FE Approaches Research Articles

Variational formulation and monolithic solution of computational homogenization methods

AbstractIn this contribution, we derive a consistent variational formulation for computational homogenization methods and show that traditional FE and IGA approaches are special discretization and solution techniques of this most general framework. This allows us to enhance dramatically the numerical analysis as well as the solution of the arising algebraic system. In particular, we expand the dimension of the continuous system, discretize the higher dimensional problem consistently and apply afterwards a discrete null‐space matrix to remove the additional dimensions. A benchmark problem, for which we can obtain an analytical solution, demonstrates the superiority of the chosen approach aiming to reduce the immense computational costs of traditional FE and IGA formulations to a fraction of the original requirements. Finally, we demonstrate a further reduction of the computational costs for the solution of general nonlinear problems.

Numerical Simulations of 122 mm M-21OF Missile Fragments Propulsion

This paper presents numerical simulations of 122 mm M-21OF rocket fragments propulsion. A simplified geometry of the rocket was constructed and analysed with two main numerical FE approaches: a mesh-based lagrangian-eulerian FSI method and a coupled meshless SPH–lagrangian approach. The resulting fragment velocities were compared with those obtained from an analytical approach (Gurney formula). The shell fragmentation process was also successfully depicted. Both numerical approaches differed from the analytical velocity results to a comparable degree. Considering that the Gurney energy of a high-explosive is obtained from cylinder expansion tests, results obtained with the Gurney method can be treated as a reference point and validation method for natural fragmentation warhead models.

A Review of Fully Endoscopic Lumbar Interbody Fusion

Over the past 10 years, fully endoscopic lumbar interbody fusion (FE-LIF) has been widely reported as a rational alternative to minimally invasive transforaminal lumbar interbody fusion (MIS-TLIF), and several FE approaches for interbody fusion have been published. The short-term surgical outcomes of FE-LIF are reportedly superior to those of MIS-TLIF and conventional posterior LIF in terms of intraoperative blood loss and short-term back pain. However, the complication rate, medium-term clinical outcomes, and fusion rate have not been reported to be different in all uncontrolled studies. The challenges associated with FE-LIF include a longer operative time, which means a steep learning curve, and limited surgical indications, which leads to patient selection bias. FE-LIF is an excellent surgical option for treating degenerative disc disease, spinal instability, and spondylolisthesis. Although the amount of evidence is very small in existing studies and the long-term follow-up data are limited, this technique shows favorable clinical outcomes in selected patients.

Hydrodynamic and aeration characteristics of an aerator of a surging water tank with a vertical baffle under a horizontal sinusoidal motion

To address the hypoxia problem in seawater, this paper proposes an aerator for a surging water tank with a vertical baffle and experimentally and numerically investigates its hydrodynamic and aeration characteristics under a horizontal sinusoidal motion. The intrinsic relationships of the dimensionless maximum wave surface run-up, maximum air pressure, and airflow rate are examined with the ratios of tank surging amplitude to still water depth, tank surging frequency to natural frequency, water exchange height to still water depth, and air hole area to plan area of the sub-tank, respectively. In particular, the dimensionless maximum wave surface run-up reaches its peak when the tank surging frequency fe approaches the natural frequency f1 of the individual sub-tank sloshing mode, and the maximum dimensionless airflow rate appears when the tank surging frequency fe approaches the natural frequency fs of the U-tube sloshing mode. The ratio of the tank surging amplitude to the still water depth and fe/fs play minor roles in the dimensionless maximum air pressure. Furthermore, two methods are used to deduce the prediction formulas for the dimensionless airflow rate. The symbolic regression method performs better than the multivariate non-linear regression method.

Locking treatment of penalty-based gradient-enhanced damage formulation for failure of compressible and nearly incompressible hyperelastic materials

Soft materials are of major interest for biomechanics applications due to their high deformability and susceptibility to experience damage events under different loading scenarios. The present study is concerned with modelling damage evolution processes in these nonlinear materials whose structural responses are prone to locking when low-order kinematic interpolation is employed in the context of nonlinear Finite Element schemes. For this reason, a pair of gradient-enhanced continuum damage schemes are proposed with the aim of tackling mechanical failure problems in applications that exhibit shear and volumetric locking. In particular, we present the consistent formulation and the assessment of the corresponding performance of (i) a mixed displacement-enhanced assumed strain Q1Q1E24 employing a total Lagrangian formulation, and (ii) a three-field mixed displacement-pressure-Jacobian Q1Q1P0 formulation. The novel Q1Q1E24 and Q1Q1P0 formulations are consistently derived and numerically implemented, providing a satisfactory agreement with respect to ABAQUS built-in elements handling the treatment of shear and volumetric locking, respectively, in conjunction to the modelling damage phenomena via the use of a penalty-based gradient-enhanced formulation. This performance is examined via several numerical applications. Furthermore, the final example justifies the need for a formulation combining both mixed FE approaches to simulate problems encompassing both locking issues (shear and volumetric locking), which can be performed using a combination of the Q1Q1E24 and Q1Q1P0 herein proposed.

Elastic-plastic analysis with pre-integrated beam finite element based on state diagrams: Elastic-perfectly plastic flow

The behaviour of a structure beyond its elastic limit involves a non-linear analysis, commonly conducted in engineering design with the benefit of Finite Element Analysis. Many structures are an assembly of one-dimensional components (beams) to form a frame. There are two main FE approaches to studying axial plastic propagation and the distribution within the cross-section of a beam: solid elements or beam elements with cross-section sampling (fiber section). The first requires a considerable number of d.o.f.’s to obtain reliable results; therefore, it is not generally used for extensive size modelling; the second, although requiring less computational efforts, necessitates an extensive sampling of cross-sections to evaluate the plastic distribution at every fiber. Furthermore, a high number of elements are needed to assess the plastic propagation. This paper provides a new approach that allows to considerably reduce the numerical heaviness by providing two ideas: i) elastic-plastic State Diagrams that allow the pre-integration of the cross-section response (that overcame the sampling within the section) ii) section-slices subdivision, that enable to build-up the tangent stiffness matrix of an entire partially plasticized beam (whatever is the plastic distribution and the section shape), with the minimum number of d.o.f.’s. The pre-integrated approach here developed assume planar bending and an elastic-perfectly plastic flow. The proposed element is validated by three test cases, comparing with the solutions obtained through FEA using solid elements and fiber-section beams. A significant enhancement in the overall efforts emerges, obtaining very similar results among the three approaches but with a considerable reduction of the computational time when using the proposed element.

Induced Magnetism of the MoS2 Monolayer during the Transition Metal (Fe/Ni) Bombardment Process: A Nonadiabatic Ab Initio Collision Dynamics Investigation.

The source of induced magnetism in the MoS2 monolayer induced by transition metal (Fe/Ni) collision is investigated using nonadiabatic ab inito molecular dynamics simulations that take into account high-spin and low-spin energy states during trajectory integration. By considering various metal firing angles, a strong interaction between the Fe/Ni atom and the MoS2 surface can be observed because of enormous increase in the kinetic energy of the metal atom. When firing along the Mo–S bond, the Fe bullet is pulled more strongly than when firing along the S–Mo–S bisector. Spin polarization of MoS2 is gradually induced when Fe approaches the surface and eliminated when Fe roams around a potential energy trap on the MoS2 layer. We observe that there is charge transfer between Fe and Mo atoms, which enhances the probability of electron pairing and leads to instantaneous vanishing of total magnetization. The Ni–MoS2 system is found to establish a total magnetization of 1.5–4 μB when Ni is 2.0 Å above the surface. Interestingly, the strong bonding attachment of Ni suppresses the band gap to at least 40%.

Catalytic Toluene Reforming with In Situ CO2 Capture via an Iron–Calcium Hybrid Absorbent for Promoted Hydrogen Production

A two‐step sol–gel method is adopted to prepare an iron–calcium hybrid absorbent (Ca–Al–Fe) integrating iron catalysis component and inert support with CaO for calcium looping gasification. Effects of Ca–Al–Fe on cyclic CO2 capture reactivity, mechanical strength, and enhanced reforming of biomass tar model component (toluene) are investigated by comparing with three reference absorbents. Results show that main components of Ca–Al–Fe are CaO, mayenite (Ca12Al14O33), and brownmillerite (Ca2Fe2O5). Ca12Al14O33 plays key roles in keeping stable cyclic carbonation reactivity and significantly promotes mechanical strength of the novel absorbent. In comparison with other absorbents without coupling Ca12Al14O33 or Ca2Fe2O5, Ca–Al–Fe approaches the highest toluene conversion (around 60%) and has the lowest coke deposition (12.2 mg g−1), due to the synergetic influences of Ca2Fe2O5 and Ca12Al14O33, which significantly promotes hydrogen production while reducing CO2 yield in reforming syngas. In addition, influences of reaction conditions such as iron loading, reaction temperature, molar ratio of H2O to carbon in toluene, and absorbent particle size on toluene reforming are examined in the presence of Ca–Al–Fe. Potential reaction routes of toluene reforming are also analyzed and discussed.

A novel hybrid iron-calcium catalyst/absorbent for enhanced hydrogen production via catalytic tar reforming with in-situ CO2 capture

An iron-calcium hybrid catalyst/absorbent (Ca–Al–Fe) is developed by a two-step sol-gel method to enhance tar conversion, cyclic CO2 capture and mechanical strength of absorbent for hydrogen production in calcium looping gasification. The developed catalyst/absorbent consists of CaO and brownmillerite (Ca2Fe2O5) with mayenite (Ca12Al14O33) as inert support. Comparing with three candidate absorbents without Ca2Fe2O5 or Ca12Al14O33, cyclic carbonation reactivity and mechanical strength of Ca–Al–Fe are largely promoted. Meanwhile, Ca–Al–Fe approaches the maximum conversion rate of 1-methyl naphthalene (1-MN) with enhanced hydrogen yield around 0.15 mol/(h·g) under reforming conditions of present study. Ca–Al–Fe also shows the largest CO2 absorption and lowest coke deposition. Influences of operation variables on 1-MN reforming are evaluated and recommended conditions can be iron to CaO mass ratio of 10%, reaction temperature of 800 °C and steam to carbon in 1-MN mole ratio of 2.0. Ca–Al–Fe hybrid catalyst/absorbent presents good potential to be applied in future.

Full-field polycrystal plasticity simulations of neutron-irradiated austenitic stainless steel: A comparison between FE and FFT-based approaches

We compare two full-field approaches – a crystal plasticity finite element method (CP-FEM) and crystal plasticity fast Fourier transform-based (CP-FFT) method – for a specific crystal plasticity law introduced for neutron-irradiated austenitic stainless steel SA304L currently used in nuclear reactor vessel internals. This particular law is employed to identify and quantify possible advantages and drawbacks of the two approaches when used in the large-scale simulations to predict the effect of irradiation damage (e.g., crack initiation) in stainless steel microstructures. A comparison is performed in a polycrystalline context for different periodic Voronoi microstructures deformed under tension. Special emphasis is put on studying the performance of the two approaches in terms of mesh convergence analysis using aggregate models with different spatial discretizations. In the CP-FEM approach, the performance of linear as well as quadratic tetrahedral meshes is investigated. A similar performance between the CP-FEM and CP-FFT methods is demonstrated in a smaller 2-grain aggregate. However, a slower mesh convergence is observed for the CP-FEM method when comparing tensile responses of a larger 100-grain polycrystal. A drop in the convergence rate is much more pronounced on linear than on quadratic tetrahedral meshes. As a consequence, largest (average) grain boundary stresses are shown to be overestimated with the linear mesh CP-FEM approach, thus raising a concern of possible over-conservatism employed in the CP-FEM prediction of crack initiation in irradiated stainless steels. On the contrary, the mesh convergence of the CP-FFT approach is found to be practically independent of the applied macroscopic strain and also aggregate size. Therefore, for such steels, the CP-FFT approach seems to be better justified.

Experiments of double curvature plate bending with induction heating and processing parameters investigation by computational analysis

plate bending with double curvature is an essential procedure in shipbuilding, which is also a bottleneck problem to restrict the fabrication schedule and dimensional accuracy. With the induction heating technology, plate bending with double curvature as saddle and sail types, was conducted experimentally. Meanwhile, due to the rated output power of induction heating, heat input as well as moving speed of induction heating coil has a significant influence on maximal temperature and final bending deformation. In addition, out-of-plane bending deformation with different patterns can be observed and their magnitudes were also measured by three-coordinate measuring machine (TMM). Computational analysis with thermal elastic plastic (TEP) and elastic FE approaches was then employed to investigate processing parameters of induction heating. Computed out-of-plane bending deformations have a good agreement with measurement about not only deformed shape but also magnitudes. Elastic FE computation with bending moment as input loading has much more obvious efficiency comparing to conventional TEP FE computation without loss of computational accuracy. Moreover, generation mechanism of bending deformation with different patterns was also examined and clarified with in-plane plastic strains caused by induction heating, which will be converted to shrinkage force and bending moment for plate bending.

Comparison of self-consistent and crystal plasticity FE approaches for modelling the high-temperature deformation of 316H austenitic stainless steel

The present article examines the predictive capabilities of a crystal plasticity model for inelastic deformation which captures the evolution of dislocation structure, precipitates and solute atom distributions at the microscale, recently developed by Hu and Cocks (2015) and Hu et al. (2013). The model is implemented within a self-consistent framework and a crystal plasticity finite element (CPFE) scheme. Through direct comparison between the two CP schemes and with an extensive material database for Type 316H stainless steel, the different types of information and the degree to which the models are consistent with experimental observations are assessed. The study demonstrates an agreement between the SCM and the CPFE schemes, providing confidence in the micromechanical deformation model employed. The multi-scale approach also allows the effects of micro-scale deformation processes, related to dislocation-obstacle interactions, on the global deformation response to be captured. Modelling results from this study and their comparison to experimental observations show that deformation of polycrystalline materials, such as 316H stainless steel, is controlled by the evolution of microstructural state of the material and the redistribution of stress between individual grains. The study suggests that the SCM is a feasible tool to simulate and explain the deformation behaviour of complex alloys under industrially-relevant thermo-mechanical operating histories. The CPFE framework captures the effects of the variation in grain geometry and provides more detailed information about the variation of stress and strain within the individual grains, particularly their distribution near grain boundaries and triple points – which are important to understand in the context of damage development and failure. The SCM predicts a “stiffer”, more creep-resistant response than a CPFE model for a given set of material parameters due to the more highly-constrained deformation modes allowed in the model. As a result, material parameters calibrated using one modelling approach are not necessarily suitable for use in another approach – although parameters obtained when fitting the different models should not vary significantly.

Modelling of multi-lateral well geometries for geothermal applications

Abstract. Well inflow modelling in different numerical simulation approaches are compared for a multi-lateral well. Specifically radial wells will be investigated, which can be created using Radial Jet Drilling (RJD). In this technique, powerful hydraulic jets are used to create small diameter laterals (25–50 mm) of limited length (up to 100 m) from a well. The laterals, also called radials, leave the backbone at a 90∘ angle. In this study we compare three numerical simulators and a semi-analytical tool for calculating inflow of a radial well. The numerical simulators are FE approaches (CSMP and GOLEM) and an FV approach with explicit well model (Eclipse®). A series of increasingly complex well configurations is simulated, including one with inflow from a fault. Although all simulators generally are reasonably close in terms of the total well flow (deviations < 4 % for the homogeneous cases), the distribution of the flow over the different parts of the well can vary significantly. Also, the FE approaches are more sensitive to grid size when the flow is dominated by radial flow to the well since they do not include a dedicated well model. In the FE approaches, lower dimensional elements (1-D for the well and 2-D for the faults) were superimposed into a 3-D space. In case the flow is dominated by fracture flow, the results from the FV approach in Eclipse deviates from the FE methods.

An ICME Process Chain for Diffusion Brazing of Alloy 247

A virtual process chain for diffusion brazing of Ni-based superalloys is presented for the example of Alloy 247. Besides phase-field simulation of different brazing processes, the chain includes solidification with equiaxed and columnar microstructures, heat treatment processes, and annealing and rafting of γ’-precipitates in 3D, as well as conversion of the resulting microstructures into finite element meshes for further evaluation of their properties by FE approaches. The challenges of setting-up a seamless simulation chain are discussed, and the importance of a correct and comprehensive handling of the relevant microstructural quantities is highlighted. Special focus is given to the initial specification and the further evolution of segregation patterns of the different alloying elements in this complex alloy system. The data describing these patterns may originate from experiments or may be generated by prior simulation runs. The description of phase transformations like melting, solidification, or precipitation further requires the simulation of diffusion of numerous chemical elements and their redistribution between existing and newly forming phases. Such multicomponent systems thus require thermodynamic and mobility data which typically are provided by Calphad-type computational tools and databases.

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

A discontinuous Petrov–Galerkin (DPG) formulation for the FEM applied to the Helmholtz equation for high wavenumbers

Pollution error is a well known source of inaccuracies in continuous or discontinuous FE approaches to solve the Helmholtz equation. This topic is widely studied in a large number of papers, e.g., (Ihlenburg and Babuska, Comput Math Appl 30(9):9–37, 1995; Ihlenburg, Finite element analysis of acoustic scattering applied mathematical sciences, vol 132. Springer, New York, 1998). Robust methodologies for structured square meshes have been developed in recent years. This work seeks to develop a methodology based on Petrov–Galerkin discontinuous formulation, to minimize phase error for Helmholtz equation for both structured and unstructured meshes. A Petrov–Galerkin finite element formulation is introduced for the Helmholtz problem in two dimensions using polynomial weighting functions. At each node of the triangular mesh, a global basis function for the weighting space is obtained, adding bilinear $$C^0$$ Lagrangian weighting function linear combinations. The optimal weighting functions, with the same support of the corresponding global test functions, are obtained after computing the coefficients of these linear combinations attending to optimal criteria. This is done numerically through a preprocessing technique that is naturally applied to non-uniform and unstructured meshes. In particular, for uniform meshes a quasi optimal interior stencil of the same order of the quasi-stabilized finite element method stencil derived by (Babuska et al., Comput Meth Appl Mech Eng 128:325–359, 1995) is obtained. The numerical results indicate a better performance in relation to the classic discontinuous Galerkin method.

A numerical investigation of effective thermoelastic properties of interconnected alumina/Al composites using FFT and FE approaches

The present paper deals with a numerical investigation of effective thermoelastic properties of interconnected alumina/Al composites. This work uses a numerical approach initially introduced for investigating the thermal conductivity of particulate composites. In this paper, adaptations are carried out in order to evaluate both thermal and elastic coefficients using FFT and FE methods. In a first step, both methodologies are set up and validated for the context of particulate composites without interconnection. Effects related to both discretisation and number of particles are discussed, and a statistical volume element is finally determined. In a second step, the complex microstructure of interconnected alumina/Al is reproduced considering interconnection areas which are introduced and controlled using the cherry-pit model. Effective thermal conductivity and Young’s modulus are assessed and compared to third-order estimates and experimental measurements. Results show a good agreement between the numerical methods and the analytical formula. However, all predictions do not meet the experimental measurements, indicating the presence of flaws within the material.

Thorium isotopes tracing the iron cycle at the Hawaii Ocean Time-series Station ALOHA

The role of iron as a limiting micronutrient motivates an effort to understand the supply and removal of lithogenic trace metals in the ocean. The long-lived thorium isotopes (232Th and 230Th) in seawater can be used to quantify the input of lithogenic metals attributable to the partial dissolution of aerosol dust. Thus, Th can help in disentangling the Fe cycle by providing an estimate of its ultimate supply and turnover rate. Here we present time-series (1994–2014) data on thorium isotopes and iron concentrations in seawater from the Hawaii Ocean Time-series Station ALOHA. By comparing Th-based dissolved Fe fluxes with measured dissolved Fe inventories, we derive Fe residence times of 6–12months for the surface ocean. Therefore, Fe inventories in the surface ocean are sensitive to seasonal changes in dust input. Ultrafiltration results further reveal that Th has a much lower colloidal content than Fe does, despite a common source. On this basis, we suggest Fe colloids may be predominantly organic in composition, at least at Station ALOHA. In the deep ocean (>2km), Fe approaches a solubility limit while Th, surprisingly, is continually leached from lithogenic particles. This distinction has implications for the relevance of Fe ligand availability in the deep ocean, but also suggests Th is not a good tracer for Fe in deep waters. While uncovering divergent behavior of these elements in the water column, this study finds that dissolved Th flux is a suitable proxy for the supply of Fe from dust in the remote surface ocean.

Measuring the Deflection of a Circular Plate on an Elastic Foundation and Comparison with Analytical and FE Approaches

The solution of the interaction between a structure and its foundation is an important problem in mechanics and technical applications. This paper presents a solution of a circular plate rested on an elastic (Winkler) foundation. A jig was created for the purpose of loading a circular plate with a specific bending moment and force on the plate circumference. Laboratory testing was performed to determine the deflection in the centre and at the edge of the plate. Measurement apparatus was assembled and measurements were carried out; the results of the measurement were compared with the analytical solutions and FEM results. On the basis of these comparisons, the foundation modulus was determined. The experiment, analytical solution and FEM give similar results, thus providing a solid basis for technical applications.

A novel three-dimensional element free Galerkin (EFG) code for simulating two-phase fluid flow in porous materials

Abstract In the past few decades, numerical simulation of multiphase flow systems has received increasing attention because of its importance in various fields of science and engineering. In this paper, a three-dimensional numerical model is developed for the analysis of simultaneous flow of two fluids through porous media. The numerical approach is fairly new based on the element-free Galerkin (EFG) method. The EFG is a type of mesh-less method which has rarely been used in the field of flow in porous media. The weak forms of the governing partial differential equations are derived by applying the weighted residual method and Galerkin technique. The penalty method is utilized for imposition of the essential boundary conditions. To create the discrete equation system, the EFG shape functions are used for spatial discretization of pore fluid pressures and a fully implicit scheme is employed for temporal discretization. The obtained numerical results indicate that the EFG method has the capability to substitute the classical FE and FD approaches from the accuracy point of view, provided that the efficiency of the EFG is improved. The developed EFG code can be used as a robust numerical tool for simulating two-phase flow processes in the subsurface layers in various engineering disciplines.