Influence of Framework Material and Posterior Implant Angulation in Full-Arch All-on-4 Implant-Supported Prosthesis Stress Concentration

This study evaluated the influence of distal implants angulation and framework material in the stress concentration of an All-on-4 full-arch prosthesis. A full-arch implant-supported prosthesis 3D model was created with different distal implant angulations and cantilever arms (30° with 10-millimeter cantilever; 45° with 10-millimeter cantilever and 45° with 6-millimeter cantilever) and framework materials (Cobalt–chrome [CoCr alloy], Yttria-stabilized tetragonal zirconia polycrystal [Y-TZP] and polyetheretherketone [PEEK]). Each solid was imported to computer-aided engineering software, and tetrahedral elements formed the mesh. Material properties were assigned to each solid with isotropic and homogeneous behavior. The contacts were considered bonded. A vertical load of 200 N was applied in the distal region of the cantilever arm, and stress was evaluated in Von Misses (σVM) for prosthesis components and the Maximum (σMAX) and Minimum (σMIN) Principal Stresses for the bone. Distal implants angled in 45° with a 10-millimeter cantilever arm showed the highest stress concentration for all structures with higher stress magnitudes when the PEEK framework was considered. However, distal implants angled in 45° with a 6-millimeter cantilever arm showed promising mechanical responses with the lowest stress peaks. For the All-on-4 concept, a 45° distal implants angulation is only beneficial if it is possible to reduce the cantilever’s length; otherwise, the use of 30° should be considered. Comparing with PEEK, the YTZP and CoCr concentrated stress in the framework structure, reducing the stress in the prosthetic screw.

A machine learning approach to predict the stress results of quadratic tetrahedral elements

Industries are always looking for an effective and efficient way to reduce the computation time of simulation because of the huge expenditure involved. From basics of Finite Element Method (FEM), it is known that, linear order finite elements consume less computation time and are less accurate compared to higher order finite elements say quadratic elements. An approach to get the benefit of less computation cost of linear elements and the good accuracy of quadratic elements can be of a good thought. The methodology to get the accurate results of quadratic elements with the advantage of less simulation run time of linear elements is presented here. Machine Learning (ML) algorithms are found to be effective in making predictions based on some known data set. The present paper discusses a methodology to implement ML model to predict the results equivalent to that of quadratic elements based on the solutions obtained from the linear elements. Here, a ML model is developed using python code, the stress results from Finite Element (FE) model of linear tetrahedral elements is given as the input to it to predict the stress results of quadratic tetrahedral elements. Abaqus is used as the FEM tool to develop the FE models. A python script is used to extract the stresses and the corresponding node numbers. The results showed that the developed ML model is successful in prediction of the accurate stress results for the set of test data. The scatter plots showed that the Z-score method was effective in removing the singularities. The proposed methodology is effective to reduce the computation time for simulation.

Stress-strain distribution in intact L4-L5 vertebrae under the influence of physiological movements: A finite element (FE) investigation

This study is aimed at finding the stress and strain distribution in functional spinal unit of L4-L5 occurring due to physiological body movements under five loading conditions, namely compression, flexion, extension, lateral bending and torsion. To this purpose, 3D finite element (FE) model has been generated using 4-noded unstructured tetrahedral elements considered both for bones and intervertebral disc, and 1D tension-only spring elements for ligaments. The analyses were performed for a compression load of 500 N and for other load cases, a moment of 10 N-m along with a preload of 500 N was applied. The model was validated against in-vitro experimental data obtained from literature and FE analysis data for a range of motion (RoM) corresponding to various loading conditions. The highest stress was predicted in the case of torsion though the angular deformation was highest in case of flexion.

Elastic solution of a polyhedral particle with a polynomial eigenstrain and particle discretization

The paper extends the recent work (JAM, 88, 061002, 2021) of the Eshelby's tensors for polynomial eigenstrains from a two dimensional (2D) to three dimensional (3D) domain, which provides the solution to the elastic field with continuously distributed eigenstrain on a polyhedral inclusion approximated by the Taylor series of polynomials. Similarly, the polynomial eigenstrain is expanded at the centroid of the polyhedral inclusion with uniform, linear and quadratic order terms, which provides tailorable accuracy of the elastic solutions of polyhedral inhomogeneity by using Eshelby's equivalent inclusion method. However, for both 2D and 3D cases, the stress distribution in the inhomogeneity exhibits a certain discrepancy from the finite element results at the neighborhood of the vertices due to the singularity of Eshelby's tensors, which makes it inaccurate to use the Taylor series of polynomials at the centroid to catch the eigenstrain at the vertices. This paper formulates the domain discretization with tetrahedral elements to accurately solve for eigenstrain distribution and predict the stress field. With the eigenstrain determined at each node, the elastic field can be predicted with the closed-form domain integral of Green's function. The parametric analysis shows the performance difference between the polynomial eigenstrain by the Taylor expansion at the centroid and the 𝐶0 continuous eigenstrain by particle discretization. Because the stress singularity is evaluated by the analytical form of the Eshelby's tensor, the elastic analysis is robust, stable and efficient.

3D inversion of time domain electromagnetic data using finite elements and a triple mesh formulation

During several decades, much research has been done to develop 3D electromagnetic inversion algorithms. Due to the computational complexity and the memory requirements for 3D time domain electromagnetic (TEM) inversion algorithms, many real world surveys are inverted with in 1D. To speed up calculations and manage memory for 3D inversions of TEM data, we propose an approach using three uncoupled meshes: an inversion mesh, a forward-model mesh, and a mesh for Jacobian calculations. The inversion mesh is a coarse regular and structured mesh, such that constraints are easily enforced between model parameters. Forward responses are calculated on a dense unstructured mesh to obtain accurate electromagnetic fields, while the Jacobian is calculated on a coarse unstructured mesh. We show that using a coarse mesh for the Jacobian is sufficient for the inversion to converge and, equally important, it provides a significant speed boost in the overall inversion process, compared to calculating it on the forward modeling mesh. The unstructured meshes are made of tetrahedral elements and the electromagnetic fields are calculated using the finite-element method. The inversion optimization uses a standard Gauss-Newton formulation. For further speed up and memory optimizing of the inversion we use domain decomposition for calculating the responses for each transmitter separately and parallelize the problem over domains using OpenMP. Compared to a 1D solution, the accuracy for the Jacobian is 1 – 5% for the dense mesh and 2 – 7 % for the coarse mesh but the calculation time is about 5.0× faster for the coarse mesh. We also demonstrate the algorithm on a small ground-based TEM dataset acquired in an area where a 3D earth distorts the electromagnetic fields to such a degree that a 1D inversion is not feasible.

A New Nodal-Integration-Based Finite Element Method for the Numerical Simulation of Welding Processes

This paper aims at introducing a new nodal-integration-based finite element method for the numerical calculation of residual stresses induced by welding processes. The main advantage of the proposed method is to be based on first-order tetrahedral meshes, thus greatly facilitating the meshing of complex geometries using currently available meshing tools. In addition, the formulation of the problem avoids any locking phenomena arising from the plastic incompressibility associated with von Mises plasticity and currently encountered with standard 4-node tetrahedral elements. The numerical results generated by the nodal approach are compared to those obtained with more classical simulations using finite elements based on mixed displacement–pressure formulations: 8-node Q1P0 hexahedra (linear displacement, constant pressure) and 4-node P1P1 tetrahedra (linear displacement, linear pressure). The comparisons evidence the efficiency of the nodal approach for the simulation of complex thermal–elastic–plastic problems.

Performance Evaluation of ANCF Tetrahedral Elements in the Analysis of Liquid Sloshing

The performance of the absolute nodal coordinate formulation (ANCF) tetrahedral element in the analysis of liquid sloshing is evaluated in this paper using a total Lagrangian nonincremental solution procedure. In this verification study, the results obtained using the ANCF tetrahedral element are compared with the results of the ANCF solid element which has been previously subjected to numerical verification and experimental validation. The tetrahedral-element model, which allows for arbitrarily large displacements including rotations, can be systematically integrated with computational multibody system (MBS) algorithms that allow for developing complex sloshing/vehicle models. The new fluid formulation allows for systematically increasing the degree of continuity in order to obtain higher degree of smoothness at the element interface, eliminate dependent variables, and reduce the model dimensionality. The effect of the fluid/container interaction is examined using a penalty contact approach. Simple benchmark problems and complex railroad vehicle sloshing scenarios are used to examine the performance of the ANCF tetrahedral element in solving liquid sloshing problems. The simulation results show that, unlike the ANCF solid element, the ANCF tetrahedral element model exhibits nonsmoothness of the free surface. This difference is attributed to the gradient discontinuity at the tetrahedral-element interface, use of different meshing rules for the solid- and tetrahedral-elements, and the interaction between elements. It is shown that applying curvature-continuity conditions leads, in general, to higher degree of smoothness. Nonetheless, a higher degree of continuity does not improve the solution accuracy when using the ANCF tetrahedral elements.