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Head acceleration measurement sensors are now widely deployed in the field to monitor head kinematic exposure in contact sports. The wealth of impact kinematics data provides valuable, yet challenging, opportunities to study the biomechanical basis of mild traumatic brain injury (mTBI) and subconcussive kinematic exposure. Head impact kinematics are translated into brain mechanical responses through physics-based computational simulations using validated brain models to study the mechanisms of injury. First, this article reviews representative legacy and contemporary brain biomechanical models primarily used for blunt impact simulation. Then, it summarizes perspectives regarding the development and validation of these models, and discusses how simulation results can be interpreted to facilitate injury risk assessment and head acceleration exposure monitoring in the context of contact sports. Recommendations and consensus statements are presented on the use of validated brain models in conjunction with kinematic sensor data to understand the biomechanics of mTBI and subconcussion. Mainly, there is general consensus that validated brain models have strong potential to improve injury prediction and interpretation of subconcussive kinematic exposure over global head kinematics alone. Nevertheless, a major roadblock to this capability is the lack of sufficient data encompassing different sports, sex, age and other factors. The authors recommend further integration of sensor data and simulations with modern data science techniques to generate large datasets of exposures and predicted brain responses along with associated clinical findings. These efforts are anticipated to help better understand the biomechanical basis of mTBI and improve the effectiveness in monitoring kinematic exposure in contact sports for risk and injury mitigation purposes.

Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our formulation is novel in that it employs the normal fluxes as the mortar variable within the mixed finite element framework, resulting in a formulation that couples the flow in the fractures with the surrounding domain with a strong notion of mass conservation. The proposed discretization handles complex, nonmatching grids and allows for fracture intersections and termination in a natural way, as well as spatially varying apertures. The discretization is applicable to both two and three spatial dimensions. A priori analysis shows the method to be optimally convergent with respect to the chosen mixed finite element spaces, which is supported by numerical examples.

A new family of hybrid/mixed finite elements optimized for numerical stability is introduced. It comprises a linear hexahedral and quadratic hexahedral and tetrahedral elements. The element formulation is derived from a consistent linearization of a well-known three-field functional and related to Simo–Taylor–Pister (STP) elements. For the quadratic hexahedral and tetrahedral elements we derive (static reduced) discontinuous hybrid elements, as well as continuous mixed finite elements with additional primary unknowns for the hydrostatic pressure and the dilation, whereas the linear hexahedral element is of the discontinuous type. The elements can readily be used in combination with any isotropic, invariant-based hyperelastic material model and can be considered as being locking-free. In a representative numerical benchmark test the elements numerical stability is assessed and compared to STP-elements and the family of discontinuous hybrid elements implemented in the commercial finite element code Abaqus/Standard. The new elements show a significant advantage concerning the numerical robustness.

We present equilibrated flux a posteriori error estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two-dimensional Poisson problem. Relying on the equilibration by the mixed finite element solution of patchwise Neumann problems, the estimates are guaranteed, locally computable, locally efficient, and robust with respect to polynomial degree. Maximal local overestimation is guaranteed as well. Numerical experiments suggest asymptotic exactness for the incomplete interior penalty discontinuous Galerkin scheme.

Steels are preferred in the building of commercial ships because they can be easily welded and supplied. Although it varies according to the parts of the ships, it is known that high-strength steels are preferred especially in bulb and side coatings where relatively high strength is desired during the building process. In the process of welding these steels, mostly gas and submerged arc welding are used. On the other hand, studies continue for the use of the new generation friction stir welding (FSW), which is known to have many advantages over existing welding methods, in the shipbuilding process. The formability of the welded plates in the construction process of the ships is extremely important to give the necessary form to the ship. On the other hand, post-weld formability properties are of great importance for determining the strength and elongation values in wave crests and wave troughs to which ships are exposed during navigation. In this context, in this study, relatively high-strength AH32 shipbuilding steel was joined with FSW and the formability behavior of the welded region was investigated comparatively by experimental, finite element analysis and artificial neural network methods. As a result of the studies, it was determined that the strength values in the weld zone of the steel joined by FSW increased compared to the pre-weld and the formability behavior did not deteriorate. In addition, it was determined that the results of finite element analysis and artificial neural networks were extremely consistent with the experimental data, and it was determined that the models created in the study would give close results to the real results even without experimental studies.

A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons/polyhedra. The WG-MFEM is capable of providing very accurate numerical approximations for both the primary and flux variables. Allowing the use of discontinuous approximating functions on arbitrary shape of polygons/polyhedra makes the method highly flexible in practical computation. Optimal order error estimates in both discrete H1H^1 and L2L^2 norms are established for the corresponding weak Galerkin mixed finite element solutions.

In the finite element method (FEM), a necessary condition for a four-node isoparametric element is that no interior angle is greater than 180° and the positivity of Jacobian determinant should be ensured in numerical implementation. In this paper, we incorporate cell-wise strain smoothing operations into conventional finite elements and propose the smoothed finite element method (SFEM) for 2D elastic problems. It is found that a quadrilateral element divided into four smoothing cells can avoid spurious modes and gives stable results for integration over the element. Compared with original FEM, the SFEM achieves more accurate results and generally higher convergence rate in energy without increasing computational cost. More importantly, as no mapping or coordinate transformation is involved in the SFEM, its element is allowed to be of arbitrary shape. Hence the restriction on the shape bilinear isoparametric elements can be removed and problem domain can be discretized in more flexible ways, as demonstrated in the example problems.

Finite element (FE) model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine. However, if a model is used to answer clinical and biomechanical questions over a certain population, their inherently large inter-subject variability has to be considered. Current FE model studies, however, generally account only for a single distinct spinal geometry with one set of material properties. This raises questions concerning their predictive power, their range of results and on their agreement with in vitro and in vivo values. Eight well-established FE models of the lumbar spine (L1-5) of different research centers around the globe were subjected to pure and combined loading modes and compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges, and their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with published median in vitro values. However, the ranges of predictions were larger and exceeded those reported in vitro, especially for the facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with measured in vivo values. In light of high inter-subject variability, the generalization of results of a single model to a population remains a concern. This study demonstrated that the pooled median of individual model results, similar to a probabilistic approach, can be used as an improved predictive tool in order to estimate the response of the lumbar spine.

Total hip arthroplasty (THA) is most likely one of the most successful surgical procedures in medicine. It is estimated that three in four patients live beyond the first post-operative year, so appropriate surgery is needed to alleviate an otherwise long-standing suboptimal functional level. However, research has shown that during a complete THA procedure, a solid hip implant inserted in the femur can damage the main arterial supply of the cortex and damage the medullary space, leading to cortical bone resorption. Therefore, this study aimed to design a porous hip implant with a focus on providing more space for better osteointegration, improving the medullary revascularisation and blood circulation of patients. Based on a review of the literature, a lightweight implant design was developed by applying topology optimisation and changing the materials of the implant. Gyroid and Voronoi lattice structures and a solid hip implant (as a control) were designed. In total, three designs of hip implants were constructed by using SolidWorks and nTopology software version 2.31. Point loads were applied at the x, y and z-axis to imitate the stance phase condition. The forces represented were x = 320 N, y = −170 N, and z = −2850 N. The materials that were used in this study were titanium alloys. All of the designs were then simulated by using Marc Mentat software version 2020 (MSC Software Corporation, Munich, Germany) via a finite element method. Analysis of the study on topology optimisation demonstrated that the Voronoi lattice structure yielded the lowest von Mises stress and displacement values, at 313.96 MPa and 1.50 mm, respectively, with titanium alloys as the materials. The results also indicate that porous hip implants have the potential to be implemented for hip implant replacement, whereby the mechanical integrity is still preserved. This result will not only help orthopaedic surgeons to justify the design choices, but could also provide new insights for future studies in biomechanics.

A procedure for generating curved meshes, suitable for high-order finite element analysis, is described. The strategy adopted is based upon curving a generated initial mesh with planar edges and faces by using a linear elasticity analogy. The analogy employs boundary loads that ensure that nodes representing curved boundaries lie on the true surface. Several examples, in both two and three dimensions, illustrate the performance of the proposed approach, with the quality of the generated meshes being analysed in terms of a distortion measure. The examples chosen involve geometries of particular interest to the computational fluid dynamics community, including anisotropic meshes for complex three dimensional configurations.