Implicit Finite Element Research Articles

Modeling the Mullins effect of rubbers used in constrained‐layer damping applications

AbstractThe benefits of incorporating rubber interlayers in lightweight laminates, such as fiber‐metal laminates, in order to compensate for their usually undesirable dynamic behavior have been studied in previous works [1,2]. In such constrained‐layer damping laminates, the rubber layers undergo large deformations due to their comparably low stiffness. This motivates the consideration of large strain phenomena commonly found in rubbers even when global laminate deformations are small such as in linear dynamic analysis. This work specifically addresses the cyclic softening of filled rubbers commonly known as the Mullins effect. As this effect significantly influences the elastic properties of the material, a change in the dynamic behavior of the laminate is to be expected. A constitutive model based on the work of Dorfmann and Ogden [3] for the prediction of the cyclic softening as well as residual strains upon unloading is presented in this study. Special consideration is given to the implementation of the model for use in a commercial implicit finite element solver by building on the work of Connolly et al. [4]. The model is validated against experimental data and compared to a current state‐of‐the‐art model with regard to its predictive quality and computational efficiency. Furthermore, the experimental identification of material parameters for said model is addressed.

Characteristics of cyclic undrained model SANISAND-MSu and their effects on response of monopiles for offshore wind structures

Optimised design is essential to reduce the cost of monopiles for offshore wind turbines. For this purpose, an in-depth understanding of the behaviour of monopile–soil interaction is required. As more wind farms are planned in seismically active areas, the undrained behaviour of sandy soils (and the possibility of soil liquefaction) and these soils’ effects on monopile cyclic response need critical evaluation. Considering the lack of well-established test programs, implicit three-dimensional (3D) finite-element (FE) methods stand out as a robust tool to identify and highlight the governing geo-mechanisms in monopile design. In this work, an implicit 3D FE implementation of SANISAND-MS for undrained soil behaviour, termed SANISAND-MSu, is deployed in OpenSees to serve these objectives. The role of pore-water pressure on monopile performance is comprehensively investigated by comparisons between drained and undrained soil behaviour. Local soil responses are studied in detail in relation to parameters in laboratory soil testing and application to monopile geotechnical design. The results of simulations are also used to evaluate numerical p–y curves as a function of the number of load cycles on the pile. The conclusions in this work contribute to ongoing research on monopile–soil interaction and support the development of lifetime analysis for monopile–soil systems.

A molecular structure-informed viscoelastic constitutive model for natural rubber materials

This paper presents a molecular structure-informed viscoelastic constitutive equation that adopts the Doi–Edward’s tube model with coarse-grained molecular dynamics simulation and primitive path analysis. Since this model contains polymer physics-related parameters directly obtained from molecular simulations, it can reflect molecular information in predictions of the viscoelastic behavior of elastomers, unlike other empirical models. The proposed incremental formulations and constitutive stiffness matrix were implemented into implicit finite element analysis codes as a user-supplied material model and viscoelastic properties (storage, loss modulus, and ) were calculated from the constitutive equation. While obtaining polymer dynamics parameter of the molecular system, a relationship between self-diffusivity coefficient () and the polymerization degree of the polymer was confirmed. Furthermore, a series of parametric studies showed that increase of the primitive path length (L) and decrease of have led to the strengthening of moduli and decrease of peak. Moreover, under the same condition, the shift of peak to low-frequency domain was observed, which implies a decline in free volume in the molecular system and an increase in the glass transition temperature.

Tray forming operation of paperboard: A case study using implicit finite element analysis

AbstractThe possibility to perform advanced forming operations of initially plane paperboard paves the way to making products like food trays, plates, cups and other containers as a part of shifting towards a circular bioeconomy. As a part of the ongoing efforts of expanding the product range using paperboard, we performed analyses of the forming operation using simulations. An implicit non‐linear finite element model is built to more accurately than previous studies simulate the tray forming process of paperboard. Two different commercial paperboards are investigated. The use of an implicit solver enabled the inclusion of the creasing pattern into the geometry of the paperboard blank resolving the formation of wrinkles during forming. The material data is extracted from tensile test curves of the investigated paperboards and was fitted accurately using Hill's plasticity with difference in tension and compression accounted for with subsequent failure evaluation. The results showed that the inclusion of the creases in the geometry is vital for getting a correct shape of the formed tray and important for decreasing the risk of failure. The results also showed that friction has a big impact on the formed shape and hence on the stress levels, and therefore supports the means of lowering friction between the blank holder and the blank during the tray forming operation. A stochastic approach is proposed to determine the probability of failure for the boards. The performed failure evaluation is consistent with the field observations. The developed approach enables more precise simulations of paperboard tray forming.

In Silico Evaluation of Bilinear Elastoplastic Coronary Artery Stents

Mechanical responses of the endovascular stent determine the arterial homeostasis and vulnerability of the atherosclerotic plaque. Given the various plaque components when the stent is deployed, the stent may apply excessive stress to the lesion and cause plaque rupture. Herein, using the interaction between the Palmaz–Schatz stent with two stent biomaterials, stainless steel, and magnesium alloy, and three different types of plaque, namely hypocellular, hypercellular, and calcified, are studied. An implicit finite element method is used to simulate and analyze the stress and strain acting on the stents, artery, and plaques. The Mooney–Rivlin hyperelastic material model is considered to study the responses of each component. The results reveal that stainless‐steel stents applied a higher level of stress to the plaques and vessel wall, which may lead to vascular damage and plaque rupture. However, a magnesium alloy stent with the similar design and geometrical parameters generates less stress on the plaque and artery. Interestingly, a minor improvement in magnesium alloy stents, increasing the strut thickness, can enhance the stent performance and lower the applied stresses to the vasculature and plaque, making them an ideal choice of material for stenting applications.

On the delamination of polyvinyl butyral laminated glass: Identification of fracture properties from numerical modelling

This work investigates the delamination behaviour of polyvinyl butyral (PVB) laminated glass under quasi-static loading based on a cohesive zone model (CZM) with an isotropic bilinear traction - separation (T – δ) law. It presents a 2D model of a through-cracked tensile (TCT) test within an implicit finite element framework of the commercial software ANSYS. Test results from literature are used to calibrate the adhesion properties of the PVB-glass interface in a numerical cohesive zone approach. The previous TCT tests were performed at a loading rate of 6 mm/min and a temperature of approx. 22 °C. Three different PVB adhesion grades, i.e., BG R10 (low), BG R15 (medium) and BG R20 (high) are considered. Given the uncertainty in the identification of adhesion parameters, including interfacial fracture energy, cohesive strength and stiffness, a parametric analysis is conducted quantifying the influences of model parameters on the simulation results. The study allows for decoupling of individual parameters in the calibration. Then, interfacial fracture energies and cohesive strengths of the PVB-laminated glass are calibrated by matching the force – displacement curves of the numerical simulations with those from the TCT experiments. One representative case was chosen for each adhesion grade. We obtain interfacial fracture energies of 425 J/m2, 650 J/m2 and 1000 J/m2 for BG R10, BG R15 and BG R20 PVBs, respectively, while the corresponding cohesive strengths are 3 MPa, 5 MPa and 10 MPa, respectively. Moreover, based on numerical simulation results, the conversion of energy during the delamination process is extracted and discussed. The mixed-mode delamination mechanism is investigated by calculating the mode I and mode II energy release rates with respect to different PVB thicknesses and adhesion. The results show that the proportion of the mode I energy release rate is around 30%∼40% of the total energy release rate at the stable delamination stage and increases with PVB thickness. The presented study contributes to the adhesion properties of various types of PVB interlayers reported in open literatures and proposes a methodology for the unique identification of adhesion properties.

A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation.

In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.

Linear and nonlinear benchmarks between the CLT code and the M3D-C1 code for the 2/1 resistive tearing mode and the 1/1 resistive kink mode

The linear and nonlinear benchmarks between the CLT code and the M3D-C1 code for the 2/1 resistive tearing mode and the 1/1 resistive kink mode are presented. CLT is an explicit finite difference code, while M3D-C1 is an implicit finite element code. Although the implementations of CLT and M3D-C1 are totally different, we find that the simulation results of the resistive-kink mode and the m/n=2/1 tearing mode from M3D-C1 and CLT are almost the same, including the linear and nonlinear growth rates, the mode structures, the nonlinear saturation levels, the Poincare plots, and the scaling laws. This confirms that the nonlinear results for the 1/1 resistive-kink mode and 2/1 tearing mode are accurate and reliable.

Conservative semi-Lagrangian kinetic scheme coupled with implicit finite element field solver for multidimensional Vlasov Maxwell system

In this paper, a conservative semi-Lagrangian (CSL) kinetic scheme coupled with an implicit finite element method (IFEM) is developed for multidimensional electromagnetic plasma simulations. The present method (CSL-IFEM) enjoys the respective advantages of the CSL and IFEM, including mass conservation, high-order spatial accuracy, as well as being free from the Courant-Friedrichs-Lewy (CFL) condition. In present CSL-IFEM, the CSL scheme with a general high order positivity-preserving limiter is utilized for the spatial discretization of the Vlasov equation, which enables the proposed method to remove the CFL limitation in phase space, exactly conserve mass, and preserve the positivity of the distribution function. The IFEM solver is developed for the spatial discretization of the Maxwell equation, which makes the current method free from CFL limitation induced by the speed of light and easily handles general field boundary conditions. To make the proposed CSL-IFEM more efficient in multidimensional simulations, the dimensional splitting procedure and sparse matrix technology are implemented in CSL and IFEM, respectively. Then the Vlasov solver CSL and Maxwell solver IFEM are coupled via the current density calculated from the general Ohm law. Finally, several numerical experiments, including electromagnetic wave (2d0v), particle gyromotion (0d2v), streaming Weibel instability (1d2v) and magnetic reconnection (2d3v), are performed to demonstrate the capabilities of the proposed method.

Efficiency of room acoustic simulations with time-domain FEM including frequency-dependent absorbing boundary conditions: Comparison with frequency-domain FEM

Recent wave-based room acoustic simulations in the time domain can incorporate frequency-dependent absorbing boundary conditions (BCs), by which time responses including a broad frequency component are calculable with a single computational run. However, their performance over the frequency-domain method remains poorly understood. This paper presents a discussion of the capabilities of a recently developed implicit time-domain finite element method (TD-FEM) for room acoustics simulation by comparison with a fourth-order accurate frequency-domain FEM (FD-FEM). First, the implicit TD-FEM accuracy is examined via an impedance tube problem, having frequency-dependent absorbing BCs at the tube end, where a specific acoustic admittance ratio of rigidly backed porous sound absorbers is imposed. Results indicate that the implicit TD-FEM has the same solution convergence rate as that of FD-FEM. The solution converges to the FD-FEM solution when using a sufficiently small time interval. A performance comparison of both methods is then made using two real-scale 2D room acoustic problems in an office room and a complexly shaped concert hall. Numerical results show that the implicit TD-FEM can be useful for acoustic simulation in practical-sized rooms at broad frequency ranges with markedly smaller computational costs than those of FD-FEM while maintaining similar accuracy.

Influence of balloon design, plaque material composition, and balloon sizing on acute post angioplasty outcomes: An implicit finite element analysis.

In this work we propose a generic modeling approach for simulating percutaneous transluminal angioplasty (PTA) endovascular treatment, and evaluating the influence of balloon design, plaque composition, and balloon sizing on acute post-procedural outcomes right after PTA, without stent implantation. Clinically-used PTA balloons were classified into two categories according to their compliance characteristics, and were modeled correspondingly. Self-defined elastoplastic constitutive laws were implemented within the plaque and artery models, after calibration based on experimental and clinical data. Finite element method (FEM) implicit solver was used to simulate balloon inflation and deflation. Besides balloon profile at max inflation, results are mainly assessed in terms of the elastic recoil ratio (ERR) and lumen gain ratio (LGR) obtained immediately after PTA. No variations in ERR nor LGR values were detected when the balloon design changed, despite the differences observed in their profile at max inflation. Moreover, LGR and ERR inversely varied with the augmentation of calcification level within the plaque (-11% vs. +4% respectively, from fully lipidic to fully calcified plaque). Furthermore, results showed a direct correlation between balloon sizing and LGR and ERR, with noticeably higher rates of change for LGR (+18% and +2% for LGR and ERR respectively for a calcified plaque and a balloon pressure increasing from 10 to 14 atm). However a larger LGR comes with a higher risk of arterial rupture. This proposed methodology opens the way for evaluation of angioplasty balloon selections towards clinical procedure optimization.

A microstructurally motivated constitutive description of collagenous soft biological tissue towards the description of their non-linear and time-dependent properties

A versatile constitutive model for load-carrying soft biological tissue should incorporate salient microstructural deformation mechanisms and be able to reliably predict complex non-linear viscoelastic behavior. The advancement of treatment and rehabilitation strategies for soft tissue injuries is inextricably linked to our understanding of the underlying tissue microstructure and how this defines its macroscopic material properties. Towards this long-term objective, we present a generalized multiscale constitutive framework based on a novel description of collagen, the most mechanically significant extracellular matrix protein. The description accounts for the gradual recruitment of undulated collagen fibrils and introduces proteoglycan mediated time-dependent fibrillar sliding. Crucially, the proteoglycan deformation allows for the reduction of overstressed fibrils towards a preferential homeostatic stress. An implicit Finite Element implementation of the model uses an interpolation strategy towards collagen fiber stress determination and results in a memory-efficient representation of the model. A number of test cases, including patient-specific geometries, establish the efficiency of the description and demonstrate its ability to explain qualitative properties reported from macroscopic experimental studies of tendon and vascular tissue.

Analysis of finite element two-grid algorithms for two-dimensional nonlinear Schrödinger equation with wave operator

Two-grid algorithms based on two conservative and implicit finite element methods are studied for two-dimensional nonlinear Schrödinger equation with wave operator. The existence and uniqueness of their solutions and the conservative laws are established for both schemes. To linearize the fully discrete nonlinear coupling problem, the original problem is decomposed into two equivalent nonlinear coupled hyperbolic–parabolic equations. Algorithm 1 has three steps based on one Newton iteration on the fine grid and further correction on coarse grid, while Algorithm 2 has three steps based on two Newton iterations on the fine grid. Optimal order Lp error estimations of the two-grid algorithms are conducted in detail by optimal order Lp error estimates of finite element methods without any time-step size conditions. Both theoretically and numerically are shown that the coarse space can be extremely coarse, with no loss in the order of accuracy, and the two-grid algorithms still achieve the optimal convergence order when the mesh sizes satisfy H=O(h13) for Algorithm 1 and H=O(h14) for Algorithm 2.

Simulating Extraocular Muscle Dynamics. A Comparison between Dynamic Implicit and Explicit Finite Element Methods

The finite element method has been widely used to investigate the mechanical behavior of biological tissues. When analyzing these particular materials subjected to dynamic requests, time integration algorithms should be considered to incorporate the inertial effects. These algorithms can be classified as implicit or explicit. Although both algorithms have been used in different scenarios, a comparative study of the outcomes of both methods is important to determine the performance of a model used to simulate the active contraction of the skeletal muscle tissue. In this work, dynamic implicit and dynamic explicit solutions are presented for the movement of the eye ball induced by the extraocular muscles. Aspects such as stability, computational time and the influence of mass-scaling for the explicit formulation were assessed using ABAQUS software. Both strategies produced similar results regarding range of movement of the eye ball, total deformation and kinetic energy. Using the implicit dynamic formulation, an important amount of computational time reduction is achieved. Although mass-scaling can reduce the simulation time, the dynamic contraction of the muscle is drastically altered.

Element activation method and non-conformal dynamic remeshing strategy to model additive manufacturing

Modeling of Additive Manufacturing (AM) at the part scale involves non-linear thermo-mechanical simulations. Such a process also imposes a very fine discretization and requires altering the geometry of the models during the simulations to model the addition of matter, which is a computational challenge by itself. The first focus of this work is the addition of an additive manufacturing module in the fully implicit in-house Finite Element code Metafor [1] which is developed at the University of Liège. The implemented method to activate elements and to activate and deactivate boundary conditions during a simulation is adapted from the element deletion algorithm implemented in Metafor in the scope of crack propagation [2]. This algorithm is modified to allow the activation of elements based on a user-specified criterion (e.g. geometrical criterion, thermal criterion, etc.). The second objective of this work is to improve the efficiency of the AM simulations, in particular by using a dynamic remeshing strategy to reduce the computational cost of the simulations. This remeshing is done using non-conformal meshes, where hanging nodes are handled via the use of Lagrange multiplier constraints. The mesh data transfer used after remeshing is based on projection methods involving finite volumes [3]. The presented model is then compared against a 2D numerical simulation of Direct Energy Deposition of a High-Speed Steel thick deposit from the literature [4].

Coupled electro-chemo-elasticity: Application to modeling the actuation response of ionic polymer–metal composites

We have formulated a large deformation thermodynamically-consistent electro-chemo-elasticity theory for modeling the actuation response of ionic polymer–metal composites. Our theory accounts for the simultaneous evolution of the electric potential, the concentration of the mobile hydrated cations, and the deformation of the host ionic polymer matrix. We have numerically implemented our theory in an implicit finite element program. We use this simulation capability to first calibrate the material parameters in the theory for a Nafion-based ionic polymer–metal composite, and then validate our theory by comparing predictions from the theory against other experimental data available in the literature. We also demonstrate the utility of our simulation capability by conducting full three-dimensional simulations of two soft-robotics applications with some geometric complexity: (i) a biomimetic fin, and (ii) a micro-gripper.

An implicit discontinuous Galerkin finite element discrete Boltzmann method for high Knudsen number flows

Simulations of the discrete Boltzmann Bhatnagar–Gross–Krook equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a discontinuous Galerkin finite element method for spatial discretization of the discrete Boltzmann equation for isothermal flows with high Knudsen numbers [Kn∼O(1)]. In conjunction with a high-order Runge–Kutta time marching scheme, this method is capable of achieving high-order accuracy in both space and time, while maintaining a compact stencil. We validate the spatial order of accuracy of the scheme on a two-dimensional Couette flow with Kn=1 and the D2Q16 velocity discretization. We then apply the scheme to lid-driven micro-cavity flow at Kn=1,2,and 8, and we compare the ability of Gauss–Hermite (GH) and Newton–Cotes (NC) velocity sets to capture the high non-linearity of the flow-field. While the GH quadrature provides higher integration strength with fewer points, the NC quadrature has more uniformly distributed nodes with weights greater than machine-zero, helping to avoid the so-called ray-effect. Broadly speaking, we anticipate that the insights from this work will help facilitate the efficient implementation and application of high-order numerical methods for complex high Knudsen number flows.

Large Deformation Finite Element Analyses for 3D X-ray CT Scanned Microscopic Structures of Polyurethane Foams.

Polyurethane foams have unique properties that make them suitable for a wide range of applications, including cushioning and seat pads. The foam mechanical properties largely depend on both the parent material and foam cell microstructure. Uniaxial loading experiments, X-ray tomography and finite element analysis can be used to investigate the relationship between the macroscopic mechanical properties and microscopic foam structure. Polyurethane foam specimens were scanned using X-ray computed tomography. The scanned geometries were converted to three-dimensional (3D) CAD models using open source, and commercially available CAD software tools. The models were meshed and used to simulate the compression tests using the implicit finite element method. The calculated uniaxial compression tests were in good agreement with experimental results for strains up to 30%. The presented method would be effective in investigating the effect of polymer foam geometrical features in macroscopic mechanical properties, and guide manufacturing methods for specific applications.

Blank thinning predictions of an aluminum alloy in hole expansion process using finite element method

The main objective of this study is to accurately predict the thinning behavior of AA6016-O aluminum alloy in the hole expansion test. In order to perform this aim, three yield functions, namely isotropic von Mises, quadratic Hill48 and non-quadratic Yld91, are considered and their prediction capabilities are evaluated in this study. Firstly, finite element (FE) model of hole expansion test is created by implicit FE software Marc, then FE simulations are performed with each yield criterion. In order to assess prediction capabilities of these yield criteria, thickness strain distributions along the three directions of the sheet (rolling, diagonal and transversal) and punch force–displacement curves are investigated. The results predicted from FE analyses are compared with experimental results. From the comparisons, it is observed that Yld91 yield criterion could successfully predict the thickness strain distributions along the rolling and transverse directions, whereas the other two criteria could only predict the thickness strain distributions along the diagonal direction. On the other hand, it is determined that punch force–displacement curves predicted from three models are identical and these predictions are overestimated compared to experimental data.

Spherical center axial hinge knee prosthesis causes lower contact stress on tibial insert and bushing compared with biaxial hinge knee prosthesis

BackgroundMotion axial system may affect contact stress of hinge knee prosthesis. However, it is unclear which axial system provides the better biomechanical effect. Therefore, the aim of this study was to compare the contact stress and stress distribution on the tibial insert and the bushing of hinge knee prostheses with a biaxial (BA) system and a spherical center axial (SA) system during a gait cycle. MethodsThree-dimensional finite-element (FE) models of the prostheses with different motion systems were included. The comparisons between experimental tests and FE analyses were performed to verify the models. Dynamic implicit FE analyses were performed to investigate the peak contact stresses and stress distributions on the tibial insert and the bushing. ResultsThe peak contact stresses on the tibial insert and the bushing of the BA prosthesis were higher than those of the SA prosthesis during most gait cycles. The contact time on the bushing is short in the SA prosthesis. The stress distributions on the superior surface of the tibial insert in the BA prosthesis were at the posterior side, but of the SA prosthesis were not fixed. ConclusionThe SA prosthesis has a lower peak contact stress on tibial insert and bushing than the BA prosthesis; in addition, the SA prosthesis has a ‘self-adjustment’ mechanism which could disperse high stress on the tibial insert to decrease the risk of wear and damage. The comparison could help designers and surgeons to better understand the future design of rotating hinge knee prostheses which should be able to achieve multiaxial motion and complete weight bearing by the tibial condylar to transmit the axial force better.