Commercial Finite Element Software Research Articles

A Modular Nitinol Model with Lode Angle-Based Asymmetry and Improved Representation of the Superelastic Loops for Medical Device Applications

Abstract We describe a phenomenological constitutive model for representing Nitinol in medical device applications. The intent is to capture some of the response features important to medical device applications that are neglected in prevalent state of the art models. These features include better representation of the response under compression which is needed to assess bending, and asymmetric plastic yield. We will refer to this implementation as the Thornton Tomasetti (TT) model to distinguish it from other existing implementations that have evolved from the baseline underlying theory. We implement the model in a modular form suitable for use in commercial finite element software and describe initialization from laboratory test data.

Direct integration of measured viscoelastic relaxation data in time-domain finite element simulations

The current approach to modeling viscoelastic materials in most commercial finite element packages is based on the General Maxwell Model, which views these materials as combinations of spring and dashpot elements. However, the data can be incorporated more directly into a transient finite element study by direct interpolation of the relaxation function. This work explores a linear interpolation scheme to the inclusion of viscoelastic relaxation functions on an example problem. The results show several benefits over the General Maxwell Model for transient studies. Included in the analysis are displacement solutions utilizing both approaches, relaxation function error calculations for both approaches, and parametric runtime studies comparing speed of calculation. The variation in computational flop counts is considered and an argument is made for the preference of the proposed approach.

Incorporation of self-heating effect into a thermo-mechanical coupled constitutive modelling for elastomeric polyurethane

Elastomeric polyurethane (EPU) is characterised by distinctive mechanical properties, including high toughness, low glass transition temperature, and high impact resistance, that render it indispensable in diverse engineering applications from soft robotics to anti-collision devices. This study presents a thermo-mechanically coupled constitutive model for EPU, systematically incorporating hyperelasticity, viscoelasticity, thermal expansion, and self-heating effect in a thermodynamically consistent manner. Experimental data, obtained from previous studies, are then used for parameter identification and model validation, including iterative updates for temperature parameters considering the self-heating effect. Subsequently, the validated model is integrated into finite element codes, i.e., user subroutine to define a material’s mechanical behaviour (UMAT) based on the commercial finite element software ABAQUS, for the computation of three-dimensional stress-strain states, facilitating the analysis of the structural response to various mechanical loads and boundary conditions. The results obtained from simulations are compared with analytical solutions to confirm the precision of Finite Element Method (FEM) implementation. The self-heating effect is further analysed under different strain rates and temperatures. To validate the engineering significance of the FEM implementation, a plate with a hole structure is also simulated. In conclusion, this research provides a robust tool for engineers and researchers working with soft materials, enhancing their understanding and predictive capabilities, notably addressing the self-heating effect in thermo-mechanical behaviours.

Boundary element method for bending-extension coupling shear deformable laminated composite plates with multiple stiffeners

In general, the laminated composite plates and stiffeners may exhibit the bending-extension coupling effect with the transverse shear deformations significantly induced. In this paper, for the first time we develop the associated boundary element method (BEM) for bending-extension coupling shear deformable laminated composite plates with multiple beams attached as stiffeners. Based upon the first order shear deformation theory, the individual boundary integral equations (BIEs) for plates and stiffeners are obtained from their corresponding matrix-form basic equations. To account for perfect bonding conditions between plate and stiffeners, we establish displacement continuity and interaction load equilibrium relations at their interfaces. To calculate the domain integrals related to unknown interaction loads, we discretize each stiffener into a series of cells using quadratic interpolation. By collecting the individual BIEs for plates and stiffeners and employing the continuity and equilibrium relations at the interfaces, we construct the entire system of linear equations to solve for all the unknown nodal quantities. Additionally, the complete solutions at the plate boundary, at internal points or along a stiffener are provided. The correctness of our present BEM formulation is verified through two representative examples by comparison with the commercial finite element software ANSYS. The numerical results demonstrate that our BEM formulation surpasses the conventional finite element method and is highly desirable for general stiffened laminated plates with bending-extension coupling and transverse shear deformations.

Thermal-magnetic coupling inhomogeneous temperature field analysis of cylindrical eddy current brakes

With the increasing requirements for safety and reliability, it is now necessary to analyze the thermal characteristics to the same extent as the electromagnetic design for eddy current brakes(ECB), because the working characteristic will be greatly influenced by temperature. In this paper, the transient thermal-magnetic coupling analysis of permanent magnet cylindrical eddy current brake, which is used as the recoil mechanism in artillery, is presented. First, the structure and working principle of this ECB are described in detail. Second, the analytical electromagnetic model is established by multilayer theory to derive the heat source of this ECB. Thirdly, the thermal-magnetic coupling model is established to calculate the dynamic inhomogeneous temperature field of the ECB. The heat conduction equation is solved in different regions with inhomogeneous internal heat source by Finite Difference method(FDM) in two-dimensional cylindrical coordinate. Finally, the validity of the proposed model is verified by commercial Finite Element software. The thermal characteristic and its effects on braking force is analyzed during working. The maximum value of temperature approximately rises by 16℃ in each firing. The braking force will decline by 8% considering temperature.

A generalization of B-differentiable equations method for elastoplastic contact problems with dual mortar discretization

In this study, a novel method based on the B-differentiable equations (BDEs) is proposed to solve the three-dimensional (3D) static and dynamic elastoplastic contact problems with friction. The contact conditions are formulated as the BDEs system, which can precisely satisfy Coulomb’s law of friction. Based on the mortar segment-to-segment contact model, the contact constraints are enforced by dual Lagrange multipliers for nonconforming meshes of the contact boundary. The non-smooth and nonlinear system equations composed of equilibrium and contact equations are simultaneously solved by the B-differentiable damping Newton method (BDNM), which has global convergence property. In each iteration, firstly, some contact displacements and contact forces, called substituted contact variables, are expressed by others according to the different contact states and contact conditions. The equilibrium equation is then solved, where the stiffness matrix is updated by substituting the contact variables. At last, the substituted contact variables will be restored. In the proposed method, the contact flexibility matrix is no longer needed, which saves the time for calculating the contact flexibility matrix due to changes in the stiffness matrix resulting from the update of stresses in the iteration step. By comparing with the results obtained by finite element commercial software ANSYS, the accuracy of the proposed algorithm is verified, and the property of convergence and efficiency are demonstrated for the elastoplastic contact problems by several numerical examples.

Influence of Fire-Flame Temperature and Duration on the Behavior of Reinforced Concrete Beams with Construction Joints

Structural members' durability and strength depend on the member’s fire resistance. This study simulates the structural response of a reinforced concrete beam with a construction joint exposed to fire. The commercial finite element software ABAQUS was used to validate the laboratory findings. The testing program tested five reinforced concrete beams with the dimensions of (200x300x2700 mm), having identical reinforcing details and a concrete compressive strength (fc'=35 MPa). These beams had a 45° angled connection at the center. Four beams were exposed to fire flames at two temperature levels (600 °C and 800 °C) and for 1.0 and 2.0 hr. periods, respectively. The fifth beam is the control beam that was not exposed to fire. Laboratory results show that the worst exposure on the beam’s construction joint was at 800 °C with an exposure period of 2 hrs. This exposure reduces the bond between the joint’s two surfaces, creating a slipping effect in which disconnection occurs after loading. After 1 and 2 hours of exposure to fire at 600 °C, the residual flexural strength was 85% and 72% of that of the control beam, respectively. Whereas, beams exposed to fire for 1 and 2 hours at 800 °C showed flexural strengths lower than the control beam at 41% and 28%, respectively. Regarding the modulus of elasticity and compressive strength, they both showed residual values of (63.5, 59.2, 50.9, and 47%), and (28, 25, 19, and 16%), respectively.

Simulation of Preload Relaxation of Bolted Joint Structures under Transverse Loading

In this study, based on the Iwan model, the connection interface of the bolted joint structure subjected to lateral loads was simulated and comparatively analyzed. Commercial finite element software was used to model the bolted joint structure. Monotonic lateral loads and cyclic displacement loads were applied to the model. The changes in the preload force of the bolted connection structure, as well as the changes in the sticking zone and stress state of the connection interface, were analyzed, and the loading results of monotonic load and cyclic displacement load were compared. The results show that the contact interface stress decreases with the increase in displacement load, and this increase is also a nonlinear relationship, which is approximately in phase with the trend of the contact surface slip curve. The amount of contact surface stress loss and the amount of preload loss are not directly related to the magnitude of the initial preload, regardless of the loading conditions. The contact surface is also circular under any form of displacement loading, whether it is stressed or slipped. The amount of preload loss is proportional to the amount of bolt compression for that variable.

Investigations on the Johnson-Cook Constitutive and Damage-Fracture Model Parameters of a Q345C Steel

Due to the rapid development of high-speed trains, the service safety of vehicle body materials and structures has become a focal point in transport and impact engineering. Numerical simulations on the collision resistance of vehicle materials and structures are crucial for the safety assessment and optimal structural design of high-speed trains but have not been fully investigated due to the lack of damage model parameters. This study focuses on the Johnson-Cook (J-C) constitutive and damage-fracture models of a typical vehicle material, Q345C steel. A series of mechanical tests are conducted on the Q345C steel, including the quasi-static and dynamic compression/tension tests, quasi-static tension tests at different temperatures, and fracture tests along different stress paths, using the material test system and the split Hopkinson pressure/tension bar. Then, the parameters of the Johnson-Cook constitutive and damage-fracture models are calibrated based on the experimental results. In terms of the damage parameters related to stress paths, a new method of combining experiments and simulations is proposed to obtain the real, local fracture strains of the Q345C steel samples. This method allows the measurements of equivalent plastic strain and stress triaxiality histories under nonlinear stress paths, which are hardly accessible from individual experiments, and facilitates the accurate calibration of stress-path-related damage parameters. In addition, a high-speed plate penetration test is used to validate the J-C parameters, which can be directly implemented in the commercial finite element software Abaqus. The projectile trajectories from the simulation and experiment agree well with each other, demonstrating the reliability of the model parameters for impact scenarios and the efficiency of the experimental procedures utilized for calibration.

A thermodynamically consistent phase field model for brittle fracture in graded coatings under thermo-mechanical loading

This paper presents a thermodynamically consistent phase field formulation designed for investigating quasi-static brittle fracture under thermo-mechanical loading conditions in functionally graded materials. The governing equations for linear momentum and crack evolution are derived by minimizing the free energy functional, which includes elastic strain energy and surface energy, with respect to displacement field and the phase field variable, respectively. A thermodynamically consistent formulation is employed to establish the governing equation for heat conduction. The proposed formulation is converted into a set of finite element equations using the Ritz method and implemented in COMSOL Multiphysics, a commercial finite element software which allows for writing governing equations in their strong form. A segregated solver is utilized to solve iteratively the coupled problem. The proposed model is verified against existing mechanical and thermo-mechanical phase field models, demonstrating good agreement with the literature. To explore the model’s capabilities, a graded layer composed of Zirconia and a Titanium alloy with a surface crack undergoing thermo-mechanical loading is considered as a case study for this investigation. Additionally, the model incorporates a thermal conductivity degradation proposed. A parametric study is performed to investigate the effect of varying parameters like volume fraction, thermal loading rate, and the thermal conductivity degradation on the load–displacement curve of the graded layer. These findings contribute to the understanding of thermo-mechanical behavior of surface graded layers and serve as a foundation for addressing more complex thermo-mechanical problems.

Dynamic characteristics testing and modeling in electromagnetic-thermal-force coupling of electromagnetic devices using parallel finite element simulation

Electromagnetic systems of Electromagnetic devices involve multiphysics coupling of electromagnetic fields, electrical circuits, mechanical motion, and temperature fields. When the digital prototype model has a large number of meshes, the commercial finite element software also has the disadvantage of long computation time in the simulation of dynamic characteristics of electrical apparatus. This paper proposes a transmission line method (TLM) based digital modeling method for the electromagnetic-thermal-force coupling to test and evaluate the static and dynamic characteristics of electromagnetic devices more accurately and efficiently. The case study is developed on a direct current (DC) contactor, and the dynamic characteristics testing and modeling in the electromagnetic-thermal-force coupling of the contactor are investigated. The numerical results of the finite element method (FEM) model for the electromagnetic system of the contactor are compared with the commercial FEM software Altair Flux and the experimental results, which demonstrate the exceptional accuracy of the proposed digital modeling method for the multiphysics coupling of the DC contactor. Meanwhile, the dynamic characteristics of the DC contactor at different ambient temperatures are measured and evaluated, and the comparison with the experimental measurements shows the applicability of the proposed digital prototype model at different ambient temperatures. Compared with the conventional Newton-Raphson (NR) iteration, when dividing fine mesh and extremely fine mesh, the TLM parallel computing significantly improves the efficiency of solving the dynamic characteristics of multiphysics coupling by about 35 % and 44 % with the same computational accuracy, respectively. The dynamic characteristics evaluation method combined with digital modeling technology and experimental measurements proposed in this paper demonstrates high accuracy and solving efficiency, making a notable contribution to the field of design and optimization of electromagnetic devices.

Parametric study for model calibration of a friction-damped turbine blade with multiple test data

Model updating using multiple test data is usually a challenging task for frictional structures. The difficulty arises from the limitations of nonlinear models which often overlook the uncertainties inherent in contact interfaces and in actual test conditions. In this paper, we present a parametric study for the model calibration process of a friction-damped turbine blade, addressing the experimentally measured response variability in computational simulations. On the experimental side, a recently developed test setup imitating a turbomachinery application with mid-span dampers is used. This setup allows measuring multiple responses and contact forces under nominally identical macroscale conditions. On the computational side, the same system is modeled in a commercial finite element software, and nonlinear vibration analyses are performed with a specifically developed in-house code. In numerical simulations, the multivalued nature of Coulomb’s law, which stems from the inherent variability range of static friction forces in permanently sticking contacts, is considered to be the main uncertainty. As the system undergoes vibration, this uncertainty propagates into the dynamic behavior, particularly under conditions of partial slip in contacts, thus resulting in response variability. A deterministic approach based on an optimization algorithm is pursued to predict the limits of the variability range. The model is iteratively calibrated to investigate the sensitivity of response limits to contact parameters and assembly misalignment. Through several iterations, we demonstrate how uncertain initial contact conditions can be numerically incorporated into dynamic analyses of friction-damped turbine blades. The results show a satisfactory level of accuracy between experiments and computational simulations. This work offers valuable insights for understanding what influences test rig response and provides practical solutions for numerical simulations to improve agreement with experimental results.

Modelling time-dependent relaxation behaviour using physically based constitutive framework

The application of interrupted die motion during the deformation process in a servo press cycle is known to enhance the forming limit of metallic materials. This observation is generally attributed to the transient effects associated with stress relaxation phenomenon. However, attempts to model stress relaxation behaviour using physically based constitutive formulations in the finite element method are scarce. In this work, a modified version of the Kocks–Mecking–Estrin (KME) dislocation density model is used to evaluate the substructural changes during relaxation. An ‘uncoupled’ elasto-viscoplastic approach is employed to accommodate the plastic strain rate effect. This modelling approach is implemented in the commercial finite element software via a user material subroutine. The model is validated through simulations of interrupted uniaxial tensile tests for aluminium alloy AA7075 under two different aging conditions. The implemented model is shown to closely capture the experimental results and account for changes in dislocation density and the athermal component of flow stress during relaxation. Subsequently, the model is applied to simulate monotonic and interrupted hole expansion tests (HET), and the results are discussed qualitatively.

3D Numerical Cross-Section Analysis of a Tapered Beam Slice

AbstractCross-section analysis is an important tool used to recover stresses and strains in a structure at specific cross-sections of arbitrary geometries, without the need for a full 3D model. This is particularly essential for large-scale structures such as aircrafts, wind turbine blades, etc. where making a full model can be computationally very expensive or impractical. The majority of currently available cross-section analysis frameworks are based on stepwise prismatic assumptions, which are hardly suited for the analysis of tapered beams. In fact, high-fidelity stress analysis obtained from analytical and full 3D models shows that predictions of stepwise prismatic approximations can significantly deviate from the correct solution of tapered beams. In this work, a prismatic 3D cross-section analysis method is extended to analyze a symmetrically tapered finite cross-section slice. In this study, the cross-section slice is discretized with 8-node and 20-node solid elements. The boundary conditions are applied as six constraint equations via the Lagrange multiplier method. The external nodal forces acting on the cross-section faces are obtained from the equivalent tractions induced by the cross-section forces. The developed numerical model is validated against the exact analytical solutions of a wedge as well as commercial finite element (FE) software COMSOL and it is shown that the numerically predicted displacement and stress fields agree well with those provided by the wedge’s analytical solution and the FE COMSOL results. This work contributes to the advancement of high-fidelity numerical tapered cross-section analysis methods with an application for many engineering structures.

Compression-Shear Specimen Stress-State Response and Distribution Characteristics with Wide Stress Triaxiality.

Conventional methods for studying the plastic behavior of materials involve uniaxial tension and uniaxial compression. However, in the metal rolling process, the deformation zone undergoes a complex loading of multidirectional compression and shear. Characterizing the corresponding plastic evolution process online poses challenges, and the existing specimen structures struggle to accurately replicate the deformation-induced loading characteristics. In this study, we aimed to design a compression-shear composite loading specimen that closely mimics the actual processing conditions. The goal was to investigate how the specimen structure influences the stress-strain response in the deformation zone. Using commercial finite element software, a compression-shear composite loading specimen was meticulously designed. Five 304 stainless steel specimens underwent uniaxial compressive loading, with variation angles between the preset notch angle (PNA) of the specimen and compression direction. We employed digital image correlation methods to capture the impact of the PNA on the strain field during compression. Additionally, we aimed to elucidate the plastic response resulting from the stress state of the specimen, particularly in relation to specimen fracture and microstructural evolution.

An isogeometric approach to coupled thermomechanics in 3D via hierarchical adaptivity

In the present work, a complete numerical scheme to perform adaptive refinement and coarsening in the context of isogeometric analysis applied to thermomechanics is introduced. In particular, truncated hierarchical B-splines (THB-splines) are considered as a basis for the analysis and suitably graded isogeometric meshes are constructed to guarantee admissible configurations at each refinement and coarsening iteration. The algorithms are developed and implemented in a full three-dimensional framework and applied to solve coupled thermoelastic problems. The proposed numerical framework is verified on two relevant problems with respect to overkill solutions, obtained either with a commercial finite element software or with uniform isogeometric meshes. Different refinement and coarsening strategies are considered and compared. The obtained results demonstrate the ability of the THB-spline-based adaptive scheme to deliver robust discretizations guaranteeing a suitable trade-off between computational accuracy and number of degrees of freedom.

Dynamic model of tissue electroporation on the basis of biological dispersion and Joule heating

Electroporation is a complex, iterative, and nonlinear phenomenon often studied through numerical simulations. In recent years, simulations of tissue electroporation have been conducted with static models. However, the results of a static model simulation are restricted to a fixed protocol signature of the pulsed electric field. In this paper, we describe a novel dynamic model of tissue electroporation that also accounts for tissue dispersion and temperature to allow time-domain simulations. We have implemented the biological dispersion of potato tubers and thermal analysis in a commercial finite-element method software. A cell electroporation model was adapted to account for the increase in tissue conductivity. The model yielded 12 parameters divided into three dynamic states of electroporation. The thermal analysis describes the dependence of tissue conductivity on temperature. The model parameters were evaluated using experiments with vegetal tissue (Solanum tuberosum) under electrochemotherapy protocols. The proposed model can accurately predict the conductivity of tissue under electroporation from 100 to 1000 V/cm. A negligible thermal effect was observed at 1000 V/cm, with a temperature increase of 0.89 °C. We believe that the proposed model is suitable to describe the electroporation at the tissue level and provides a hint of the effects on the cell membrane.

Dynamic modeling and vibration control optimization of a rotating hollow beam with ESACLD treatment

As an active and passive hybrid control technology, enhanced segmented active constrained layer damping (ESACLD) is an intelligent damping structure for suppressing adverse vibrations in flexible structures. In this study, the three-dimensional spatial dynamic model of a rotating hollow beam with improved ESACLD treatment is established based on the finite element method in a floating frame of reference. The damping effects of the ESACLD with both edge elements and incisions are considered in the dynamic model for the first time. Simulation results show the damping performance of the ESACLD is better than traditional active constrained layer damping with or without incisions (SACLD or ACLD). The Genetic Algorithm-Backpropagation (GA-BP) neural network is used to optimize the physical parameters of ESACLD, and the optimized model can effectively suppress the transverse and flapping bending vibration. It is also found that flapping and transverse bending vibrations exhibit differential dependence on nutation and precession angular velocities; higher nutation and lower precession velocities suppress flapping bending. The existing commercial finite element software has some problems, such as low efficiency and inaccuracy. The new finite element proposed in this paper uses a new form function to ensure accuracy in the simulation of rotation and vibration and has obvious advantages in dealing with rotational structures and complex boundary conditions. Research in this work can provide a design framework for vibration prediction and control of flexible beam-like structures.

Microstructure and residual stress distribution of electron beam-welded joints of a 50 mm-thick TA15 titanium alloy plate

Abstract Vacuum electron beam welding was applied to a 50 mm-thick TA15 titanium alloy plate. Microstructure observation and microhardness testing were performed. Meanwhile, the residual stress on the surface at different distances from the weld centre was measured via the hole drilling method. A finite element model for electron beam welding of the TA15 titanium alloy plate was constructed on commercial finite element software. Experimental results showed that the microstructure of the weld zone consisted of a basket martensitic phase. The highest microhardness in the weld zone was 409 HV, and the microhardness of the base metal was the lowest. The maximum gradient change area was located at the HAZ near the base metal. The peak value of longitudinal residual stress from the simulation was 880 MPa, which was in the weld metal. The sharp change area of longitudinal residual stress gradient was located in the base metal near HAZ.

Bending-extension coupling analysis of shear deformable laminated composite curved beams with non-uniform thickness

In this paper, the boundary-based finite element method (BFEM) is developed for the bending-extension coupling analysis of shear deformable laminated composite curved beams with non-uniform thickness. The curved beams are discretized into a series of uniform straight segments. Based upon the first order shear deformation theory and the reciprocal theorem of Betti and Rayleigh, the boundary integral equations (BIEs) associated with each beam segment are derived and expressed in explicit form. The fundamental solutions required in the BIEs are obtained explicitly from the associated Green’s function. Since no singular integrals, numerical integrations and function interpolations are involved in the BIEs, our proposed BFEM provides an exact solution for a straight beam with uniform thickness, and only one single element with two end nodes is required for our analysis. Even only an approximate solution is provided for a curved beam with non-uniform thickness, BFEM converges faster than the conventional finite element method, and the results are in well agreement with those obtained by the commercial finite element software. Through the illustrated numerical examples, its generality is shown by: (1) stacking sequence of laminates: symmetric or unsymmetric; (2) beam geometries: straight, stepped, or curvilinear with uniform or non-uniform thickness; (3) loading types: axial force, transverse force and/or bending moment; distributed or concentrated; and (4) supporting conditions: clamped, simply supported, or free; with or without internal supports.