to the other angle-type conditions commonly used in interpolation theory and in finite element analysis are discussed. [ABSTRACT FROM AUTHOR]

Successful interpretation of DC resistivity data depends on the availability of a proper forward modeling scheme. In this study, a threedimensional DC resistivity forward modeling scheme was developed using the finite element method. The finite element equations were obtained using a weakened form of the weighted-residual method called the Galerkin method. Discretization of the modeling domain was carried out by dividing it into smaller three-dimensional blocks and subdividing each block into five tetrahedral elements. A linear interpolation function was employed and elemental linear equations were set up, followed by formation of global matrix systems of equation and incorporation of proper boundary conditions. The conjugate gradient method was applied to solve the global system of equations, which in this study was proven to be more efficient than a direct solver, contributing to a 67% time reduction. Using a Wenner array configuration, comparison with theoretical calculation of the electric potential for a homogeneous model yielded a relative error of 3.66%. To confirm the applicability of this forward modeling scheme, apparent resistivity profiles for several basic three-dimensional subsurface resistivity models were compared with the analytical profiles, yielding an acceptable level of fitting. [ABSTRACT FROM AUTHOR]

• Parametric test-rig devoted to crossing and veering phenomena. • Test-rig analysed numerically and experimentally. • For numerical simulations, different models are compared to show mode interactions. • Experimental validation is provided with 10 experimental modal identifications. • Very similar behaviours between experiments and simulations. • Good correlation through modal indexes are discussed. The present paper focuses on a deep investigation of crossing and veering phenomena in a specific mechanical structure. A deep analysis of the state of the art has been developed to highlight the key features of crossing and veering of frequencies during parametric changes of a structure. The analysed structure is an improvement of an existing test-rig, developed to have a system parameter that can be piloted for getting crossing and veering, to purposely couple the bending modes of the orthogonal planes. Both numerical simulations, from a simple 1-dimensional elements model to a full second-order tetrahedral model, and experimental tests were used to evaluate the presence of crossing and veering and to investigate and correlate the corresponding indexes. A good correlation was evidenced and the mode-shapes variation in the crossing and veering zones was presented and discussed by means of a derived index of the modal assurance criterion for parametric analyses. [ABSTRACT FROM AUTHOR]

A new type of smoothed finite element method (S-FEM), F-barES-FEM-T4, is demonstrated in static large deformation elastoplastic cases. F-barES-FEM-T4 combines the edge-based S-FEM (ES-FEM) and the node-based S-FEM (NS-FEM) for 4-node tetrahedral (T4) elements with the aid of the F-bar method in order to resolve the major issues of Selective ES/NS-FEM-T4. As well as most of the other S-FEMs, F-barES-FEM-T4 inherits pure displacement-based formulation and thus has no increase in DOF.Moreover, the cyclic smoothing procedure introduced in F-barES-FEM-T4 is effective to adjust the smoothing level so that pressure checkerboarding (oscillation) is suppressed reasonably. Some examples of static large deformation analyses for elastoplastic materials proof the excellent performance of F-barES-FEM-T4 in contrast to the conventional hybrid T4 element formulation. [ABSTRACT FROM AUTHOR]

In this paper, a stable node-based smoothed finite element method (SNS-FEM) is presented for analyzing metal forming problems using linear triangular or tetrahedral elements. In present method, the numerical integration domains are approximately circular or spherical regions of the node-based smoothing domains generated by the node-based smoothed finite element method (NS-FEM). Four or six supplementary integration points, which are symmetrically located at the crossover points of the region and the coordinate axis, are employed for each node to form the stabilization items associated with the variance of smoothed shape function gradient. Through this operation without the introducing of any uncertain parameter, the SNS-FEM not only significantly cures the temporal instability of NS-FEM but also performs better in effectiveness and efficiency than FEM, which is well validated by several numerical examples containing benchmark cases. Additionally, a simple but effective contact algorithm including contact searching and contact force computation is presented. [ABSTRACT FROM AUTHOR]

We present new and efficient quadrature rules for computing the stiffness matrices of mass-lumped tetrahedral elements for wave propagation modeling. These quadrature rules allow for a more efficient implementation of the mass-lumped finite element method and can handle materials that are heterogeneous within the element without loss of the convergence rate. The quadrature rules are designed for the specific function spaces of recently developed mass-lumped tetrahedra, which consist of standard polynomial function spaces enriched with higher-degree bubble functions. For the degree-2 mass-lumped tetrahedron, the most efficient quadrature rule seems to be an existing 14- point quadrature rule, but for tetrahedra of degrees 3 and 4, we construct new quadrature rules that require fewer integration points than those currently available in the literature. Several numerical examples confirm that this approach is more efficient than computing the stiffness matrix exactly and that an optimal order of convergence is maintained, even when material properties vary within the element. [ABSTRACT FROM AUTHOR]

Many tasks in geometry processing are modelled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh. Unfortunately, tetrahedral meshing remains an open challenge and existing methods either struggle to conform to complex boundary surfaces or require manual intervention to prevent failure. Rather than create a single volumetric mesh for the entire shape, we advocate for solid geometry processing on deconstructed domains, where a large and complex shape is composed of overlapping solid subdomains. As each smaller and simpler part is now easier to tetrahedralize, the question becomes how to account for overlaps during problem modelling and how to couple solutions on each subdomain together algebraically. We explore how and why previous coupling methods fail, and propose a method that couples solid domains only along their boundary surfaces. We demonstrate the superiority of this method through empirical convergence tests and qualitative applications to solid geometry processing on a variety of popular second‐order and fourth‐order partial differential equations. [ABSTRACT FROM AUTHOR]

Hyperthermia treatments require precise control of thermal energy to form the coagulation zones which sufficiently cover the tumor without affecting surrounding healthy tissues. This has led modeling of soft tissue thermal damage to become important in hyperthermia treatments to completely eradicate tumors without inducing tissue damage to surrounding healthy tissues. This paper presents a methodology based on GPU acceleration for modeling and analysis of bio-heat conduction and associated thermal-induced tissue damage for prediction of soft tissue damage in thermal ablation, which is a typical hyperthermia therapy. The proposed methodology combines the Arrhenius Burn integration with Pennes' bio-heat transfer for prediction of temperature field and thermal damage in soft tissues. The problem domain is spatially discretized on 3-D linear tetrahedral meshes by the Galerkin finite element method and temporally discretized by the explicit forward finite difference method. To address the expensive computation load involved in the finite element method, GPU acceleration is implemented using the High-Level Shader Language and achieved via a sequential execution of compute shaders in the GPU rendering pipeline. Simulations on a cube-shape specimen and comparison analysis with standalone CPU execution were conducted, demonstrating the proposed GPU-accelerated finite element method can effectively predict the temperature distribution and associated thermal damage in real time. Results show that the peak temperature is achieved at the heat source point and the variation of temperature is mainly dominated in its direct neighbourhood. It is also found that by the continuous application of point-source heat energy, the tissue at the heat source point is quickly necrotized in a matter of seconds, while the entire neighbouring tissues are fully necrotized in several minutes. Further, the proposed GPU acceleration significantly improves the computational performance for soft tissue thermal damage prediction, leading to a maximum reduction of 55.3 times in computation time comparing to standalone CPU execution. [ABSTRACT FROM AUTHOR]

This paper presents a simple and effective strain smoothing method (the strain-smoothed element method) for 3-node triangular and 4-node tetrahedral solid finite elements. While piecewise constant strain fields are constructed through smoothing domains in previous strain smoothing methods, in the proposed method, linear strain fields are constructed within finite elements using constant strains of neighboring finite elements. When the new strain smoothing method is adopted, the triangular and tetrahedral solid finite elements pass all the basic tests; patch, isotropy and zero energy mode tests, and show improved predictive capability. The formulation of the proposed method is presented in detail. Through various numerical examples, we demonstrate the accuracy improvement achieved. [ABSTRACT FROM AUTHOR]

This paper presents a second order edge-based finite element method based on a new type of second order edge element for numerical modeling of 3D controlled source electromagnetic data in an anisotropic conductive medium. We adopt the anomalous potential field formulation to avoid the effect of source’s singularity. The computational domain was subdivided into unstructured tetrahedral elements. The sparse linear system was solved using the Induced dimensional reduction (IDR(s)) method with an incomplete LU preconditioner. We have applied the developed algorithm to compute a typical MCSEM response over several 3D models, we compare the numerical results from our method and FEM solution based on conventional first and second order element. The results of comparison shown that our algorithm can significantly reduce the computation cost without loss to much accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a goal-oriented adaptive edge-based finite element (FE) algorithm for modelling marine controlled-source electromagnetic (CSEM) responses in three-dimensional (3-D) dipping anisotropic conductive media. We adopt the secondary field formulation for quasi-static Maxwell's equations to avoid the source singularity. The algorithm is implemented on unstructured tetrahedral grids, which allow for the simulation of complex model geometries, including tilted electrical interfaces and bathymetry. We validate the adaptive finite element code against a one-dimensional (1-D) layered model with vertical anisotropy. Further, we compare the 3-D FE numerical solutions with those obtained by a 2-D FE code for a two-dimensional dipping anisotropic model. The modelling results from the new 3-D FE algorithm are in good agreement with both the analytical solutions derived from the 1-D code and the numerical results from the anisotropic 2-D FE algorithm. We then use the algorithm to simulate the marine CSEM responses over different anisotropic 3-D models, including an anisotropic reservoir, anisotropic surrounding sediments, and an anisotropic overburden, and performed a detailed analysis of the effect of VTI, HTI, and TTI anisotropy on 3-D marine CSEM response. The modelling results illustrate that marine CSEM responses are considerably influenced by various anisotropic parameters, but to different extents. The research on different types of anisotropy within different media can help us avoid the misinterpretation of marine CSEM data when processing and interpreting of the measured geophysical electromagnetic data. • 3D marine CSEM modelling based on the Goal-oriented adaptive FE method. • Effects of three types of anisotropy (TIV, TIH & TTI) on marine CSEM responses. • Visualize EM energy in the anisotropic layer through time-averaged Poynting vectors. [ABSTRACT FROM AUTHOR]

We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies. [ABSTRACT FROM AUTHOR]

We solve the 3D controlled-source electromagnetic (CSEM) problem using the edge-based finite element method. The modeling domain is discretized using unstructured tetrahedral mesh. We adopt the total field formulation for the quasi-static variant of Maxwell's equation and the computation cost to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast Hankel transform. By using this new type of boundary condition, the computation cost can be reduced significantly and the modeling accuracy can be improved. We consider that the conductivity can be anisotropic. We solve the finite element system of equations using a parallelized multifrontal solver which works efficiently for multiple source and large scale electromagnetic modeling. [ABSTRACT FROM AUTHOR]

• Implementation of a powerful and memory-efficient inversion method for the 3-D CSEM. • Comparisons of iterative solvers for the linear system of the inversion. • Inversion of realistic models using unstructured tetrahedral grids. In this study, a minimum-structure inversion procedure for controlled-source electromagnetic data that parameterizes the Earth model in terms of an unstructured tetrahedral grid is presented. To minimize the objective function defining the inversion problem Gauss–Newton iterations are used. Iterative solvers are employed for the solution of the system of equations at each Gauss–Newton step. These solvers do not need the matrix to be explicitly formed to solve the linear system, and hence, these kinds of solvers ensure memory efficiency of the developed algorithm. For the forward-modelling problem, a potentials formulation, in which the electric field is expressed in terms of vector and scalar potentials and the relevant partial differential equations are the Helmholtz and conservation of charge equations, is discretized by the finite-element method. This decomposition results in a well conditioned matrix equation compared to the E-field equation and gives a more natural description of electromagnetic phenomena. The linear system of equations for the forward-modelling problem is solved by a direct solver. The advantage of this type of solver is that the factorization that is generated, which takes up the bulk of the solution time for this system, can be reused when solving for multiple right-hand sides. This is important for the efficient calculation of the matrix–vector products in the above-mentioned Gauss–Newton systems. Two synthetic examples are given to illustrate the capabilities and efficiency of the presented procedure. In the first example, inversion of a dataset generated over a geometric shaped conductive body for a flat Earth's surface is presented. In the second example, a realistic scenario is given. This example shows that topography and a realistic ore body can be naturally and effectively handled by unstructured grids. [ABSTRACT FROM AUTHOR]

In this paper, the smooth finite element methods (S-FEMs) for accurate and reliable dynamic analysis are proposed to improve the wear resistance of road header picks. Experimentally measured forces and smoothing operations are used to establish a numerical model of conical picks subjected to dynamic forces that changes with time during the rock-cutting process. The S-FEMs are extended for dynamics problems of rock picks, so that tetrahedral elements can be used for model generation. The proposed dynamic analysis procedure has been found with several features, including upper bounds for dynamic problems of the Node-based S-FEM, "ultra-accuracy" in both displacement and energy norms in dynamics solutions of the Edge-based S-FEM. These features are beneficial to practical engineering problems whose exact solutions are difficult to obtain, and hence offer an efficient numerical tool for investigating the effects of actual parameters on the performance of picks subjected to various dynamic forces. • S-FEM and explicit integral algorithms for pick dynamic analysis. • ES-FEM is efficient and accurate for pick dynamic analysis. • Accurate stress field contributes to the analysis of pick wear mechanism. • NS-FEM and FEM are used to obtain the upper and lower bounds of the stress energy solution. [ABSTRACT FROM AUTHOR]

Hexahedral-dominant modeling approaches strike a balance of meshing ease and accuracy/efficiency by exploiting wedge (and/or pyramid) elements to transition from hexahedral elements to volumes filled by other types. Unfortunately, first-order wedges are frequently very poor performers and are the only ones typically contained in explicit solid dynamic programs. The historic preference of first-order elements with explicit methods has frequently been for simplicity and cost, but has also been from the lack of both a satisfactory consistent nodal loading distribution and an acceptable mass lumping technique for serendipity elements. Row summation lumping, for example, produces negative and zero vertex node masses for the popular fifteen and eighteen node wedges, respectively, and zero vertex nodal loads from a uniform traction on the triangular faces. The paper first presents twenty-one node wedge element formulations that produce all positive nodal loads from uniform tractions and row summation mass lumping for this element is shown to produce all positive nodal masses. In addition, they are compatible with other second-order elements applicable to lumped mass explicit methods. Performance is assessed in standard benchmark problems and practical applications using various elastic and elastic-plastic material models and involving very large strains/deformations, severe distortions, and contact-impact. These wedge elements are evaluated on their own as well as part of hexahedral-dominant meshes that use wedges for fill regions and transition from hexahedral to tetrahedral elements. In all cases, these elements performed satisfactorily and thus demonstrate their viability and benefits for practical applications, especially for fill and transition regions of low interest. [ABSTRACT FROM AUTHOR]

This paper introduces a three-dimensional finite element (FE) formulation to accurately model the linear elastic deformation of fractured media under compressive loading. The presented method applies the classic Augmented Lagrangian(AL)-Uzawa method, to evaluate the growth of multiple interacting and intersecting discrete fractures. The volume and surfaces are discretized by unstructured quadratic triangle-tetrahedral meshes; quarter-point triangles and tetrahedra are placed around fracture tips. Frictional contact between crack faces for high contact precisions is modeled using isoparametric integration point-to-integration point contact discretization, and a gap-based augmentation procedure. Contact forces are updated by interpolating tractions over elements that are adjacent to fracture tips, and have boundaries that are excluded from the contact region. Stress intensity factors are computed numerically using the methods of displacement correlation and disk-shaped domain integral. A novel square-root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. Tractions and compressive stress intensity factors are validated against analytical solutions. Numerical examples of cubes containing one, two, twenty four and seventy interacting and intersecting fractures are presented. [ABSTRACT FROM AUTHOR]

A construction for high order continuous finite elements on partitions consisting of tetrahedra, hexahedra and pyramids based on polynomial Bernstein-Bézier shape functions is presented along with algorithms that allow the computation of the system matrices in optimal complexity O ( 1 ) per entry. [ABSTRACT FROM AUTHOR]

Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio ( www.febio.org ) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. [ABSTRACT FROM AUTHOR]

The paper presented results of the research on process of production of highly important element of passenger car. The main object of the research was influence of production process and material factors on fatigue strength of tubular stabilizer bar. The scope of the research included the stabilizer bar hot bent at the bending table, hardened in oil and tempered. The bending radii I, II and III were metalographically tested. The stabilizer bar was also subjected to fatigue tests. For analysis purpose the finite element method (FEM) calculation have been conducted. The analysis of relationship of outer diameter to wall thickness is very important. The analysed bar has broken early. The paper presents the reasons for premature failure of the tubular stabilizer bar. [ABSTRACT FROM AUTHOR]

Multiscale models are needed in simulations of mechanical and thermal properties that consider the microstructural heterogeneity of materials, in which a coupling is essential between the numerical models that deal with the different scales. In the class of cellular automata-finite element (CA-FE) or CAFE models, the use of a regular FE mesh restricts the model versatility due to the limited variety of engineering problems that can be simulated with such meshes. A novel methodology is proposed to create the homogeneous cells of the CA model from a mesh that is formed by irregular tetrahedrons. The result is more versatile and capable of modelling complex geometries, improving its applicability. The problem is solved through a subdivision algorithm that creates homogeneous tetrahedral cells, using a methodology to insert microstructures that can be described by particles, pores or fibres. Its use is demonstrated in a multi-scale Finite Element Microstructure MEshfree (FEMME) framework to calculate the elastic strains caused by microstructural features (pores); the method is shown to have a significantly lower computational cost than finite element simulations of equivalent levels of discretization. [ABSTRACT FROM AUTHOR]

This study formulates a simple tetrahedral finite element equipped with rotational degrees of freedom that can be used effectively to solve problems for both Cosserat and Cauchy continua. The formulation makes no assumption regarding the symmetry of the stress tensor, and such symmetry is achieved at convergence for the Cauchy problems. The numerical implementation of the new element is straightforward, and numerical tests demonstrate second-order accuracy in the case of both Cosserat and Cauchy elasticity. [ABSTRACT FROM AUTHOR]