Remeshing Strategy Research Articles

Conformal higher‐order remeshing schemes for implicitly defined interface problems

SummaryA new higher‐order accurate method is proposed that combines the advantages of the classical p‐version of the FEM on body‐fitted meshes with embedded domain methods. A background mesh composed by higher‐order Lagrange elements is used. Boundaries and interfaces are described implicitly by the level set method and are within elements. In the elements cut by the boundaries or interfaces, an automatic decomposition into higher‐order accurate sub‐elements is realized. Therefore, the zero level sets are detected and meshed in a first step, which is called reconstruction. Then, based on the topological situation in the cut element, higher‐order sub‐elements are mapped to the two sides of the boundary or interface. The quality of the reconstruction and the mapping largely determines the properties of the resulting, automatically generated conforming mesh. It is found that optimal convergence rates are possible although the resulting sub‐elements are not always well‐shaped. Copyright © 2016 John Wiley & Sons, Ltd.

Three-dimensional finite element modeling of ductile crack initiation and propagation

A crack initiation and propagation algorithm driven by non-local ductile damage is proposed in a three-dimensional finite strain framework. The evolution of plastic strain and stress triaxiality govern a non-local ductile damage field via constitutive equations. When the damage reaches a critical threshold, a discontinuity in the form of a crack surface is inserted into the three-dimensional continuum. The location and direction of the introduced discontinuity directly result from the damage field. Crack growth is also determined by the evolution of damage at the crack tip and the crack surface is adaptively extended in the computed direction. Frequent remeshing is used to computationally track the initiation and propagation of cracks, as well as to simultaneously maintain a good quality of the finite elements undergoing large deformations. This damage driven remeshing strategy towards fracture allows one to simulate arbitrary crack paths in three-dimensional evolving geometries. It has a significant potential for a wide range of industrial applications. Numerical examples are solved to demonstrate the ability of the proposed framework.

Adapting Feature Curve Networks to a Prescribed Scale

AbstractFeature curves on surface meshes are usually defined solely based on local shape properties such as dihedral angles and principal curvatures. From the application perspective, however, the meaningfulness of a network of feature curves also depends on a global scale parameter that takes the distance between feature curves into account, i.e., on a coarse scale, nearby feature curves should be merged or suppressed if the surface region between them is not representable at the given scale/resolution. In this paper, we propose a computational approach to the intuitive notion of scale conforming feature curve networks where the density of feature curves on the surface adapts to a global scale parameter. We present a constrained global optimization algorithm that computes scale conforming feature curve networks by eliminating curve segments that represent surface features, which are not compatible to the prescribed scale. To demonstrate the usefulness of our approach we apply isotropic and anisotropic remeshing schemes that take our feature curve networks as input. For a number of example meshes, we thus generate high quality shape approximations at various levels of detail.

Stability of Statics Aware Voronoi Grid-Shells

Grid-shells are lightweight structures used to cover long spans with few load-bearing material, as they excel for lightness, elegance and transparency. In this paper we analyze the stability of hex-dominant free-form grid-shells, generated with the Statics Aware Voronoi Remeshing scheme introduced in Pietroni et al. (2015). This is a novel hex-dominant, organic-like and non uniform remeshing pattern that manages to take into account the statics of the underlying surface. We show how this pattern is particularly suitable for free-form grid-shells, providing good performance in terms of both aesthetics and structural behavior. To reach this goal, we select a set of four contemporary architectural surfaces and we establish a systematic comparative analysis between Statics Aware Voronoi Grid-Shells and equivalent state of the art triangular and quadrilateral grid-shells. For each dataset and for each grid-shell topology, imperfection sensitivity analyses are carried out and the worst response diagrams compared. It turns out that, in spite of the intrinsic weakness of the hexagonal topology, free-form Statics Aware Voronoi Grid-Shells are much more effective than their state-of-the-art quadrilateral counterparts.

A Magnetodynamic Error Criterion and an Adaptive Meshing Strategy for Eddy Current Evaluation

In order to address their considerable impacts on both the energy efficiency and performance requirements, eddy current modeling and its accuracy are discussed from a thermodynamic approach. An energy-based error criterion for automatic mesh adaption is developed. Coupled with a remeshing strategy that preserves mesh quality, some numerical results are given on an induction machine.

A locally anisotropic fluid–structure interaction remeshing strategy for thin structures with application to a hinged rigid leaflet

SummaryAn immersed finite element fluid–structure interaction algorithm with an anisotropic remeshing strategy for thin rigid structures is presented in two dimensions. One specific feature of the algorithm consists of remeshing only the fluid elements that are cut by the solid such that they fit the solid geometry. This approach allows to keep the initial (given) fluid mesh during the entire simulation while remeshing is performed locally. Furthermore, constraints between the fluid and the solid may be directly enforced with both an essential treatment and elements allowing the stress to be discontinuous across the structure. Remeshed elements may be strongly anisotropic. Classical interpolation schemes – inf–sup stable on isotropic meshes – may be unstable on anisotropic ones. We specifically focus on a proper finite element pair choice. As for the time advancing of the fluid–structure interaction solver, we perform a geometrical linearization with a sequential solution of fluid and structure in a backward Euler framework. Using the proposed methodology, we extensively address the motion of a hinged rigid leaflet. Numerical tests demonstrate that some finite element pairs are inf–sup unstable with our algorithm, in particular with a discontinuous pressure. Copyright © 2015 John Wiley & Sons, Ltd.

Extended layerwise method of laminated composite shells

This paper deals with the accurate description of the multiple delaminations and transverse cracks in double-curved laminated composite shells by using the extended finite element method (XFEM) and layerwise theory (LWT), and develops an extended layerwise method (XLWM) which had been applied to the laminated beams in our previous work (Li et al., 2015 [1]). In the displacement assumption of XLWM, the discontinuous function along the thickness direction is adopted to simulate the displacement discontinuous resulted from multiple delaminations. While the transverse cracks are modeled in in-plane displacements discretization by XFEM. The level set method (LSM) is employed in the present method to track the interfaces resulted from the transverse cracks. The interaction integral method and maximum circumferential tensile criterion are used to calculate the stress intensity factor (SIF) and crack growth angle, respectively. In order to ensure the accuracy of Gauss integral when certain nodes are very close to the crack surface as the crack grows, a local remeshing scheme is developed to shift these nodes without scarifying the mesh quality. In the numerical examples, spherical shells, cylindrical shells and plates with/without multiple delaminations and/or transverse crack are considered to the problems of static responses analysis, SIF calculation and transverse crack arbitrary growth.

Micromechanical modeling of large deformation in sepiolite reinforced rubber sealing composites under transverse tension

This article presents an experimental and numerical study on mechanical behavior of sepiolite reinforced rubber sealing composites (SRRC), which are subjected to the transverse tensile loads. A finite element model of composites with fibers in square and random distribution is adopted for the numerical study. The representative volume elements with different fiber volume fraction are established and analyzed. A successive remeshing strategy is employed to achieve the large deformation of SRRC. The results show that the tensile strength and breaking elongation of SRRC can be improved by addition of sepiolite fiber, and they reach a maximum at 42% fiber volume fraction. The stress‐strain curve of SRRC with fibers in the random distribution agrees well with that measured in the experiments. However, there exists a significant difference between experimental and numerical results as fiber volume fraction increases. POLYM. COMPOS., 38:381–388, 2017. © 2015 Society of Plastics Engineers

A semi-implicit finite element method for viscous lipid membranes

A finite element formulation to approximate the behavior of lipid membranes is proposed. The mathematical model incorporates tangential viscous stresses and bending elastic forces, together with the inextensibility constraint and the enclosed volume constraint. The membrane is discretized by a surface mesh made up of planar triangles, over which a mixed formulation (velocity–curvature) is built based on the viscous bilinear form (Boussinesq–Scriven operator) and the Laplace–Beltrami identity relating position and curvature. A semi-implicit approach is then used to discretize in time, with piecewise linear interpolants for all variables. Two stabilization terms are needed: The first one stabilizes the inextensibility constraint by a pressure–gradient–projection scheme (Codina and Blasco (1997) [33]), the second couples curvature and velocity to improve temporal stability, as proposed by Bänsch (2001) [36]. The volume constraint is handled by a Lagrange multiplier (which turns out to be the internal pressure), and an analogous strategy is used to filter out rigid-body motions. The nodal positions are updated in a Lagrangian manner according to the velocity solution at each time step. An automatic remeshing strategy maintains suitable refinement and mesh quality throughout the simulation.Numerical experiments show the convergent and robust behavior of the proposed method. Stability limits are obtained from numerous relaxation tests, and convergence with mesh refinement is confirmed both in the relaxation transient and in the final equilibrium shape. Virtual tweezing experiments are also reported, computing the dependence of the deformed membrane shape with the tweezing velocity (a purely dynamical effect). For sufficiently high velocities, a tether develops which shows good agreement, both in its final radius and in its transient behavior, with available analytical solutions. Finally, simulation results of a membrane subject to the simultaneous action of six tweezers illustrate the robustness of the method.

An exact general remeshing scheme applied to physically conservative voxelization

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems.We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh. We refer to this as “physically conservative voxelization.”At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara [48], who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain.We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.

Comparison of 3D Adaptive Remeshing Strategies for Finite Element Simulations of Electromagnetic Heating of Gold Nanoparticles

The optical properties of metallic nanoparticles are well known, but the study of their thermal behavior is in its infancy. However the local heating of surrounding medium, induced by illuminated nanostructures, opens the way to new sensors and devices. Consequently the accurate calculation of the electromagnetically induced heating of nanostructures is of interest. The proposed multiphysics problem cannot be directly solved with the classical refinement method of Comsol Multiphysics and a 3D adaptive remeshing process based on ana posteriorierror estimator is used. In this paper the efficiency of three remeshing strategies for solving the multiphysics problem is compared. The first strategy uses independent remeshing for each physical quantity to reach a given accuracy. The second strategy only controls the accuracy on temperature. The third strategy uses a linear combination of the two normalized targets (the electric field intensity and the temperature). The analysis of the performance of each strategy is based on the convergence of the remeshing process in terms of number of elements. The efficiency of each strategy is also characterized by the number of computation iterations, the number of elements, the CPU time, and the RAM required to achieve a given target accuracy.

Fast simulation of incremental sheet metal forming by adaptive remeshing and subcycling

In order to use incremental sheet forming (ISF) in an industrial context, it is necessary to provide fast and accurate simulation methods for virtual process design. Without reliable process simulations, first-time right production seams infeasible and the process loses its advantage of offering a short lead time. Previous work indicates that implicit finite element (FE) methods are at present not efficient enough to allow for the simulation of AISF for industrially relevant parts, mostly due to the fact that the moving contact requires a very small time step. Finite element methods based on explicit time integration can be sped up using mass or time scaling to enable the simulation of large-scale sheet metal forming problems. However, AISF still requires dedicated adaptive meshing methods to further reduce the calculation times. In this paper, an adaptive remeshing strategy based on a multi-mesh method is developed and applied to the simulation of AISF. It is combined with subcycling to further reduce the calculation times. For the forming of a cone shape, it is shown that savings in CPU time of up to 80 % are possible with acceptable loss of accuracy, and that the simulation time scales more moderately when the part size is increased, so that larger, industrially relevant parts become feasible.

A new finite element approach for modelling ductile damage void nucleation and growth—analysis of loading path effect on damage mechanisms

A two-dimensional finite element (FE) model is presented to model the nucleation and void growth stages in ductile damage phenomena on the microstructure scale. This model is based on a level-set (LS) method coupled with an advanced re-meshing strategy. Both nucleation modes (interface debonding and inclusion fracture) are modelled through the introduction of micro-voids according to stress-based criteria. The LS method and mesh adaptation are used to accommodate the topology modification of the microstructure and to model multiple void nucleation and growth for different loading paths. The enhanced FE model is adopted to analyse the key features of the damage mechanisms on the micro-scale. The effects of inclusion orientation and of a complex loading path on nucleation and void growth are addressed. Good agreement is found with available experimental and numerical data found in the literature. The results exhibit that the loading path is a key point in damage growth. The proposed FE framework is an efficient technique to study damage phenomena on both simple and realistic microstructures. In the future, such an approach can be used to calibrate macroscopic ductile damage models for a complex loading path.

Research on dynamic simulation method of leakage prediction for hydraulic system

The dynamic simulation method of leakage prediction for hydraulic system is presented in this paper. A model is built for the method to analyze its composition and functions of the modules in it. Considering that there is friction between the seal and the rod, thermo-mechanical coupled method is applied to get the pressure distribution in the contacting region. The influence of the seal wear on the leakage is also included. A remeshing strategy based on the finite element technique is employed to simulate wear process. In order to find the inflection points precisely, a correction method based on hydrodynamic theory is used. Finally, the realization of the dynamic simulation method for the leakage prediction is given. To validate the simulation method, the simulation results are compared with the test results. The two results are in good agreement. The simulation method presented in this paper will be a reliable and time-saving one to predict the leakage for the hydraulic system.

Rigid-Plastic Finite Element Simulation of Cold Forging and Sheet Metal Forming by Eulerian Meshing Method

A computational technique of rigid-plastic finite element method by using the Eulerian meshing method was developed to deal with large deformation problem in metal forming by replacing the conventional way of applying complicated remeshing schemes when using the Lagrange’s elements. During metal forming process, a workpiece normally undergoes large deformation and causes severe distortion of elements in finite element analysis. The distorted element may lead to instability in numerical calculation and divergence of non-linear solution in finite element analysis. With Eulerian elements, the initial elements are generated to fix into a specified analytical region with particles implanted as markers to form the body of a workpiece. The particles are allowed to flow between the elements after each deformation step to show the deforming pattern of material. Four types of cold forging and sheet metal clinching were conducted to investigate the effectiveness of the presented method. The proposed method is found to be effective by comparing the results on dimension of the final product, material flow behaviour and punch load versus stroke obtained from simulation and experiment.

Quarter elliptical crack growth using three dimensional finite element method and crack closure technique

Shape evolution of a quarter-elliptical crack emanating from a hole is studied. Three dimensional elastic-plastic finite element analysis of the fatigue crack closure was considered and the stress intensity factor was calculated based on the duplicated elastic model at each crack tip node. The crack front node was advanced proportional to the imposed effective stress intensity factor. Remeshing was applied at each step of the crack growth and solution mapping algorithm was considered. Crack growth retardation at free surfaces was successfully observed. A MATLAB-ABAQUS interference code was developed for the first time to perform crack growth on the basis of crack closure. Simulation results indicated that crack shape is sensitive to the remeshing strategy. Predictions based on the proposed models were in good agreement with Carlson’s experiments results.

A Lagrangian particle/panel method for the barotropic vorticity equations on a rotating sphere

We present a Lagrangian particle/panel method for geophysical fluid flow described by the barotropic vorticity equations on a rotating sphere. The particles carry vorticity and the panels are used in discretizing the Biot–Savart integral for the velocity. Adaptive panel refinement and a new Lagrangian remeshing scheme are applied to reduce the computational cost and maintain accuracy as the flow evolves. Computed examples include a Rossby–Haurwitz wave, a Gaussian vortex, and a perturbed zonal jet. To validate the method, a comparison is made with results obtained using the Lin–Rood finite–volume scheme.

Re-Meshing in Finite Element Simulations of Hot Working Including a Microstructural Evolution Model

Material models that couple the evolution of flow stress to the evolution of the microstructure are important for the simulation of hot working processes in which the microstructure undergoes large changes. Among the microstructural evolution mechanisms in hot working, dynamic recrystallization (DRX) plays a central role as it occurs during deformation. When the workpiece deforms, the element shape may deteriorate, which makes re-meshing necessary. At the same time, certain regions of the finite element mesh undergo DRX and a sharp interface between recrystallized and non-recrystallized portions of the workpiece develops. Elements of the old mesh that are cut by the interface contain nodes with a non-zero recrystallized volume fraction and nodes where the recrystallized volume fraction is zero. During re-meshing, when the microstructural data is transferred to the new mesh, nodes or integration points that are actually in region of the workpiece that is not yet recrystallized may be assigned a non-zero recrystallized volume fraction. As a consequence, the interface moves, which is unwanted and may produce large errors when re-meshing is frequently done. In this paper, the problem of the propagation of the DRX interface during re-meshing is treated. It is shown that the propagation occurs with standard data mapping algorithms and produces a large error at the interface. A re-meshing scheme is proposed that uses a smooth mesh-free interpolating function based on radial basis functions to interpolate the recrystallized volume fraction. The interface is the zero level set of this interpolant. Performing the mapping as a least squares fit of the interpolant allows for a substantial reduction of the mapping error and suppresses the propagation of the DRX front.

Deformation embedding for point-based elastoplastic simulation

We present a straightforward, easy-to-implement, point-based approach for animating elastoplastic materials. The core idea of our approach is the introduction of embedded space —the least-squares best fit of the material's rest state into three dimensions. Nearest-neighbor queries in the embedded space efficiently update particle neighborhoods to account for plastic flow. These queries are simpler and more efficient than remeshing strategies employed in mesh-based finite element methods. We also introduce a new estimate for the volume of a particle, allowing particle masses to vary spatially and temporally with fixed density. Our approach can handle simultaneous extreme elastic and plastic deformations. We demonstrate our approach on a variety of examples that exhibit a wide range of material behaviors.

Numerical simulation of continuous damage and fracture in metal-forming processes with 2D mesh adaptive methodology

An h-adaptive remeshing scheme dedicated to the simulation of macroscopic ductile cracks initiation and propagation during metal forming processes, is proposed. Cracks are represented using a procedure based on fully damaged elements deletion. Element size inside the domain and along the crack path, located inside highly localized zones, is driven by error indicators based on geometrical considerations and the derivatives of physical quantities calculated by diffuse approximation. Saw tooth effects along the crack are smoothed with the use of Bezier curves in order to reduce computational inaccuracy. The mesh can be refined and an important issue of this work is mesh coarsening in order to ensure a reasonable computational cost. Multiple domains can be handled. The procedure can be easily integrated in any standard nonlinear explicit finite element code. Specific fields transfer procedures and an automatic adaptation of the time loading sequences are also presented. The efficiency and robustness of the proposed strategy are validated through some examples which show a good agreement with experimentally observed ductile crack paths under large inelastic strains.