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As a method of lightweight design, multi-material design aims to make targeted use of materials in order to reduce CO2 emissions. In this context, it can be described as one of the product development methods used to meet the challenges of climate change. However, since the design of structures in multi-material design is complex, topology optimization can be used to support the product developer. In this article, a multi-material topology optimization method is developed that combines the Velocity Field Level Set method with the Reconciled Level Set method. Furthermore, the current design is explicitly resolved in each iteration by means of multi-material remeshing. The edge collapse phase in the remeshing process is achieved by applying the producer consumer pattern. The developed method is then validated using known examples from the state of research, and the influence of the parameters of the method on the result is analyzed by means of studies. [ABSTRACT FROM AUTHOR]

The present article proposes an hybrid equilibrium element (HEE) formulation for the prediction of cohesive fracture formation and propagation with the crack modelled by extrinsic interface embedded at element sides. The hybrid equilibrium element formulation can model high order (quadratic, cubic and quartic) stress fields which strongly satisfy homogeneous equilibrium equations, inter‐element and boundary equilibrium equations. The HEE can implicitly model both the initially rigid behaviour of an extrinsic interface and its debonding condition with separation displacement and softening. The extrinsic interface is embedded at the element sides and its behaviour is governed by means of the same degrees of freedom of HEE (generalized stresses), without any additional degree of freedom. The proposed extrinsic cohesive model is developed in the thermodynamic framework of damage mechanics. The proposed crack propagation criterion states that crack grows when the maximum principal stress reaches the tensile strength value, in a direction orthogonal to the principal stress direction. The crack is embedded at an element side and the mesh around crack tip is adapted, by rotation of the element sides, in order to have the interface aligned to the crack growth direction. Three classic two‐dimensional problems of fracture propagation are numerically reproduced and the results compared to the experimental data or to the other numerical results. [ABSTRACT FROM AUTHOR]

Large strain analysis is a challenging task, especially in fictitious or immersed boundary domain methods, since badly broken elements/cells can lead to an ill-conditioned global tangent stiffness matrix, resulting in convergence problems of the incremental/iterative solution approach. In this work, the finite cell method is employed as a fictitious domain approach, in conjunction with an eigenvalue stabilization technique, to ensure the stability of the solution procedure. Additionally, a remeshing strategy is applied to accommodate highly deformed configurations of the geometry. Radial basis functions and inverse distance weighting interpolation schemes are utilized to map the displacement gradient and internal variables between the old and new meshes during the remeshing process. For the first time, we demonstrate the effectiveness of the remeshing approach using various numerical examples in the context of finite strain elastoplasticity. [ABSTRACT FROM AUTHOR]

This paper presents a Computational Fluid Dynamics (CFD) simulation of the quenching process based on ISO 9950, focusing on the heat flux and heat transfer coefficient integrated over a metal specimen. The numerical method, which employs the two-fluid VOF method and frozen turbulence approach (Cukrov et al., Appl. Sci. 2023, 13, 9144), is used for the transient simulation. Since quenching processes involve complex boiling phenomena shifting from film boiling to nucleate boiling, a standard method based on VOF cannot be applied. The comparison of the simulation results with the ones obtained using correlation, and the data obtained using the Inverse Heat Transfer Analysis (IHTA) method have revealed that the proposed method can accurately predict the heat flux and heat transfer coefficient in the film boiling regime of the immersion quenching process. Note that the previous paper (Cukrov et al., Energies. 2023, 16, 7926.) presented the immersion process modeling and the temperature distribution, while the current paper examines the heat transfer characteristics of the immersion quenching process.

Surface Reconstruction from raw Pointclouds generates polygonal meshes characterised by typical local issues that need to be addressed by a global reorganisation of mesh connectivity during the Remeshing process. While in the applications for which remeshing algorithms have historically been developed, the problem can be addressed without affecting the mesh polycount, for the authoring of 3D assets intended for Real-Time Rendering applications, maintaining a low polycount is mandatory. However, there is a trade-off between the number of polygons and accuracy. Hence, in cases where accuracy is a primary concern, such as with Digital Cultural Heritage Objects, the topology of the mesh that ensures this reduction becomes crucial since, to an even polycount, the dimensional discrepancy between the original and different simplified meshes can vary significantly.Therefore, it is vital to evaluate the characteristic quality obtainable from different remeshing algorithms with simplification, but despite the importance of the matter, there is a lack of metrics to perform such comparative benchmarks. This study aims to address this gap by defining and testing a Shape Complexity Index on real-world case studies, which is applicable uniformly and consistently to geometric shapes of generic complexity. Such index allows for pre-determine a target polycount and subsequently normalising signed distance computations among different test simplified meshes, posing the basis for both quantitative and qualitative analysis of accuracy achievable by any automatic remeshing tool. Additionally, the proposed workflow is employable as an instrument for planning, monitoring, and reporting a digitisation campaign of objects belonging to the Cultural Heritage.DOI: https://doi.org/10.20365/disegnarecon.32.2024.10

This article presents an adaptive remeshing strategy between the finite element method (FEM) and the discrete element method (DEM). To achieve this strategy, an edge‐to‐edge coupling method based on Lagrange multipliers has been set‐up to ensure the continuity of velocities at the interface. To switch from a computation initially purely FEM to a FEM‐DEM one, a field transfer method was required. In particular, a displacement field transfer method has been set‐up. The switching from a FEM subdomain to a DEM one is activated by a transition criterion. Each time a FEM subdomain is substituted by a DEM one, the DEM subdomain microscopic properties are set‐up with respect to the subdomain geometry and desired particle refinement. This is performed thanks to the linking to the so‐called "Cooker," a tool distributed along with the GranOO Workbench. Two subdomain remeshing cases were dealt with: that of an initially FEM subdomain that is converted to DEM, and that of DEM subdomains which coalesce. A numerical test case shows that the dynamic remeshing method behaves as expected: FEM subdomains are substituted by DEM ones when the transition criterion is met, and DEM subdomains coalesce when required. The final numerical test case shows a good agreement with a crack propagation experiment of the literature, while a speedup of about 20 was observed when compared to pure DEM computation. [ABSTRACT FROM AUTHOR]

The Smoothed Particle Finite Element Method (SPFEM) has gained popularity as an effective numerical method for modelling geotechnical problems involving large deformations. To promote the research and application of SPFEM in geotechnical engineering, we present ESPFEM2D, an open-source two-dimensional SPFEM solver developed using MATLAB. ESPFEM2D discretizes the problem domain into computable particle clouds and generates the finite element mesh using Delaunay triangulation and the α -shape technique to resolve mesh distortion issues. Additionally, it incorporates a nodal integration technique based on strain smoothing, effectively eliminating defects associated with the state variable mapping after remeshing. Furthermore, the solver adopts a simple yet robust approach to prevent the rank-deficiency problem due to under-integration by using only nodes as integration points. The Drucker-Prager model is adopted to describe the soil's constitutive behavior as a demonstration. Implemented in MATLAB, this open-source solver ensures easy accessibility and readability for researchers interested in utilizing SPFEM. ESPFEM2D can be easily extended and effectively coupled with other existing codes, enabling its application to simulate a wide range of large geomechanical deformation problems. Through rigorous validation using four numerical examples, namely the oscillation of an elastic cantilever beam, non-cohesive soil collapse, cohesive soil collapse, and slope stability analysis, the accuracy, effectiveness and stability of this open-source solver have been thoroughly confirmed. [ABSTRACT FROM AUTHOR]

In this work, a three-dimensional fluid-structural and vibro-acoustics coupled model of a gear pump is presented. Gear pumps represent the majority of the positive displacement machines used for flow generation in fluid power systems. Typically, the dynamics of gear pumps are dependent on the characteristics of the fluid dynamics inside the pump, which translates into vibrations to the housing. These vibrations then propagate to the surrounding medium and emit sound. The purpose of this study is to propose a three-dimensional fully integrated computational model to simulate the complete gear pump behaviour from the fluid dynamics to the structural vibrations, up to the vibroacoustic response. In this hybrid configuration, a transient CFD (Computational Fluid Dynamics) model is first developed to simulate the 3D flow field with a deforming and re-meshing approach to take into account the variation of the volume between the gears. Second, the internal pressure field calculated at each time step is then used as a loading into a structural FEM (Finite Element Method) model of the gear pump to compute the actual stresses and deformations of the housing. Third, the results of the structural response are used as excitation in a vibroacoustic sub-model to simulate the radiated noise using a high-order FEM technique. The comparison between the numerical and experimental flow curves validates the CFD model. The sound power calculations from the vibroacoustic model show good comparison with the sound intensity measurements around the pump casing, confirming the validity of the proposed coupled model. The described CFD-FEM approach proves to be a powerful gear pump design tool: it provides a reliable estimate of gear pump working parameters such as fluid power and vibroacoustic characteristics, starting from the CAD (Computer-Aided Design) geometry of the components. Furthermore, being one of the first multi-domain simulation models of a gear pump, this work can be useful to researchers as a starting point to correlate the noise emitted with the internal flow in full 3D conditions. [ABSTRACT FROM AUTHOR]

In this work, a three-dimensional fluid-structural and vibro-acoustics coupled model of a gear pump is presented. Gear pumps represent the majority of the positive displacement machines used for flow generation in fluid power systems. Typically, the dynamics of gear pumps are dependent on the characteristics of the fluid dynamics inside the pump, which translates into vibrations to the housing. These vibrations then propagate to the surrounding medium and emit sound. The purpose of this study is to propose a three-dimensional fully integrated computational model to simulate the complete gear pump behaviour from the fluid dynamics to the structural vibrations, up to the vibroacoustic response. In this hybrid configuration, a transient CFD (Computational Fluid Dynamics) model is first developed to simulate the 3D flow field with a deforming and re-meshing approach to take into account the variation of the volume between the gears. Second, the internal pressure field calculated at each time step is then used as a loading into a structural FEM (Finite Element Method) model of the gear pump to compute the actual stresses and deformations of the housing. Third, the results of the structural response are used as excitation in a vibroacoustic sub-model to simulate the radiated noise using a high-order FEM technique. The comparison between the numerical and experimental flow curves validates the CFD model. The sound power calculations from the vibroacoustic model show good comparison with the sound intensity measurements around the pump casing, confirming the validity of the proposed coupled model. The described CFD-FEM approach proves to be a powerful gear pump design tool: it provides a reliable estimate of gear pump working parameters such as fluid power and vibroacoustic characteristics, starting from the CAD (Computer-Aided Design) geometry of the components. Furthermore, being one of the first multi-domain simulation models of a gear pump, this work can be useful to researchers as a starting point to correlate the noise emitted with the internal flow in full 3D conditions.

The computational model that is able to estimate the temperature distribution inside a solid specimen during the film boiling phase of immersion quenching (water entry) process has been presented in this paper. It is based on the prescribed initial temperatures of the solid specimen and the liquid quenchant. In addition, the turbulence effects have to be considered using the assumed turbulence kinetic energy value, i.e., the "frozen turbulence" approach, that remains constant thorough the simulation. The studied material is nickel alloy, Inconel 600, for which extensive experimental data are available. The work has been carried out using ANSYS Fluent computational fluid dynamics software and the methods for solution of Stefan problem by Eulerian two fluid VOF model. A satisfactory agreement between the experimental and the calculated data has been achieved, yielding thereby the computationally obtained data that fit to a great extent the prescribed error band of ±10% during the estimated film boiling phase of the immersion quenching process itself. It was, however, found that the temperature calculated in the center of a specimen fits this error band until reaching somewhere t < 6 s due to low presumed turbulence level in the domain. In addition, the explosion of the vapor phase after the body reaches the free surface of the quenchant has also been successfully tracked using the numerical simulation model proposed herein. The major novelty of the present research lies in the fact that a moving boundary problem has been successfully resolved in conjunction with, to a great extent, basic-principle-based heat and mass transfer in a turbulent flow conjugate heat transfer (CHT) numerical simulation using moderate computational resources. [ABSTRACT FROM AUTHOR]

При численном моделировании процесса нарастания льда на поверхности обтекаемого тела важную роль играет задача геометрического перестроения поверхностной расчетной сетки согласно интенсивности ледообразования. В данной задаче по интенсивности нарастания льда в узлах или ячейках рассматриваемой сетки необходимо вычислить новые положения узлов сетки, чтобы получившаяся конфигурация эволюционировавшей расчетной сетки адекватно отражала поверхность с образовавшимся на ней ледяным покровом. Одним из критичных требований к алгоритму перестроения сетки является его надежность, возможность работать с произвольными поверхностными сетками, способность работать с сильными изгибами сетки, складками и шумами, а также бороться с потенциальными самопересечениями. В данной статье рассматривается алгоритм перестроения поверхностной сетки, в котором новое положение узла расчетной сетки определяется как точка пересечения траектории движения узла и общей огибающей семейства сфер с центрами в точках роста льда и радиусами, соответствующими интенсивности роста льда. Предложенный алгоритм предназначен для работы с телами со сложной геометрией, при его использовании происходит затягивание локальных впадин, а также сглаживание острых пиков, что повышает качество итоговой сетки. Основным качеством разработанного алгоритма является его надежность, что позволяет ему работать с сетками произвольной сложности и с сетками, обладающими геометрическими дефектами.

Micro-meshes (μ-meshes) are a new structured graphics primitive supporting a large increase in geometric fidelity, without commensurate memory and run-time processing costs, consisting of a base mesh enriched by a displacement map. A new generation of GPUs supports this structure with native hardware μ-mesh ray-tracing, that leverages a self-bounding, compressed displacement mapping scheme to achieve these efficiencies. In this paper, we present anautomatic method to convert an existing multi-million triangle mesh into this compact format, unlocking the advantages of the data representation for a large number of scenarios. We identify the requirements for high-quality μ-meshes, and show how existing re-meshing and displacement-map baking tools are ill-suited for their generation. Our method is based on a simplification scheme tailored to the generation of high-quality base meshes, optimized for tessellation and displacement sampling, in conjunction with algorithms for determining displacement vectors to control the direction and range of displacements. We also explore the optimization of μ-meshes for texture maps and the representation of boundaries. We demonstrate our method with extensive batch processing, converting an existing collection of high-resolution scanned models to the micro-mesh representation, providing an open-source reference implementation, and, as additional material, the data and an inspection tool. [ABSTRACT FROM AUTHOR]

We propose a robust re-meshing approach that can automatically generate visual-preserving low-poly meshes for any high-poly models found in the wild. Our method can be seamlessly integrated into current mesh-based 3D asset production pipelines. Given an input high-poly, our method proceeds in two stages: 1) Robustly extracting an offset surface mesh that is feature-preserving, and guaranteed to be watertight, manifold, and self-intersection free; 2) Progressively simplifying and flowing the offset mesh to bring it close to the input. The simplicity and the visual-preservation of the generated low-poly is controlled by a user-required target screen size of the input: decreasing the screen size reduces the element count of the low-poly but enlarges its visual difference from the input. We have evaluated our method on a subset of the Thingi10K dataset that contains models created by practitioners in different domains, with varying topological and geometric complexities. Compared to state-of-the-art approaches and widely used software, our method demonstrates its superiority in terms of the element count, visual preservation, geometry, and topology guarantees of the generated low-polys. [ABSTRACT FROM AUTHOR]

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Powell‐Sabin B‐splines are employed to model progressive fracturing in a fluid‐saturated porous medium. These splines are defined on triangles and are 풞1‐continuous throughout the domain, including the crack tips, so that crack initiation can be evaluated directly at the tip. On one hand, the method captures stresses and fluid fluxes more accurately than when using standard Lagrange elements, enabling a direct assessment of the fracture criterion at the crack tip and ensuring local mass conservation. On the other hand, the method avoids limitations for discrete crack analysis which adhere to isogeometric analysis. A crack is introduced directly in the physical domain. Due to the use of triangles, remeshing and crack path tracking are straightforward. During remeshing transfer of state vectors (displacement, fluid pressure) is required from the old to the new mesh. The transfer is done using a new approach which exploits a least‐squares fit with the energy balance and conservation of mass as constraints. The versatility and accuracy to simulate free crack propagation are assessed for mode‐I and mixed‐mode fracture problems. [ABSTRACT FROM AUTHOR]

This paper addresses fluid‐driven crack propagation in a porous medium. Cohesive interface elements are employed to model the behaviour of the crack. To simulate hydraulic fracturing, a fluid pressure degree of freedom is introduced inside the crack, separate from the fluid degrees of freedom in the bulk. Powell‐Sabin B‐splines, which are based on triangles, are employed to describe the geometry of the domain and to interpolate the field variables: displacements and interstitial fluid pressure. Due to their C1$\mathcal {C}^1$‐continuity, the stress and pressure gradient are smooth throughout the whole domain, enabling a direct assessment of the fracture criterion at the crack tip and ensuring local mass conservation. Due to the use of triangles, crack insertion and remeshing are straightforward and can be done directly in the physical domain. During remeshing a mapping of the state vector (displacement and interstitial fluid pressure) is required. For this, a new methodology is exploited based on a least‐square fit with the energy balance and mass conservation as constraints. The accuracy to model free crack propagation is demonstrated by two numerical examples, including crack propagation in a plate with two notches. [ABSTRACT FROM AUTHOR]

A sequence of 3D models generated using volumetric capture has the advantage of retaining the characteristics of dynamic objects and scenes. However, in volumetric data, since 3D mesh and texture are synthesized for every frame, the mesh of every frame has a different shape, and the brightness and color quality of the texture is various. This paper proposes an algorithm to consistently create a mesh of 4D volumetric data using dynamic reconstruction. The proposed algorithm comprises remeshing, correspondence searching, and target frame reconstruction by key frame deformation. We make non-rigid deformation possible by applying the surface deformation method of the key frame. Finally, we propose a method of compressing the target frame using the target frame reconstructed using the key frame with error rates of up to 98.88% and at least 20.39% compared to previous studies. The experimental results show the proposed method's effectiveness by measuring the geometric error between the deformed key frame and the target frame. Further, by calculating the residual between two frames, the ratio of data transmitted is measured to show a compression performance of 18.48%. [ABSTRACT FROM AUTHOR]

We present here a GPU-friendly algorithm for uniform Voronoi tessellation (UVT) of a digital manifold, which, in particular, may be conceived as the voxelized representation of a 2-manifold surface. Its pipeline integrates several novel ideas, such as local directional field, which is used to estimate field energy, and when combined with Voronoi energy, provides an estimate of the uniformity of tessellation in each iteration. For selection of seeds needed to initialize field computation and Voronoi tessellation, an efficient strategy of functional partitioning is used to partition the digital manifold into a collection of functional components. Over successive iterations, the seeds are updated to effectuate energy optimization, and thus to gradually converge towards a uniform tessellation. As its application in 3D modeling, we have also shown how the energy-optimizing tessellation iteratively transforms a 2-manifold surface (e.g., a triangulated mesh) into an isotropic mesh while preserving the surface details. As our algorithm works entirely in voxel space, it is readily implementable in GPU for all associated computations. Experimental results on different datasets have been presented to demonstrate its efficiency and robustness. [ABSTRACT FROM AUTHOR]

We present a novel method for joint optimization and remeshing and apply it to inverse rendering. Rapid advances in differentiable rendering during the last years paved the way for fast inverse rendering of complex scenes. But serious problems with gradient‐based optimization of triangle meshes remain. Applying gradient steps to the vertices can lead to mesh defects, such as flipped triangles, crumpled regions, and self‐intersections. Choosing a good vertex count is crucial for the optimization quality and performance but is usually done by hand. Moreover, meshes with fixed triangulation struggle to adapt to complex geometry. Our novel method tackles all these problems by applying an adaptive remeshing step in each single iteration of the optimization loop. By immediately collapsing suspicious triangles, we avoid and heal mesh defects. We use a closed‐loop‐controlled location‐dependent edge length. We compare our solution to state‐of‐the‐art methods and find that it is faster and more accurate. It produces finer meshes with fewer defects, requires less parameter tuning and can reconstruct more complex objects. [ABSTRACT FROM AUTHOR]

A multiscale crack iteration and remeshing model was proposed and implemented to predict the low-cycle crack propagation behavior for steel. Crack propagation behavior was quantified by fatigue indicator parameters (FIPs) in the crystal plasticity model. Once the crack propagation rate and direction were determined in the grain, the crack seam was inserted into the model by remeshing in postprocessing. To further relax the fatigue driving force and reduce the impact of FIP variation, an iteration procedure, in which sufficient computational cycles were preselected and iterated during the simulation, was applied to the mesoscale model. Additionally, the boundary conditions of the mesoscale model were obtained from the macroscale model by the multiscale simulation method. A three-point bending fatigue test was carried out to validate the iteration and remeshing model. The experimental results showed two cracks generated from the upper and lower surfaces during the fatigue test, and the crack propagation rate increased as the crack grew toward the center region. Meanwhile, the numerical model, including two initiated cracks, was implemented corresponding to the central region in the experimental specimen. By applying the boundary condition from the macroscale simulation associated with the experiment, the two cracks grew during the iteration and remeshing. The simulation results showed two cracks growing gradually toward the region with a reasonable number of cycles. The zigzag pattern simulated from the mesoscale model also qualitatively correlates well with the observation from experimental results. [ABSTRACT FROM AUTHOR]

We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input that connect the PQ strips. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling-based representations of developable surfaces while still obtaining developable, curvature-aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its isolines are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight isolines is non-linear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle-based interactive freeform modeling of developable shapes. [ABSTRACT FROM AUTHOR]

This paper describes a numerically robust data structure for encoding intrinsic triangulations of polyhedral surfaces. Many applications demand a correspondence between the intrinsic triangulation and the input surface, but existing data structures either rely on floating point values to encode correspondence, or do not support remeshing operations beyond basic edge flips. We instead provide an integer-based data structure that guarantees valid correspondence, even for meshes with near-degenerate elements. Our starting point is the framework of normal coordinates from geometric topology, which we extend to the broader set of operations needed for mesh processing (vertex insertion, edge splits, etc.). The resulting data structure can be used as a drop-in replacement for earlier schemes, automatically improving reliability across a wide variety of applications. As a stress test, we successfully compute an intrinsic Delaunay refinement and associated subdivision for all manifold meshes in the Thingi10k dataset. In turn, we can compute reliable and highly accurate solutions to partial differential equations even on extremely low-quality meshes. [ABSTRACT FROM AUTHOR]

The simulation of machining processes holds the opportunity for process improvement on many levels. Possible benefits that can be derived from accurate representations of the real processes on the tool from simulations include a prediction of tool wear, the shape of the chips produced, the forces, frictions and temperatures that arise and the residual stresses in the workpiece. These predictions can be used to improve the process in terms of its economic and ecological behaviour: Increasing the service life of the tools used through an improved understanding of the tool-workpiece interaction. The finite element method (FEM), among others, has emerged as a common method for simulating these processes. When simulating machining processes using FEM, a major challenge is to avoid or compensate for the mesh distortions caused by the massive, fast-moving deformation processes, but at the same time to allow the mesh to be discretised in some way to ensure chip removal. To this end, various approaches will be presented in the course of this work and the mesh-based approaches will be explored in depth. Among other things, a remeshing approach for these investigations was developed. The machining of TI6AL4V is used to illustrate these approaches, as its tendency to form segmented chips is particularly challenging to model. [ABSTRACT FROM AUTHOR]

Inspired by the ability of water to assimilate any shape, if being poured into it, regardless if flat, round, sharp, or pointy, we present a novel, high-quality meshing method. Our algorithm creates a triangulated mesh, which automatically refines where necessary and accurately aligns to any target, given as mesh, point cloud, or volumetric function. Our core optimization iterates over steps for mesh uniformity, point cloud projection, and mesh topology corrections, always guaranteeing mesh integrity and ϵ -close surface reconstructions. In contrast with similar approaches, our simple algorithm operates on an individual vertex basis. This allows for automated and seamless transitions between the optimization phases for rough shape approximation and fine detail reconstruction. Therefore, our proposed algorithm equals established techniques in terms of accuracy and robustness but supersedes them in terms of simplicity and better feature reconstruction, all controlled by a single parameter, the intended edge length. Due to the overall increased versatility of input scenarios and robustness of the assimilation, our technique furthermore generalizes multiple established approaches such as ballooning or shrink wrapping. [ABSTRACT FROM AUTHOR]

Near-surface voids and pores are generated in metal processing operations as diverse as additive manufacturing and powder processing, but their effect on indentation hardness has not been explored outside homogenized frameworks. Here we model the micromechanics of near-surface void deformation up to closure in a wedge-indentation field in ductile metal, and reveal the considerable softening effect of voids on the indentation hardness. Both symmetrically and eccentrically located voids, at various depths below the free surface, are studied. Notably, the extent of apparent reduction in the elastic modulus due to a void is much smaller than its effect on apparent hardness, e.g. 6.5% against 55% for the same void. Critical to the simulations is an adaptive remeshing finite element (FE) framework that allows accurate capture of processes like void closure and void-wall self-contact. The simulations reveal the subsurface plastic strain, strain-rate, and velocity fields with high fidelity, and their radical differences from the radial indentation field in a void-free specimen. These differences include the presence of localized pockets of high and low strain, and the initial accommodation of material displaced by the indenter by a corresponding reduction in void area. Unlike voids under uniform compression, the void-area evolution in indentation shows a characteristic sigmoidal pattern of reduction with indentation depth for all but the smallest voids. Interestingly, the indented surface profile can exhibit a one-sided pile-up feature which is diagnostic of the presence of an eccentrically located sub-surface void. Our remeshing scheme is versatile, as exemplified by its ability to model the extreme deformation associated with two nearly closed-spaced voids under an indenter. Our work shows that void-closure simulations in related applications like forming could benefit from the adoption of a remeshing framework. • First study of sub-surface void mechanics in an indentation field. • Quantification of softening effect of voids on indentation hardness. • Diagnostic changes to indented surface due to subsurface voids identified. • Void area evolution under wedge indenter is characteristically sigmoidal. • Remeshing-based simulations critical for accurate capture of void closure. [ABSTRACT FROM AUTHOR]

Tessellating CAD models into triangular meshes is a long-lasting problem. Size field is widely used to accommodate varieties of requirements in remeshing, and it is usually discretized and optimized on a prescribed background mesh and kept constant in the subsequent remeshing procedure. Instead, we propose optimizing the size field on the current mesh, then using it as guidance to generate the next mesh. This simple strategy eliminates the need of building a proper background mesh and greatly simplifies the size field query. For better quality and convergence, we also propose a geodesic distance based initialization and adaptive re-weighting strategy in size field optimization. Similar to existing methods, we also view the remeshing of a CAD model as the remeshing of its parameterization domain, which guarantees that all the vertices lie exactly on the CAD surfaces and eliminates the need for costly and error-prone projection operations. However, for vertex smoothing which is important for mesh quality, we carefully optimize the vertex's location in the parameterization domain for the optimal Delaunay triangulation condition, along with a high-order cubature scheme for better accuracy. Experiments show that our method is fast, accurate and controllable. Compared with state-of-the-art methods, our approach is fast and usually generates meshes with smaller Hausdorff error, larger minimal angle with a comparable number of triangles. • A novel framework for alternative size field optimization and meshing. • Size field optimization with a penalty, initialization and re-weighting strategies. • Parameterization domain vertex smoothing with an accurate ODT condition on the surface. [ABSTRACT FROM AUTHOR]

In this work, a novel and robust remeshing algorithm for crack opening problems is proposed, combined with triangular plane stress finite elements. In the proposed algorithm, the crack tip efficiently propagates until a pre-established maximum crack length is achieved and the crack propagation direction is defined considering the maximum tangential stress criterion. The stress state at the crack tip is obtained using a weighted average of the stresses of the integration points adjacent to the crack tip, to smoothen the stress field near the crack tip. In order to achieve accurate stress fields in the vicinity of the singularity, the proposed algorithm establishes that there is always a fixed number of nodes and elements surrounding the crack tip. To verify the accuracy of the algorithm, three benchmark tests were analyzed and the solutions were compared with results available in the literature. It was observed that the proposed technique allows to maintain the meshes regular during the propagation process, significantly reducing the number of distorted elements, which solves one of the main problems when simulating crack propagation with the finite element method (FEM). Additionally, the obtained results allowed to understand that this algorithm generally leads to accurate crack paths. [ABSTRACT FROM AUTHOR]

Abstract With the development of biomolecular modeling and simulation, especially implicit solvent modeling, higher requirements are set for the stability, efficiency and mesh quality of molecular mesh generation software. In this review, we summarize the recent works in biomolecular mesh generation and molecular visualization. First, we introduce various definitions of molecular surface and corresponding meshing software. Second, as the mesh quality significantly influences biomolecular simulation, we investigate some remeshing methods in the fields of computer graphics and molecular modeling. Then, we show the application of biomolecular mesh in the boundary element method (BEM) and the finite element method (FEM). Finally, to conveniently visualize the numerical results based on the mesh, we present two types of molecular visualization systems.

The simulation of large structural deformations with the finite element method poses several challenges. The severe distortion of elements may deteriorate the accuracy and robustness of the method and restrict it to smaller deformations than desired. This issue is especially present in the finite cell method (FCM), where complex geometries are discretized with a non-conforming Cartesian grid introducing a fictitious material with very low stiffness. The remeshing strategy presented here improves the robustness at the cost of generating a new Cartesian grid of the deformed geometry at load steps where the element distortion becomes critical. This allows us to use larger load steps and to further deform the structure under consideration. We use radial basis functions to transfer the displacements and the displacement gradients from one mesh to the next one. The method is investigated in combination with a hyperelastic material and exemplary applied to simulate a pore of a foam. [ABSTRACT FROM AUTHOR]

Multiple crack propagation and coalescence in two-dimensional linear elastic media were modeled using the finite-element method (FEM) in conjunction with the subregion generalized variational principle. The proposed approach computes the stress intensity factor (SIF) accurately, as proved in a previous work. The approach results in regular geometric meshes. A multiple crack propagation scheme was developed in this study. The scheme follows the crack propagation by moving just the complementary energy subregion on the basis of the regular mesh. Consequently, it requires only minimal local remeshing without affecting most of the existing mesh. The scheme can handle crack coalescence easily. These advantages simplify the modeling and thus improve the efficiency. Four numerical examples, including a structure containing 10 cracks, were investigated to demonstrate the accuracy and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Although the flow drill screw (FDS) joining technique has been successfully used for connecting dissimilar materials in lightweight structures design, forming simulation of the FDS joining process is still challenging, due to the fact that modeling of the severe plastic deformation and material failure is still difficult. In this work, the FDS forming process was successfully simulated through an optimized remeshing method for joining of the DP590/Al6061-T6 in lap structure as a case study. The effectiveness and accuracy of the numerical model developed in the current study were compared with those of the model based on the Lagrangian method and calibrated by experimental data. The results show that the FDS process can be simulated accurately through remeshing the distorted elements to regular tetrahedral elements, with accurate petal, bushing, and thread formed. And the local temperature rising surrounding the screw and axial force change of the FDS process were also predicted accurately. The simulation precision of the forming of the petal and bushing and the peak temperature are 95% and 2%, while the error of the first peak force is 19.3%. It was found that the forming of the petal and bushing is under the axial extrusion force, whereas the forming of the thread is under the plane extrusion force. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel numerical method that redistributes unevenly given points on an evolving closed curve to satisfy equi-arclength(-like) condition. Without substantial difficulty, it is also capable of remeshing or employing adaptive mesh refinement. The key idea is to find the discrete inverse of the arclength(-like) function in the framework of the Fourier spectral method to obtain overall spectral accuracy. Both equi-arclength and curvature-dependent redistributions are extensively studied, and their spectral accuracy is verified by application to smoothly perturbed points on various curves. We further confirm that our method converges even for the points being perturbed nonsmoothly and randomly. To leverage the robustness of our method, a remeshing technique is applied in which the accuracy is not affected. Application to a periodic planar curve without any modification of our algorithm is also discussed. Then, to show the practical applicability, an evolving curve with large deformation is studied by coupling with point redistribution and remeshing in various flows such as mean curvature flow, Willmore flow, and Stokes flow. [ABSTRACT FROM AUTHOR]

The numerical analysis, based on the finite element modeling (FEM), presents nowadays an efficient computational tool. It allows a better understanding of several thermo-mechanical phenomena involved during the machining process. However, its reliability heavily depends on the accurate definition of the numerical model. In this regard, a FE analysis focused on the 2D modeling of the Ti6Al4V dry orthogonal machining was carried out in this study. The relevance of different numerical meshing approaches and finite elements topologies was studied. The effect of the friction coefficient on the numerical chip morphology, its geometry, the cutting and the feed forces was investigated. The adequacy of several compared adaptive meshing approaches, in terms of the modeling of severe contact conditions taking place around the cutting-edge radius, was underlined in the current study. However, numerical serrated chips, closer to the experimental ones, were only predicted when the pure Lagrangian formulation was adopted and a proper determination of the failure energy was carried out. The definition of different mesh topologies highlighted the efficiency of the 4-node quadrangular mesh, with a suitable edge length, in increasing the agreement with the experimental data, while reducing the computing times. [ABSTRACT FROM AUTHOR]

For the large deformation and distortion of the mesh on the numerical simulation of rubber,using the solving and transformation between grids of the adaptive technique of Abaqus software,the rubber model was remeshed several times. In this paper,the key parts of the packer were used as the research object and the final rubber deformation results were obtained by two remeshing before solving the mapping to the new mesh for further solving. The results of numerical simulation show that remeshing can reduce the occurrence of distortion and solve the problem of nonlinear analysis of large deformation caused by mesh distortion.Remeshing can improve the accuracy of data transmission between the old and new grid when the old mesh has a smaller distortion. It provides a significant research method for the sealing performance of the rubber,which also has some reference value for other hyperelastic materials.

In numerical analyses based on unstructured meshes represented by the finite element method, quadrilateral and hexa-hedral meshes are used for a two-dimensional and a three-dimensional analyses, respectively, from the viewpoint of calculation accuracy and computation time. However, a method for automatically generating quadrilateral and hexahedral meshes has not been established thus far; in addition, a considerable amount of effort is required to perform manual mesh modifications. Mesh generation based on the frame field method is an effective technique to extract high quality quadrilateral and hexahedral meshes through the optimization of the posture of a frame with rotational symmetry. This method needs to solve a mixed-integer programming (MIP) problem while extracting the quadrilateral and hexahedral mesh using integer grid maps. When solving an MIP using a greedy method, solving a simultaneous equation is required approximately O(M) times, where M is the number of integer constraints. In this study, we propose a method to obtain a quadrilateral mesh by solving a simultaneous equation approximately O(1) times. In this method, the frame field is calculated using finite element discretization, and the finite element mesh is appropriately remeshed to be aligned with the integer grid resulting from the frame field optimization. The proposed method can reduce the amount of computation required to obtain integer grid maps for mesh extraction, without impairing the mesh quality. The proposed method is evaluated with respect to by mesh quality using the aspect ratio and the scaled Jacobian. Numerical examples demonstrate that the mesh quality is comparable to or better than that produced by conventional methods and manual procedures.

Summary: The analysis of (dynamic) fracture often requires multiple changes to the discretisation during crack propagation. The state vector from the previous time step must then be transferred to provide the initial values of the next time step. A novel methodology based on a least‐squares fit is proposed for this mapping. The energy balance is taken as a constraint in the mapping, which results in a complete energy preservation. Apart from capturing the physics better, this also has advantages for numerical stability. To further improve the accuracy, Powell‐Sabin B‐splines, which are based on triangles, have been used for the discretisation. Since C1 continuity of the displacement field holds at crack tips for Powell‐Sabin B‐splines, the stresses at and around crack tips are captured much more accurately than when using elements with a standard Lagrangian interpolation, or with NURBS and T‐splines. The versatility and accuracy of the approach to simulate dynamic crack propagation are assessed in two case studies, featuring mode‐I and mixed‐mode crack propagation. [ABSTRACT FROM AUTHOR]

We introduce a new method to efficiently track complex interfaces among multi-phase immiscible fluids. Unlike existing techniques, we use a mesh-based representation for global liquid surfaces while selectively modeling some local surficial regions with regional level sets (RLS) to handle complex geometries that are difficult to resolve with explicit topology operations. Such a semi-explicit surface mechanism can preserve volume, fine features and foam-like thin films under a relatively low computational expenditure. Our method processes the surface evolution by sampling the fluid domain onto a spectrally refined grid (SRG) and performs efficient grid scanning, generalized interpolations and topology operations on the basis of this grid structure. For the RLS surface part, we propose an accurate advection scheme targeted at SRG. For the explicit mesh part, we develop a fast grid-scanning technique to voxelize the meshes and introduce novel strategies to detect grid cells that contain inconsistent mesh components. A robust algorithm is proposed to construct consistent local meshes to resolve mesh penetrations, and handle the coupling between explicit mesh and RLS surficial regions. We also provide further improvement on handling complicated topological variations, and strategies for remeshing mesh/RLS interconversions. [ABSTRACT FROM AUTHOR]

• We propose an efficient and practical method to do bounded-error remeshing. • If vertices are added into the mesh, the error is easily reduced and finally bounded. • We adaptively refine the mesh to satisfy the error-bounded constraint. • We alternately do remeshing based on an edge length field and adaptively adjust it. We propose an efficient and practically robust method to isotropically remesh an input triangular mesh with bounded approximation error. Our method is based on a key observation, that is, when more uniformly distributed vertices are added into the remeshed mesh, the error-bounded constraint is usually satisfied. Then our algorithm adaptively refines the remeshed mesh to satisfy the error-bounded constraint and avoid heavy computational load. To that end, we present an iterative approach that alternates in each iteration a pass to do an edge-based remeshing using the computed edge length field and a pass to adaptively adjust the edge length field. The robustness of our method is demonstrated by performing tests on complex shapes, as well as models containing sharp features or boundaries. Compared to the state-of-the-art error-bounded methods, our technique is much faster and more practically robust. [ABSTRACT FROM AUTHOR]

We present a data structure that makes it easy to run a large class of algorithms from computational geometry and scientific computing on extremely poor-quality surface meshes. Rather than changing the geometry, as in traditional remeshing, we consider intrinsic triangulations which connect vertices by straight paths along the exact geometry of the input mesh. Our key insight is that such a triangulation can be encoded implicitly by storing the direction and distance to neighboring vertices. The resulting signpost data structure then allows geometric and topological queries to be made on-demand by tracing paths across the surface. Existing algorithms can be easily translated into the intrinsic setting, since this data structure supports the same basic operations as an ordinary triangle mesh (vertex insertions, edge splits, etc.). The output of intrinsic algorithms can then be stored on an ordinary mesh for subsequent use; unlike previous data structures, we use a constant amount of memory and do not need to explicitly construct an overlay mesh unless it is specifically requested. Working in the intrinsic setting incurs little computational overhead, yet we can run algorithms on extremely degenerate inputs, including all manifold meshes from the Thingi10k data set. To evaluate our data structure we implement several fundamental geometric algorithms including intrinsic versions of Delaunay refinement and optimal Delaunay triangulation, approximation of Steiner trees, adaptive mesh refinement for PDEs, and computation of Poisson equations, geodesic distance, and flip-free tangent vector fields. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present a fully automatic framework that tessellates industrial computer-aided design (CAD) models into high-quality triangular meshes. In contrast to previous approaches that are purely parametric or performed directly in 3D space, our method is based on a remeshing algorithm that can achieve accuracy and high-quality simultaneously. Given an input standard CAD model, which is represented by B-rep format,we first rebuild the parametric domain for each surface patch according to an initial triangulation, and then the boundaries of the parametric domain are retriangulated by exploiting the Constrained Delaunay Triangulation (CDT). In the second stage, the 2D triangulation is projected back to the 3D space, and a modified global isotropic remeshing process is applied, which further improves the regularity and angle quality of the tessellated meshes. Experiments demonstrate the validity of the proposed approach and its ability to generate high-quality meshes. Moreover, we evaluate our technique and compare it with state-of-the-art CAD model tessellation approaches. Highlights • An automatic surface tessellation framework for complex industrial CAD models. • Improvement of previous remeshing approach to generate high-quality surface meshes. • Introduction of simple yet effective heuristics to merge the small patches. [ABSTRACT FROM AUTHOR]