Implicit Finite Element Research Articles

Exact Newton method with third-order convergence to model the dynamics of bubbles in incompressible flow

In this letter, we present a computational framework based on the use of the Newton and level set methods and tailored for the modeling of bubbles with surface tension in a surrounding Newtonian fluid. We describe a fully implicit and monolithic finite element method that maintains stability for significantly larger time steps compared to the usual explicit method and features substantial computational savings. A suitable transformation avoids the introduction of an additional mixed variable in the variational problem. An exact tangent problem is derived and the nonlinear problem is solved by a quadratically convergent Newton method. In addition, we consider a generalization to the multidimensional case of the Kou’s and McDougall’s methods, resulting in a faster convergence. The method is benchmarked against known results with the aim of illustrating its accuracy and robustness.

Impact or blast induced fire simulation of bi-directional PSC panel considering concrete confinement and spalling effect

In recent years, numerous explosion and collision related tragedies due to military attack, terrorist bombing, and vehicle accident have occurred all over the world. However, researches on Prestressed Concrete (PSC) infrastructures such as Prestressed Concrete Containment Vessels (PCCVs) and LNG storage tanks under extreme loading such as impact, blast, and fire loading scenario are not being studied sufficiently. Especially, researches on possible secondary fire after bomb explosion or accidental collision on concrete structures has not been performed, while most of the past researches related to extreme loadings on structures focused on ideal isolated extreme loading event researches. Therefore, in this study, the PSC panel such as wall of PCCV and LNG storage tank is analytically evaluated under impact-blast-fire combined loading scenarios. For the analytical simulations of impact/blast and fire loaded behavior of the PSC panel, commercial finite element analysis program of LS-DYNA and MIDAS FEA, respectively, were used. Then, a simulation procedure coupling LS-DYNA and MIDAS FEA using element elimination algorithm is proposed to couple explicit and implicit finite element analyses (FEA) to perform structural analysis of impact or blast induced fire loading scenario. Then, the simulation results from the PSC and RC specimens applied with impact induced fire or blast induced fire loadings were compared with those of undamaged PSC and RC specimens. The results showed that PSC panel was more severely damaged from the fire due to the confining effect of prestressing forces. Confining effect increased the thermal conductivity of concrete due to compaction of concrete. Also, the spalling of concrete caused by impact loading followed by fire loading were implemented to the simulation model using the element elimination procedure proposed in the study. The simulation results obtained from the proposed simulation procedure agree well with the impact induced fire test results.

Progressive damage modeling in carbon fibers/carbon nanotubes reinforced polymer composites

Abstract Damage in carbon fibers/Epoxy laminate composites containing carbon nanotubes (CNTs) is described. This investigation presents the third part of paper series on composite materials based CNTs. Experimental characterization and numerical homogenizations were published in order to obtain effective elastic orthotropic properties. Therefore, the homogenized properties are used as input data for investigation of damage initiation and propagations in the specimens for Open Hole tensile tests. The numerical intralaminar damage model is created under ABAQUS software with Hashin's criteria. The model is formulated according to damage mechanics. The prediction of ply delamination in laminated composites containing CNTs is modeled by using interface elements. The numerical approach is based on the cohesive zone model, provides an efficient description of the delamination growth. The numerical study is performed in the quasi-static regime and an implicit finite element scheme is used. The force-displacement curves obtained numerically shows a good agreement with the experimental.

Comparison of Explicit and Implicit Finite Element Methods and its Effectiveness for Drop Test of Electronic Control Unit

Engine control unit consists of many electronic components like capacitors, inductor coils, Ball Grid Array (BGA) and Ceramic chips which are prone to fail during drop. As per ISO 16750-3 standard electronic components are dropped from one meter height on rigid wall in six different dimensional axis to check the reliability of the system [4]. Unless the ECU mechanical structure fails or components inside housing separates from PCB drop failures cannot be noticed. Designing drop reliable electronic components are critical to improve the quality of ECU and vehicle.This paper discusses the effectiveness of four simulation methods used to simulate electronic control unit (ECU) drop test. Explicit and Implicit simulation methods are considered in this study. Under implicit simulation technique full transient, steady state static and mode super position methods are studied and they are compared with explicit method. Explicit simulation method is conditionally stable whereas implicit methods are un-conditionally stable, this makes the explicit method computationally costlier and time consuming. Convergence and absence to capture the dynamic response are the major challenges in implicit method. For this study the electronic control unit is simplified with bare printed circuit board (PCB) and frame for drop simulation. PCB in-plane strains and displacements are evaluated for one meter height drop on rigid floor and all corresponding results are compared to find the effectiveness of each method.

Adaptive implicit finite element methods for multicomponent compressible flow in heterogeneous and fractured porous media

AbstractThis work presents adaptive implicit first‐order and second‐order discontinuous Galerkin (DG) methods for the transport of multicomponent compressible fluids in heterogeneous and fractured porous media, discretized by triangular, quadrilateral, and hexahedral grids. The adaptive implicit method (AIM) combines the advantages of purely explicit or implicit methods (in time). In grid cells with high fluxes or low pore volumes, the transport update is done implicitly to alleviate the Courant‐Friedrichs‐Lewy (CFL) time step constraints of the conditionally stable explicit approach. Grid cells with a large CFL condition are updated explicitly. Combined, this allows higher efficiency than explicit methods, but it reduces the “penalty” of implicit methods, which exhibit high numerical dispersion and are more computationally and storage expensive per time step. The advantages of AIM are modest for uniform grids and rock properties. However, in heterogeneous or fractured reservoirs explicit methods may become impractical, while a fully implicit approach introduces unnecessary numerical dispersion and is overkill for low‐permeability layers and matrix blocks. In such applications, AIM is shown to be significantly more efficient and accurate. The division between explicit and implicit grid cells is made adaptively in space and time. This allows for a high level of explicitness and can also adapt to high fluxes caused by, e.g., viscous and gravitational flow instabilities. Numerical examples demonstrate the powerful features of AIM to model, e.g., solute transport, carbon sequestration in saline aquifers, and miscible gas injection in fractured oil and gas reservoirs.

FEM and EFG Quasi-Static Explicit Buckling Analysis for Thin-Walled Members

The quasi-static explicit finite element method (FEM) and element free Galerkin (EFG) method are applied to trace the post-buckling equilibrium path of thin-walled members in this paper. The factors that primarily control the explicit buckling solutions, such as the computation time, loading function and dynamic relaxation, are investigated and suggested for the buckling analysis of thin-walled members. Three examples of different buckling modes, namely snap-through, overall and local buckling, are studied based on the implicit FEM, quasi-static explicit FEM and EFG method via the commercial software LS-DYNA. The convergence rate and accuracy of the explicit methods are compared with the conventional implicit arc-length method. It is drawn that EFG quasi-static explicit buckling analysis presents the same accurate results as implicit finite element solution, but is without convergence problem and of less-consumption of computing time than FEM.

Static recovery of an AlMg4.5Mn aluminium alloy during multi-pass hot-rolling

Abstract In multi-pass hot-rolling of aluminium alloys stored energy is created by the plastic deformation in the form of dislocations and sub-grains. The energy dissipates due to sub-grain growth and the annihilation or rearrangement of dislocations. Both mechanisms lead to a reduction of dislocation density and hence a decrease in yield stress, i.e. to recovery and softening. Reliable quantitative results on these aspects, experimental as well as theoretical, are of high technological importance. Literature provides many results on the hardening and softening behaviour of aluminium alloys during plastic deformation. Few quantitative investigations, however, deal with the static softening after hot deformation. In this contribution we share recent quantitative results on the static softening behaviour of an AlMg4.5Mn aluminium alloy and its implications for the industrial hot-rolling process. We show the static softening behaviour derived from stress relaxation tests on a Baehr DIL805 dilatometer. The results agree well with a microstructure model, which is based on thermally activated dislocation climb. The activation energy for static recovery, however, is found to be outside the range predicted by theory. The relaxation results together with additional thermomechanical characterization are used to calibrate a material model based on the Kocks-Mecking equation, which has been implemented in a commercial implicit Finite-Element software. Numerical results from a three-dimensional Finite-Element model of the industrial multi-pass hot-rolling process show how static recovery affects the distribution of dislocation density across the rolling ingot between passes.

An Implicit Methodology for the Numerical Modeling of Locally Inextensible Membranes

We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

A parallel implementation of an implicit discontinuous Galerkin finite element scheme for fluid flow problems

The discontinuous Galerkin (DG) method is frequently used in computational fluid dynamics for its stability and high order of accuracy. A disadvantage of the DG method is its high computational demands. The aim of this paper is to weaken this drawback by means of parallelization of the DG algorithm. The computation is performed on a network of computers with distributed memory using the Java Remote Method Invocation, which is included in the Java programming language. The partition of the boundary value problem into n subproblems, which is then solved by n computers separately, is based on the overlapping Schwarz method. On basis of physical nature of the problem, the present paper proposes minimal size of the overlap that allows for only one Schwarz iteration thereby increasing efficiency of parallelization. The scalability and efficiency of the presented parallelization approach is demonstrated on several test problems. In order to stabilize the DG method in presence of shocks, a recently developed technique by Huerta et al. (Int. J. Numer. Meth. Fluids 69(10), 2012, 1614–1632), which introduces discontinuities in basis functions in regions with a shock, is adopted here. A modification of this approach, which lowers the computational and implementational demands, is presented here.

Energy absorption in lattice structures in dynamics: Nonlinear FE simulations

An experimental study of the stress–strain behaviour of titanium alloy (Ti6Al4V) lattice structures across a range of loading rates has been reported in a previous paper [1]. The present work develops simple numerical models of re-entrant and diamond lattice structures, for the first time, to accurately reproduce quasi-static and Hopkinson Pressure Bar (HPB) test results presented in the previous paper. Following the development of lattice models using implicit and explicit non-linear finite element (FE) codes, the numerical models are first validated against the experimental results and then utilised to explore further the phenomena associated with impact, the failure modes and strain-rate sensitivity of these materials. We have found that experimental results can be captured with good accuracy by using relatively simple numerical models with beam elements. Numerical HPB simulations demonstrate that intrinsic strain rate dependence of Ti6Al4V is not sufficient to explain the emergent rate dependence of the re-entrant cube samples. There is also evidence that, whilst re-entrant cube specimens made up of multiple layers of unit cells are load rate sensitive, the mechanical properties of individual lattice structure cell layers are relatively insensitive to load rate. These results imply that a rate-independent load-deflection model of the unit cell layers could be used in a simple multi degree of freedom (MDoF) model to represent the impact behaviour of a multi-layer specimen and capture the microscopic rate dependence.

Computational cardiology: A modified Hill model to describe the electro-visco-elasticity of the myocardium

This contribution presents a novel three-dimensional constitutive model which describes the orthotropic electro-visco-elastic response of the myocardium. The model can be regarded as the viscoelastic extension of the recently proposed generalized Hill model for orthotropic active muscle cells. The formulation extends the recent contributions of Cansız et al. (CMBBE 18: 1160–1172, 2015) and Göktepe et al. (JMPS 72: 20–39, 2014) in a novel rheological description which incorporates the active (electrical) and mechanical (viscous and elastic) deformations in a multiplicative format. To this end, the stress response is additively decomposed into passive (purely mechanical) and visco-active (electro-visco-elastic) contributions in line with a rheological model in which the passive part is connected parallel to a branch that consists of an elastic spring, a dashpot and a contractile element in serial. The former branch is assumed to be a function of the total deformation gradient while the formulation of the latter one is based on a multiplicative decomposition of the total deformation gradient into a mechanical and an active part. The active deformation gradient is devised by means of the prescribed active stretch which arises from the electrical excitation of the myocardial tissue and is governed by the intracellular calcium concentration. Thanks to the proposed rheology, marked differences are observed in isometric and isotonic tests between viscoelastic and elastic cases that are performed on material level. Moreover, novel evolution equations for the description of active stretch and intracellular calcium concentration having superiorities over the existing approaches have been proposed. On the numerical side, a fully implicit finite element formulation along with surface elements accounting for blood pressure evolution in the ventricles during successive phases of the cardiac cycle is presented. The argument of the constitutive equation describing the ventricular blood pressure is specified as the associated ventricular cavity volume which leads to the mutual interaction of the non-adjacent surface elements. The performance of the theory and algorithms are demonstrated by means of representative multi-field initial–boundary value problems. The results indicate that viscous effects significantly alter the electromechanical response of the cardiac tissue and is thought to be crucial in the virtual assessment of the cardiac function.

Modelling of the post yield response of amorphous polymers under different stress states

In this contribution, an elasto-viscoplastic constitutive model based on the single mode EGP (Eindhoven Glassy Polymer) model is proposed to describe the deformation behaviour of solid polymers subjected to finite deformations under different stress states. The polymeric material examined in this work is a specific commercial grade of Bisphenol, a polycarbonate called Makrolon 2607, for which there were experimental results available in the open literature for: uniaxial compression, plane strain compression and tensile test on a dumbbell shape specimen. The material properties of the original model are determined and calibrated from a uniaxial compression-loading test. Then, several numerical examples under different stress states are presented to illustrate the limitations of the single mode EGP model. A more general elasto-viscoplastic model is proposed, which preserves the isotropy of the original model, using the lode angle parameter to distinguish shear-dominated stress states and capture the material post yield response. The numerical treatment of the model, including the state update procedure and also the consistent tangent operator, required for the finite implementation of the model within an implicit finite element scheme, is presented. A comprehensive set of numerical examples is employed to compare the predictions of the original and new models against experimental results and to investigate the effect of the proposed modifications. The numerical results show that the proposed model provides a closer agreement with experimental evidence and opens the possibility for computational simulations of amorphous polymers under different stress states.

Linking macroscopic deformation processes to microstructure evolution using an FE‐FFT‐based micro‐macro transition and non‐conserved phase‐fields

AbstractThe purpose of this work is the multiscale FE‐FFT‐based prediction of macroscopic material behavior, micromechanical fields and bulk microstructure evolution in polycrystalline materials subjected to macroscopic mechanical loading. The macroscopic boundary value problem (BVP) is solved using implicit finite element (FE) methods. In each macroscopic integration point, the microscopic BVP is embedded, the solution of which is found employing fast Fourier transform (FFT), fixed‐point and Green's function methods. The mean material response is determined by the stress‐strain relation at the micro scale or rather the volume average of the micromechanical fields. The evolution of the microstructure is modeled by means of non‐conserved phase‐fields. As an example, the proposed methodology is applied to the modeling of stress‐induced martensitic phase transformations in metal alloys. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of Leaflet Design on Transvalvular Gradients of Bioprosthetic Heart Valves.

Bioprosthetic aortic valves (BAVs) are becoming the prostheses of choice in heart valve replacement. The objective of this paper is to assess the effects of leaflet geometry on the mechanics and hemodynamics of BAVs in a fluid structure interaction model. The curvature and angle of leaflets were varied in 10 case studies whereby the following design parameters were altered: a circular arch, a line, and a parabola for the radial curvature, and a circular arch, a spline, and a parabola for the circumferential curvature. Six different leaflet angles (representative of the inclination of the leaflets toward the surrounding aortic wall) were analyzed. The 3-dimensional geometry of the models were created using SolidWorks, Pointwise was used for meshing, and Comsol Multiphysics was used for implicit finite element calculations. Realistic loading was enforced by considering the time-dependent strongly-coupled interaction between blood flow and leaflets. Higher mean pressure gradients as well as von Mises stresses were obtained with a parabolic or circular curvature for radial curvature or a parabolic or spline curvature for the circumferential curvature. A smaller leaflet angle was associated with a lower pressure gradient, and, a lower von Mises stress. The leaflet curvature and angle noticeably affected the speed of valve opening, and closing. When a parabola was used for circumferential or radial curvature, leaflets displacements were asymmetric, and they opened and closed more slowly. A circular circumferential leaflet curvature, a linear leaflet radial curvature, and leaflet inclination toward the surrounding aortic wall were associated with superior BAVs mechanics.

Implicit finite volume and discontinuous Galerkin methods for multicomponent flow in unstructured 3D fractured porous media

We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit: pressures and fluxes are updated with an implicit Mixed Hybrid Finite Element (MHFE) method, and the transport of each species is approximated with an implicit second-order Discontinuous Galerkin (DG) FE method. Discrete fractures are incorporated with a cross-flow equilibrium approach. This is the first investigation of all-implicit higher-order MHFE-DG for unstructured triangular, quadrilateral (2D), and hexahedral (3D) grids and discrete fractures. A lowest-order implicit finite volume (FV) transport update is also developed for the same grid types. The implicit methods are compared to an Implicit-Pressure-Explicit-Composition (IMPEC) scheme. For fractured domains, the unconditionally stable implicit transport update is shown to increase computational efficiency by orders of magnitude as compared to IMPEC, which has a time-step constraint proportional to the pore volume of discrete fracture grid cells. However, when lowest-order Euler time-discretizations are used, numerical errors increase linearly with the larger implicit time-steps, resulting in high numerical dispersion. Second-order Crank–Nicolson implicit MHFE-DG and MHFE-FV are therefore presented as well. Convergence analyses show twice the convergence rate for the DG methods as compared to FV, resulting in two to three orders of magnitude higher computational efficiency. Numerical experiments demonstrate the efficiency and robustness in modeling compressible multicomponent flow on irregular and fractured 2D and 3D grids, even in the presence of fingering instabilities.

Coupling elasto-plastic self-consistent crystal plasticity and implicit finite elements: Applications to compression, cyclic tension-compression, and bending to large strains

In this work, we describe a finite element (FE) implementation of an elasto-plastic self-consistent (EPSC) polycrystal plasticity model termed FE-EPSC, which is intended for simulations of metal forming. To this end, we present an analytical Jacobian, which is necessary for the implicit coupling and ensuring a fast convergence. Every FE integration point is a material point that can be represented either by a single crystal or a polycrystalline material. The constituent crystal can deform by a combination of anisotropic elasticity, crystallographic slip, and deformation twinning. The model is validated and applied to a suite of tests, including monotonic compression, cyclic forward loading, unloading and reverse loading and non-monotonic four-point bending, and materials, such as different alloy compositions, crystal structures, and initial microstructures. The same FE-EPSC framework is applied for all these cases with the main differences pertaining to intrinsic properties, such as the available slip and twinning deformation modes, and the material parameters for activating and hardening of these modes. Full characterization for these parameters for high-purity α-Ti is presented here for the first time. Through these examples we show that, in addition to being predictive with great accuracy, the key advantage of this model lies in its versatility. It accounts for the development of backstress aided dislocation glide, thermally activated storage of dislocations, elastic anisotropy, crystallographic slip and deformation twinning via multiple modes, and de-twinning as well as multi-level homogenizations.

Analysis of the non-linear load and temperature-dependent creep behaviour of thermoplastic composite materials

Fibre-reinforced thermoplastic composite materials can be manufactured rapidly using a thermoforming process. The assortment of thermoplastic matrix systems is manifold and starts from bulk plastic like polypropylene (PP) up to high-performance systems like polyether ether ketone. High-performance thermoplastic polymers have durable properties but relatively high raw material costs. For structural application, engineering methods are needed to ensure the availability for use over the full range of the life cycle of parts. This equates to at least 15 years under exposure to varying climatic conditions for an automobile component. Bulk plastics have complex viscoelastic behaviour, which means that advanced methods are needed to ensure the long-term behaviour of both the pure plastic or fibre-reinforced materials with such a matrix system. In the following study, the creep behaviour of a glass fibre-reinforced PP material is investigated using different uniaxially loaded creep tests at different load and temperature levels. Starting from this empirical base, two characteristic creep functions are derived using a modified Burgers approach. To transfer the results of uniaxial creep situations to a three-dimensional multiaxial stress state, a method to interpolate the experimental creep curves is presented. This developed creep model is integrated into the implicit non-linear finite element program SAMCEF/Mecano and used to predict the creep behaviour of a complex laminate. The results are then validated against the performed experiments.

A Numerical Analysis on the Local Deformation of a Spacer Grid Structure for Nuclear Fuel Cells

The result of a preliminary numerical investigation on local deformation characteristics of a multi-layered spacer-grid structure with five guide tubes is reported based on implicit finite element analysis. For the numerical analysis, displacements of top and bottom cross sections of each guide tube in a single-layer model were constrained while a lateral displacement was imposed on the single layer. Unlike the impact hammer test that is generally employed to characterize the deformation characteristics of the space-grid structure, the buckling phenomenon occurs locally in this study; it takes place at the inner grids around each tube and the degree of bucking is more apparent for tubes near the lateral surface where the lateral displacement was imposed.

Whole process modeling of joining of flareless AA 6061-T4 tube by extrusion-bulging forming using a polyurethane elastomer medium

The tube joining by plastic deformation proves to be a more efficient and environmentally friendly way to achieve the tube-tube joining compared with other traditional types, such as metallurgical joining and mechanical joining. In this study, to reveal the effects of the processing parameters on the filling quality and residual contact stress, an axisymmetric finite element (FE) model of the whole joining process, including extrusion-bulging forming and unloading, was established and validated. The aluminum alloy (AA) 6061-T4 tubes, the stainless steel (ST) 15-5PH sleeve and polyurethane (PU) elastomer medium were characterized and modeled. And the implicit algorithm was adopted by comparing the prediction results between explicit and implicit FE models. The characteristics of stress distribution and plastic strain for the tube, PU elastomer and sleeve were discussed.

Simulated hail impacts on flexible photovoltaic laminates: testing and modelling

The problem of simulated low-velocity hail impacts on flexible photovoltaic (PV) modules resting on a substrate with variable stiffness is investigated. For this type of PV module it is shown that the prescriptions of the IEC 61215 International Standard for quality control used for rigid (glass-covered) PV modules should be augmented by taking into account their real mounting condition and the stiffness of the substrate in the simulated hail impact tests. Moreover, electroluminescence inspection of the crack pattern should be made in addition to electric power output measurements. An implicit finite element simulation of the contact problem in dynamics is also proposed, with two different degrees of accuracy, to interpret the experimentally observed extension of cracking. Results pinpoint the important role of stress wave propagation and reflection in the case of soft substrates.