Implicit Finite Element Analysis Research Articles

Robust and efficient implementation of finite strain generalized continuum models for material failure: Analytical, numerical, and automatic differentiation with hyper-dual numbers

Generalized continuum models for representing nonlinear material behavior including material failure in the finite strain regime are commonly formulated based on scalar elastic and dissipation potential functions. The evolution of stresses and internal variables, i.e., the material state, is governed by partial derivatives of the potential functions with respect to deformation and stress measures. Furthermore, for application of such models in implicit nonlinear finite element analysis tangent operators, consistent with the numerical integration algorithm, are required. In this work, we study analytical, numerical and automatic differentiation schemes for the implementation of coupled, generalized continuum models considering finite inelastic deformations and fracture. This includes the application of finite difference approximations, complex-step derivative approximations and automatic differentiation based on hyper-dual numbers. For the use of automatic differentiation, a semi-analytical split approach is introduced for increasing the computational efficiency. Based on a comprehensive 2D and 3D finite element study, we demonstrate the superior properties of automatic differentiation compared to numerical differentiation methods with regards to accuracy and robustness. Furthermore, the additional computational cost for automatic differentiation using the proposed split approach becomes negligible for large problems.

Implicit multiscale finite element analysis of polymer physics-based multiscale constitutive model for elastomers

This paper proposes a multiscale visco-hyperelastic constitutive model that can predict the material behavior bridging molecular properties to response at the continuum level and its integration within implicit finite element analysis. The proposed model incorporates all parameters having actual physical meaning obtained from molecular simulations based on the tube theory. Despite the advantages that the constitutive equation was determined from molecular network characteristics, applications of the model have been restricted to the simple shape of Finite Element (FE) models with a few cases of specific deformations, owing to its complexity and absence of the implicit formulation. Therefore, the application of the model to the 3D implicit FE analysis with a tangent stiffness was proposed by applying numerical differentiation with the complex step derivative approximation (CSDA) method. Combined with the Neo-Hookean hyperelasticity model, the results from the example analysis applied to the tensile specimen model were examined to manifest the visco-hyperelastic characteristics of elastomers under cyclic loading, stability of the analysis, and further discussion on the visco-hyperelastic constitutive model were proposed.

Numerical investigation of monopiles in structured clay under cyclic loading

Offshore wind is undergoing rapid growth and is expected to play a vital role in the transition to a low-carbon global economy. This paper presents the results of implicit three-dimensional finite element analyses investigating cyclic lateral loading on a large diameter monopile in structured London Clay. The cyclic behaviour of the clay was simulated using the subloading tij constitutive model. Symmetric and asymmetric two-way and one-way low frequency cyclic lateral loads were used with an amplitude representing offshore wind turbine production loading conditions. Simulations showed that one-way loads induced greater cumulative pile deformation and rotation relative to two-way loads. For all load configurations, the rate of accumulation of lateral pile displacement and rotation at mudline reduced with each subsequent cycle. In contrast, the cyclic secant stiffness progressively degraded with its rate of decay reducing with each ensuing cycle. Findings are indicative of the incidence of strain softening, reconsolidation and densification during low-frequency cyclic loading. It was established that assuming the clay to be unstructured would be conservative in the design of monopiles.

Non-iterative stress integration method for anisotropic materials

A non-iterative stress update method is proposed to accelerate finite element simulations while retaining the numerical robustness and accuracy in rate-independent plasticity. The stress tensor is directly integrated on the basis of the elastoplastic constitutive law without a recursive root-finding process such as the Newton-Raphson method. The iterative return mapping process for stress integration is avoided by first introducing an equation that guarantees the positive-definite nature of the effective plastic strain increment. Furthermore, the uncertainty of the yield condition fulfillment in a non-iterative stress update method is completely resolved by employing a stress projection technique. The numerical robustness, accuracy, and computational efficiency are comprehensively assessed through a wide range of strain increments in both implicit and explicit finite element analyses. Consequently, the computation time is remarkably reduced by more or less 50% with high fidelity in a variety of finite element simulation examples.

Nonlinear dynamics of flexible heliogyro subject to sinusoidal root pitch command

A heliogyro is a particular solar sail configuration whose reflective surface is divided into a number of long and slender blades, which are stiffened by a suitable spin-induced centrifugal force. The reflective blades can rotate around their longitudinal axes to change (either collectively or cyclically) the pitch angles and allow the spacecraft attitude (and so the thrust vector) to be effectively controlled. The aim of this paper is to perform implicit nonlinear finite element analyses of a heliogyro solar sail in order to investigate the dynamic response of the structure subject to a sinusoidal pitch command, while centrifugal stiffening and solar radiation pressure are acting on it. Using a parametric modeling approach, sensitivity studies relative to a set of design parameters are conducted for identifying possible solutions that improve the heliogyro maneuverability. In particular, by adopting the design of the proposed HELIOS spacecraft as a reference configuration, the influence of some geometric parameters and the effect of a number of structural arrangements are investigated. The performed analyses demonstrate that, compared to the reference configuration, the arrangement with a lower blade aspect ratio, same tip mass, and one traversal reinforcement at the tip is the only configuration without irreversible torsional instability of the blades when the pitch command has an amplitude of 25 deg.

Numerical Modeling of Damage Caused by Seawater Exposure on Mechanical Strength in Fiber-Reinforced Polymer Composites.

Fiber-reinforced polymer composites are frequently used in marine environments which may limit their durability. The development of accurate engineering tools capable of simulating the effect of seawater on material strength can improve design and reduce structural costs. This paper presents a numerical-based approach to predict the stress–strain response of fiber-reinforced polymer composites exposed to different seawater immersion times, ranging from 0 to 900 days. A three-dimensional numerical model has been implemented using a static implicit finite element analysis along with a user-defined material (UMAT) subroutine. Puck’s failure criterion was used for ultimate failure analysis of the laminates, while Fick’s first diffusion law was used to predict the seawater absorption rate. Overall, the simulated stress–strain curves were close to those obtained experimentally. Moreover, the model agreed well with the experimental data regarding the maximum stress and the strain at failure leading to maximum errors lower than 9% and 11%, respectively. Additionally, the simulated strain fields agreed well with the experimental results measured by digital image correlation. Finally, the proposed procedure was also used to identify the most critical surfaces to protect the mechanical components from marine environments.

Computational morphology design of duplex structure considering interface debonding

A finite volume interface is an interface region with interface strength, and is most often generated during the fabrication (3D printing) of a duplex structure. However, it is often neglected in morphology design due to numerical complexity and computational difficulties. In addition, a sharp and perfect-bonding interface is usually assumed in literatures. However, such assumptions bring failure risks, thus limiting the industrial applicability of the morphology designs of duplex structures. This study aims to identify the optimal morphology design though a computational design method, considering the finite volume interface and debonding of a duplex structure. This method is based on topology optimization, which utilizes a level-set function for optimizing material distribution in the design space. To introduce finite volume interfaces in morphology design, a simple interface debonding model is integrated into implicit finite element analysis, based on the finite strain theory. Moreover, a distance function is employed to describe the interface region in addition to a level-set function for topology optimization. Further, a topological derivative based on an adjoint variable method is formulated for a debonding interface state in a nonlinear finite element analysis, which is incorporated in topology optimization to obtain the optimal duplex structures. The numerical demonstrations verified the applicability of the proposed approach. The zigzag interface was proven to be one of the features of the optimal duplex structures, considering interface debonding. The results also indicated the optimal duplex structures considering interface debonding to be non-symmetric, in which the interfaces are primarily enriched in compression areas to ensure structural integrity.

Finite Element Modeling Approaches, Experimentally Assessed, for the Simulation of Guided Wave Propagation in Composites

Today, structural health monitoring (SHM) systems based on guided wave (GW) propagation represent an effective methodology for understating the structural integrity of primary and secondary structures, also made of composite materials. However, the sensitivity to damage detection promoted by these systems can be altered by such factors as the geometry of the monitored parts, as well as the environmental and operational conditions (EOCs). Experimental investigations are fundamental but require a long time period and are costly, especially for tests in real-life scenarios. Experimentally validated simulations can help designers to improve SHM effectiveness due to the possibility of further broadening study on the different geometries, load cases, and material types with less effort. From this point of view, this paper presents two finite element (FE) modeling approaches for the simulation of GW propagation in composite panels. The case study consists of a flat and a curved composite panel. The two approaches herein investigated are based on implicit and explicit finite element analysis (FEA) formulations. The comparison of the predicted measures against the experimental dataset allowed the assessment of the levels of accuracy provided by both modeling approaches with respect to the dispersion curves. Furthermore, to assess the different curvature sensitivities of the proposed numerical and experimental approaches, the extracted dispersion curves for both flat and curved panels were compared.

Implicit finite element analysis of ductile fracture of a steel frame under cyclic deformation

AbstractA ductile fracture model is implemented to an elastoplastic constitutive model of steel material for large‐scale finite element analysis of steel frames. The stress modified critical strain model is extended to simulate the structural response after initiation of ductile fracture. The yield stress, Young's modulus, as well as the stress are reduced using the fracture variable. Positive definiteness of the material tangent stiffness matrix is always maintained, and the unbalanced loads are carried over to the succeeding step to analyze the responses in the range of degrading strength using an implicit finite element analysis. It is shown using a notched rod model and a double notched plate that the proposed model can simulate steep stiffness degradation due to strain localization after ductile fracture. Applicability to a large‐scale finite element analysis is investigated using a component frame of moment frame subjected to cyclic forced deformation.

Characterization and modeling of continuous carbon fiber-reinforced polycarbonate under multiaxial loads

The presented work considers the characterization of a continuous fiber-reinforced thermoplastic (FRTP) with unidirectional plies under quasi-static, multiaxial loading conditions and the modeling of the non-linear mechanical behavior. For the experimental investigation, hoop wound tubular specimens fabricated from carbon fiber-reinforced polycarbonate (CF-PC) tape were tested on an electromechanical static testing machine with an axial and torsional drive. The multiaxial material response was determined for an extensive set of tests performed at several load ratios of in-plane shear to transverse stress. For modeling the non-linear mechanical response, an elasto-plastic framework is used which is kept preferably simple in order to facilitate the application in numerical analysis. Based on the generated experimental data, suitable criteria for fracture and yielding are proposed. The defined yield criterion respects the special characteristics of a FRTP such as the different mechanical behavior under transverse tensile and compressive loading as well as a linear material response in the direction of the fiber reinforcement . Furthermore, the implementation of the proposed model as a user-defined material (UMAT) routine for implicit finite element analysis (FEA) using Abaqus /Standard is described and the calibration of the plasticity approach using only the data of the in-plane shear and transverse compression tests is discussed. The model predictions for multiaxial loads are validated using the determined biaxial material data. • Multiaxial experimental data for a continuous fiber-reinforced thermoplastic • Full dataset of the arithmetic mean stress–strain curves is provided • Selection of a suitable fracture criterion and definition of a yield criterion • Development and implementation of a non-linear elasto-plastic material model • Calibration and validation of the material model using the determined multiaxial data

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.

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.

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.

Direct measurement of shot velocity and numerical analysis of residual stress from pneumatic shot peening

Shot peening is widely used in several fields to improve the fatigue strength of manufactured parts via the introduction of compressive residual stresses. The shot velocity is significant physical factor; however, it is difficult to measure this velocity directly in pneumatic shot peening. In this study, an experiment was performed to record shot movement with a high-speed camera. Particle image velocimetry (PIV) was used to measure the shot velocity distribution: the shot accelerated after being projected from the nozzle and reached a steady shot velocity at approximately 80 mm from the nozzle. The steady shot velocity was proportional to approximately the 0.51st power of the air pressure: 30 m/s at 0.14 MPa and 49 m/s at 0.35 MPa for steel shot ASR170. For an A7075 aluminum alloy, the depth of the compressive residual stress increased with the shot velocity and was greater than 0.5 mm at 0.35 MPa air pressure. Finite element analysis (FEA) was performed on the residual stress distribution with the shot velocity measured by PIV as the input value. Peening with multiple shots was evaluated through dynamic explicit FEA. The residual stress distribution after shot peening was obtained through subsequent static implicit FEA. The analytical results for the residual stress distribution complied with the experimental results. Thus, the shot velocity measurement technology and the FEA model that were used to calculate the residual stress from shot peening were both validated.

Finite Element Analysis of O-ring Sealing Performance of Manned Submersible Viewports

This paper studies the effects of compression rate, sealing gap, working medium pressure, and rubber hardness on the O-ring sealing performance of manned submersible viewports. Large-deformation contact analysis between the viewport and the seat under water depth 100–500 m is performed using implicit finite element analysis (FEA), after introducing the Mooney–Rivlin hyperelastic constitutive model for the nitrile rubber O-ring. The influence laws of various parameters above on the O-ring sealing performance of viewport are obtained by studying the distributions of the von Mises stress and contact stress as well as the contact width. This work provides numerical approach for design and analysis of the O-ring sealing of viewports.

Numerical simulation of tool wear in drilling Inconel 718 under flood and cryogenic cooling conditions

This paper aims to model and simulate tool wear in drilling of Inconel 718 under two different cooling conditions, using an innovative numerical procedure. Although tool wear models can be implemented in most of finite element analysis (FEA) software to calculate the tool wear rate, there is a great limit due to the inability of all these software to update the geometry of the worn tool. In order to overcome this limitation, a subroutine able to modify the tool geometry based on a given tool wear model was developed and implemented in DEFORM 3D, an implicit FEA software. Experimental tests were performed to measure tool wear in drilling using conventional metal working fluids (MWF) and liquid nitrogen (LN2) cooling. Experimental data were used to calibrate the tool wear model and to validate the drilling models. A comparison between simulated and measured results demonstrated the suitability of the developed drilling model to predict tool wear under both MWF and LN2 cooling conditions. Therefore, the developed model can be efficiently used to evaluate the influence of the cutting conditions (including cooling conditions) on tool wear, minimizing the number of expensive and time-consuming tool wear tests.

Three-Dimensional Explicit Finite Element Simulation of Piled-Raft Foundation

This paper aims to validate a proposed finite element model to be adopted in predicting displacement and soil stresses of a piled-raft foundation. The proposed model adopts the solid element to simulate the raft, piles, and soil mass. An explicit integration scheme has been used to simulate nonlinear static aspects of the piled-raft foundation and to avoid the computational difficulties associated with the implicit finite element analysis.
 The validation process is based on comparing the results of the proposed finite element model with those of a scaled-down experimental work achieved by other researchers. Centrifuge apparatus has been used in the experimental work to generate the required stresses to simulate the actual geostatic stress on the site. Comparing between numerical and experimental results indicate that the proposed finite element model is accurate and adequate and it can be used in future work to simulate more complicated practical problems of piled-raft foundations.
 After its validation, this model was used to investigate the effectiveness of using piled with a raft foundation that subjected to eccentric loading. In this parametric study, the value of eccentricity was taken equal to , , and . The numerical results indicated that there is a significant decrease in the bearing capacity for unpiled raft foundation compared to the piled raft foundation for the same eccentricity of the applied load.

Further study on thermal deformation reduction for CFRP-based improved ball screws

To determine the thermal deformation of ball screw in actual working condition, a novel method for determining thermal deformation of ball screws in complicated working condition is proposed based on G-code and finite-element (FE) method. In the complicated working condition, it is difficult to obtain and import the nut movement into FE model due to the complex nut movement. In this research, the nut movement is directly determined from G-code by MATLAB code programming. The nut location is recorded with time in a file. The thermal parameters can be determined according to the nut speed with time as well. In the implicit FE analysis, the nut location is read from the input file instead of nut location calculation before every time step. And then, the effect of factors, such as working condition and materials, on thermal deformation reduction of ball screw is studied. The thermal deformation reduction of ball screws under different rotational speed, actual working condition, and different axial elastic modulus of composites is discussed, which can provide the guidelines to evaluate the thermal deformation reduction and design the composite in improved ball screws.

Quasi-Dynamic Implicit Finite Element Analysis of Steel-Clad, Wood-Framed Shear Walls

HighlightsA new finite element modeling method was developed to predict performance of steel-clad, wood-framed diaphragms.The new method overcomes limitations of previous models and accurately predicts yielding and buckling behaviors.The new method will save time and money in developing design values for steel-clad, wood-frame diaphragms.Abstract. Various finite element codes and solution techniques have been developed for steel-clad, wood-framed (SCWF) shear walls over the past few decades. Most previous finite element models for SCWF shear walls under monotonic loading were based on a static implicit solution technique. Previous researchers stated that the static implicit technique showed promise for modeling SCWF diaphragms; however, the solution technique failed to converge to equilibrium as local instabilities in the form of snap-through buckling of steel cladding occurred or geometric nonlinearities were included in the model. In this study, a nonlinear quasi-dynamic implicit finite element analysis (FEA) of SCWF shear walls subjected to monotonic loading was developed to overcome the deficiencies of the static implicit approach. Three types of elements were used, including beam elements to model wood framing, shell elements to model steel cladding, and nonlinear spring elements to model connectors. Screw connector tests were conducted to obtain the load-displacement constitutive relationships needed for finite element models. Nine types of SCWF shear walls with and without lap seam stitching were tested to validate the finite element model. The ratios of predicted to test values for ultimate shear strength averaged 0.97 with a coefficient of variation (COV) of 8.1%, and the ratios for effective shear modulus averaged 1.13 with a COV of 30%. The quasi-dynamic implicit FEA is a significant improvement over previous static implicit techniques and should be a useful tool to predict the ultimate shear strength and effective shear modulus of SCWF shear walls under monotonic loading. Keywords: Diaphragm design, Post-frame building, Steel-clad wood-frame diaphragm.