Commercial Finite Element Code Research Articles

A comparison of finite strain viscoelastic models based on the multiplicative decomposition

The constitutive equations of several finite strain viscoelastic models, based on the multiplicative decomposition of the deformation gradient tensor and written in a thermodynamically consistent framework, are reviewed to demonstrate their similarities and differences. The proposed analysis shows that dissipation formulations, which may appear different, are similar when formulated in the same configuration, allowing the definition of a unified general model. Then, the general model’s ability to reproduce the main features of the behavior of rubbers is explored. First, by comparing its responses to the ones of finite linear viscoelastic models commonly implemented in commercial finite element codes. Cases of monotonic uniaxial tension and simple shear, relaxation, and sinusoidal simple shear are considered. Second, by confronting a classic generalized Maxwell rheological scheme to a Zener one with a non-constant viscosity and exploring the relevance of both options within the general model’s constitutive equations.

Analysis of High-Rise Building Using Opensees

Numerical simulation has increasingly become an effective method and powerful tool for performance-based earthquake engineering research. Most existing numerical analyses use general-purpose commercial software, which can limit in-depth investigations on specific, complex topics. Consequently, this research focuses on the dynamic analysis of high-rise reinforced concrete (RC) frame-core tube structures using the open-source finite element (FE) code OpenSees to perform nonlinear seismic analyses. Various shear walls, a frame-core tube structure, and a tall building are simulated. The rationality and reliability of the proposed analysis method are validated through comparison with available experimental data and the analytical results of a well-validated commercial FE code. The research outcomes will provide a useful reference and an effective tool for further numerical analysis of the seismic behavior of tall buildings.

Finite element simulation of the complete sheet metal blanking cycle: Effect of blanking clearance on force curve and cut edge quality

Sheet metal blanking process is a manufacturing process that is widely used in sheet metal forming and particularly in the electronics and automotive industries. The outcome and quality of the blanked parts are affected by various parameters such as the blanking clearance, the sheet metal mechanical properties and the wear of tools. However, experimental campaigns to assess the effects of these parameters on the process outcome can be prohibitively expensive for the industry. As a result, numerical simulation of the blanking process is becoming increasingly important to gain insight into the process and study these effects.The present paper provides a novel finite element (FE) simulation procedure to predict the complete blanking cycle including sheet metal cutting, sheet metal springback, punch penetration in die, and stripping phases. A blanking force curve showing the punch force at all phases can thus be obtained. The commercial finite element code ABAQUS® has been chosen to develop this procedure using ABAQUS/Explicit® code for the cutting phase and ABAQUS/Standard® code for the remaining phases. Based on this procedure, the influence of the blanking clearance on the punch force-displacement curve and on the cut edge quality has been studied. The obtained results have been compared to previous literature results and experimental findings.

Buckling and free vibration of grid-stiffened composite conical panels using Extended Kantorovich Method

This paper develops very accurate closed-form solutions for buckling and free vibration of grid-stiffened composite conical panels using a semi-analytical method. On the base of first-order shear deformation theory (FSDT), the governing formulations are derived while an appropriate unit cell is used to derive the material properties of the lattice from their bulk properties. Multiple systems of ordinary differential equations (ODEs) are obtained by applying the Extended Kantorovich Method (EKM) to solve the governing system of partial differential equations (PDEs). The resulting ODEs are then solved using semi-analytical closed-form solutions to study buckling and free vibration of grid-stiffened panels. It is interesting to note that due to the general formulation of the conical panel, it is very easy to obtain other useful geometries including cylindrical panels, and even rectangular plates with general unit cell configurations. Regarding stability, fast convergence, and very low computing cost, the effectiveness of the proposed technique is investigated. The accuracy of the critical buckling loads and natural frequencies for various cases is studied which shows very good agreement in comparison with results obtained from the commercial finite element code ANSYS.

Efficient numerical simulations on the forest barrier for seismic wave attenuation: engineering safe constructions

This paper aims to elucidate the clear visibility of attenuating seismic waves (SWs) with forest trees as natural metamaterials known as forest metamaterials (FMs) arranged in a periodic pattern around the protected area. In analyzing the changeability of the FM models, five distinct cases of “metawall” configurations were considered. Numerical simulations were conducted to study the characteristics of bandgaps (BGs) and vibration modes for each model. The finite element method (FEM) was used to illustrate the generation of BGs in low frequency ranges. The commercial finite element code COMSOL Multiphysics 5.4a was adopted to carry out the numerical analysis, utilizing the sound cone method and the strain energy method. Wide BGs were generated for the Bragg scattering BGs and local resonance BGs owing to the gradual variations in tree height and the addition of a vertical load in the form of mass to simulate the tree foliage. The results were promising and confirmed the applicability of FEM based on the parametric design language ANSYS 17.2 software to apply the boundary conditions of the proposed models at frequencies below 100 Hz. The effects of the mechanical properties of the six layers of soil and the geometric parameters of FMs were studied intensively. Unit cell layouts and an engineered configuration for arranging FMs based on periodic theory to achieve significant results in controlling ground vibrations, which are valuable for protecting a large number of structures or an entire city, are recommended. Prior to construction, protecting a region and exerting control over FM characteristics are advantageous. The results exhibited the effect of the ‘trees’ upper portion (e.g., leaves, crown, and lateral bulky branches) and the gradual change in tree height on the width and position of BGs, which refers to the attenuation mechanism. Low frequency ranges of less than 100 Hz were particularly well suited for attenuating SWs with FMs. However, an engineering method for a safe city construction should be proposed on the basis of the arrangement of urban trees to allow for the shielding of SWs in specific frequency ranges.

Method of exact solutions code verification of a superelastic constitutive model in a commercial finite element solver

The superelastic constitutive model implemented in the commercial finite element code ABAQUS is verified using the method of exact solutions (MES). An analytical solution for uniaxial strain is first developed under monotonic loading. Numerical simulations are then performed, and simulation predictions are compared to the exact analytical solutions. Results reveal the superelasticity model agrees with the analytical solution to within one ten-thousandth of a percent (0.0001%) or less for stress and strain quantities of interest when using displacement-driven boundary conditions. Full derivation of the analytical solution is provided in an Appendix, and simulation input files and post-processing scripts are provided as supplemental material.

BROM: An extension of beam theory through model order reduction

Beam analysis played a crucial role in the design of structures throughout modern history. Classical beam theories rely on analytical derivations under certain a priori kinematic assumptions (and are accurate with low computational cost), but they are not amenable to, for example, orthotropic materials and arbitrary cross sections. On the other hand, full 3D linear elasticity theory solved via the Finite Element (FE) method provides solutions for a wide range of engineering problems at the expense of a high computational cost. Reduced-order models try to provide a theory as general as 3D linear elasticity but as efficient as classical beam theories by assuming the solution to be represented in a low-dimensional basis. Among the several options available in the literature, the domain decomposition and hyperreduction via Empirical Cubature Method (ECM), which we name ddROM [1], exhibits this compelling feature. However, ddROM applied to beam structures, may provide more Degrees of Freedom (DoF) per node than most standard commercial FE codes which only consider rigid body motion of the cross section. This paper presents a methodology, called beam Reduced Order Model (bROM), to integrate ddROM in standard FE codes by means of a condensation process followed by a regression procedure. Condensation gives the stiffness matrix, required by FE commercial codes, of a super-element of a given length. This is achieved by assembling several elements and finding the relationship between applied displacements and reactions (Lagrange multipliers). The condensation process is then used to create a database of stiffness matrices as a function of the beam length over which a regression is performed. Some numerical examples are first presented to validate the proposed methodology against the classical beam theory for the case of isotropic beams, and finally, two orthotropic beam showing the utility of the method in comparison with FE.

NUMERICAL IMPLEMENTATION OF THE TSCHOEGL–CHANG–BLOCH NONLINEAR VISCOELASTIC CONSTITUTIVE LAW FOR UNVULCANIZED CARBON BLACK–FILLED RUBBERS

ABSTRACT Rubber engineering design analysis requires a fundamental understanding of the mechanical behavior of polymers, especially in their unvulcanized state. It necessitates the establishment of a three-dimensional constitutive material to account for the observed mechanical behavior. This law is required to produce realistic descriptions of the viscoelastic performance in a mathematically simple form that is easy to implement in engineering applications. This article describes the theory of the Tschoegl–Chang–Bloch time-dependent nonlinear viscoelastic constitutive law. The experimental verification of this law is provided under different deformation fields and multiple load steps. Laboratory test procedures to obtain the parameters required to describe the material under consideration are provided in detail. A recursive form of the constitutive law, suitable for finite element application, is derived and coded in the finite element commercial code Abaqus via the user subroutine UMAT. Comparisons between the experimental observations, the theoretical results, and the numerical data are drawn for simple test models examined under creep or shear relaxation conditions. The excellent agreements observed indicate the suitability of the governing law in analyzing viscoelastic problems of unvulcanized carbon black–filled rubbers.

Multi-scale FE[formula omitted] investigation of non linear rate dependent 3D composite structures accounting for fiber–matrix damage

In the present paper, a two-scale FE2 technique based on periodic homogenization theory is investigated to predict the macroscopic non-linear behavior of polymer matrix composite structures.The computational technique accounts for the fiber/matrix interfacial damage, the matrix ductile damage and the effect of 3D periodic microstructure. The developed approach integrates the geometric description and the non-linear time-dependent local behavior of the different constituents (fibers, matrix and interface). For numerical calculations, advanced User Defined Material and User Element subroutines are developed at the two scales, simultaneously activated to solve macroscopic and microscopic problems through an incremental scheme in the finite element commercial code Abaqus/Implicit The computational efficiency of the developed multi-scale approach is demonstrated by predicting the overall response of 3D composite structures under complex loading paths. The composite structures consist of thermoplastic polymer matrix with elasto-viscoplastic behavior and ductile damage, reinforced by elastic aligned short fibers that are coated by a cohesive zone, which obeys the general unified potential. The numerical results obtained by FE2 simulation with and without accounting for interface effect are analyzed and compared for two examples: Meuwissen-like and 3D corner shape structures. The main benefits of the developed approach lie in accessing the microscopic strain fields, the distributions of the internal variables and the damage evolution in both polymer matrix and interface, as well as identifying their repercussions on the macroscopic response.

Three-dimensional creep calculation model for reliability analysis of concrete-filled steel tubular (CFST) structure

For long-span concrete-filled steel tube (CFST) structure, it is essential to implement efficient and realistic prediction models for the long-term processes of core concrete creep. In order to systematically study the main influential factors in CFST structure creep effects, a probabilistic analysis can be performed. The objective of this paper is to analyse the long-term response of CFST structure by using time-dependent reliability method. To address the problem of creep calculation, a novel and comprehensive presentation was developed. By converting the integral-type creep law to a differential-type form with internal variables, based on the Kelvin chain model, an elastic structural analysis with generally orthotropic elastic moduli and eigenstrains was established. We have compiled a three-dimensional (3-D) finite-element analysis programme that considers the creep Poisson effect of core concrete to analyse the long-term performance of the CFST structure. This is achieved by developing a commercial finite element code, such as Usermat in ANSYS. As calculation examples, several time-dependent analyses of a CFST stub column and long-span CFST arch bridge were performed. The calculated results of long-term behaviour agree well with experimental and measured data. Considering the randomness of various input parameters, such as physical dimensions and materials of the CFST structure, we have analysed the uncertainty using the Latin-hypercube-sampling (LHS) stochastic finite-element method. The results of creep sensitivity analysis revealed that coefficient of creep model uncertainty, steel and concrete elastic modulus were the three most influential parameters for CFST stub columns’ creep, and load, coefficient of creep model uncertainty, relative humidity, steel and concrete elastic modulus were the five for CFST arch bridges’ long-term deflection. In addition, the use of Monte Carlo (MC) and response surface (RS) methods for structural stochastic reliability analysis demonstrates the ability of these approaches to assess the reliability index of long-span CFST arch bridges. This provides a valuable reference for the design and performance evaluation of CFST structures.

A homogenization-based model of the Gurson type for porous metals comprising randomly oriented spheroidal voids

In this work, we propose a new fully explicit isotropic, rate-independent, elasto-plastic model for porous materials comprising a random with uniform probability, isotropic distribution of randomly oriented spheroidal voids of the same shape. The proposed model is based on earlier homogenization estimates that use a linear comparison composite theory. The resulting expressions exhibit the simplicity of the well known Gurson model and, thus, its numerical implementation in a finite element code is straightforward. To assess the accuracy of the analytical model, we carry out detailed finite-strain, three-dimensional finite element (FE) simulations of representative volume elements (RVEs) with the corresponding microstructures. Proper minimal parameter calibration of the model leads to fairly accurate agreement of the analytical predictions with the corresponding FE average stresses and porosity evolution. We show, both analytically and numerically, that the initial aspect ratio of the voids has a significant effect on the homogenized yield surface of the porous material leading to extremely soft responses for flat oblate voids (e.g. aspect ratio less than 0.5) especially at large triaxialities. Finally, after numerical implementation of the model in a commercial finite element code (ABAQUS), we solve the industrially important problem of hole expansion and comment on the role of porous compressible plasticity versus classical incompressible plasticity.

NUMERICAL IMPLEMENTATION OF THE TSCHOEGL–CHANG–BLOCH NONLINEAR VISCOELASTIC CONSTITUTIVE LAW FOR UNVULCANIZED CARBON BLACK–FILLED RUBBERS

ABSTRACT Rubber engineering design analysis requires a fundamental understanding of the mechanical behavior of polymers, especially in their unvulcanized state. It necessitates the establishment of a three-dimensional constitutive material to account for the observed mechanical behavior. This law is required to produce realistic descriptions of the viscoelastic performance in a mathematically simple form that is easy to implement in engineering applications. This article describes the theory of the Tschoegl–Chang–Bloch time-dependent nonlinear viscoelastic constitutive law. The experimental verification of this law is provided under different deformation fields and multiple load steps. Laboratory test procedures to obtain the parameters required to describe the material under consideration are provided in detail. A recursive form of the constitutive law, suitable for finite element application, is derived and coded in the finite element commercial code Abaqus via the user subroutine UMAT. Comparisons between the experimental observations, the theoretical results, and the numerical data are drawn for simple test models examined under creep or shear relaxation conditions. The excellent agreements observed indicate the suitability of the governing law in analyzing viscoelastic problems of unvulcanized carbon black–filled rubbers.

INTEGRAL TRANSFORM SOLUTION OF HEAT CONDUCTION IN ANISOTROPIC HETEROGENEOUS MEDIA

The generalized integral transform technique (GITT) is advanced to deal with conduction heat transfer in anisotropic heterogeneous media. A formal solution for exact integral transformation of conduction in anisotropic media is extended to account for heterogeneities expressed as space variable equation coefficients and source terms. The proposed eigenfunction expansion is based on biorthogonal eigenvalue problems, which results in an exact integral transformation for a class of linear problems and in a coupled transformed ordinary differential system for nonlinear situations. An algorithm is proposed for the associated eigenvalue problems, also handled through the GITT, by considering simpler biorthogonal eigenvalue problems of known analytical solution, leading to transformed algebraic eigenvalue problems. A single domain reformulation strategy is adopted to merge the information from multiple regions and materials, either isotropic or anisotropic, into one single diffusion equation. A two-dimensional transient test case is considered that presents an abrupt transition between isotropic and anisotropic materials yielding a marked change in thermal behavior in a defined region of interest formed by the anisotropic inclusion. Convergence behavior of the integral transform solution is illustrated, and the fully converged results are employed as a benchmark to inspect the accuracy of a commercial finite element code for automatically defined mesh refinement levels.

Multiscale topology optimization with Direct FE2

Together with the rapid development in manufacturing technology, multiscale structural topology optimization presents opportunities for the design of components at both the structural and sub-structural scales. A few works on topological optimization based on FE2 computational homogenization to concurrently evolve the structure and sub-structure have been reported. However, significant expertise and coding are required in the conventional implementation of FE2. It is shown that multiscale FE2 optimization can be readily implemented on commercial finite element codes using the Direct FE2 approach. The multiscale analysis is carried out as a single topology optimization job on commercial FE software. Numerical example problems are solved using ABAQUS to demonstrate the proposed method for stiffness optimization. It is shown that Direct FE2 optimization takes only a fraction of the computational time required for optimization with a fine mesh and yet gives comparable optimized stiffness.

On a 3D material modelling of smart nanocomposite structures

Smart composites (SCs) are utilized in electro-mechanical systems such as actuators and energy harvesters. Typically, thin-walled components such as beams, plates, and shells are employed as structural elements to achieve the mechanical behavior desired in these composites. SCs exhibit various advanced properties, ranging from lower order phenomena like piezoelectricity and piezomagneticity, to higher order effects including flexoelectricity and flexomagneticity. The recently discovered flexomagneticity in smart composites has been investigated under limited conditions. A review of the existing literature indicates a lack of evaluation in three-dimensional (3D) elasticity analysis of SCs when the flexomagnetic effect (FM) exists. To address this issue, the governing equations will incorporate the term ∂/∂z, where z represents the thickness coordinate. The variational technique will guide us in further developing these governing equations. By using hypotheses and theories such as a 3D beam model, von Kármán's strain nonlinearity, Hamilton's principle, and well-established direct and converse FM models, we will derive the constitutive equations for a thick composite beam. Conducting a 3D analysis implies that the strain and strain gradient tensors must be expressed in 3D forms. The inclusion of the term ∂/∂z necessitates the construction of a different model. It should be noted that current commercial finite element codes are not equipped to accurately and adequately handle micro- and nano-sized solids, thus making it impractical to model a flexomagnetic composite structure using these programs. Therefore, we will transform the derived characteristic linear three-dimensional bending equations into a 3D semi-analytical Polynomial domain to obtain numerical results. This study demonstrates the importance of conducting 3D mechanical analyses to explore the coupling effects of multiple physical phenomena in smart structures.

Aircraft crashworthiness: modelling of fuel inside a conformable tank

With the aid of modern computing systems and commercial finite element (FE) codes, the expensive and non-repeatable experimental crashworthiness testing of complex fuselage sections can be simulated accurately. However, some key problems associated with the virtual drop tests have yet to be resolved. One such example is the vertical impact test of the fuselage section with an onboard auxiliary fuel tank, which contains a large amount of fuel inside the fuel tank, where an inevitable fluid-structure interaction (FSI) takes place during crashworthiness. Despite this fact, to date, the researchers have adopted mass distribution techniques where fuel modelling is excluded to avoid the FSI and the total mass of the fuel is distributed over the fuel tank surfaces. Therefore, in this present study, an effort is made to evaluate the importance of FSI over mass distribution techniques to model the fuel adopting the FE code Ansys Explicit. Investigated crash outcomes of the fuselage section based on plastic energy dissipation, plastic deformation, and seat track acceleration responses suggest that in the case of mass distribution techniques, the tank body behaves as rigid, which eventually limits the fuel tank from absorbing much less plastic energy compared to FSI. This also leads to a different failure mechanism for the ribs, which are mainly crashing for mass distribution techniques, while plastic hinge failure occurs for FSI. Finally, after a detailed comparison and discussion, it is concluded that the FSI method is more suitable to represent fuel inside an auxiliary fuel tank.

Thermal–Structural Linear Static Analysis of Functionally Graded Beams Using Reddy Beam Theory

In this work, a finite element model to perform the thermal–structural analysis of beams made of functionally graded material (FGM) is presented. The formulation is based on the third-order shear deformation theory. The constituents of the FGM are considered to vary only in the thickness direction, and the effective material properties are evaluated by means of the rule of mixtures. The volume distribution of the top constituent is modeled using the power law form. A comparison of the present finite element model with the numerical results available in the literature reveals that they are in good agreement. In addition, a routine to study functionally graded plane models in a commercial finite element code is used to verify the performance of the proposed model. In the present work, displacements for different values of the power law exponent and surface temperatures are presented. Furthermore, the normal stress variation along the thickness is shown for several power law exponents of functionally graded beams subjected to thermal and mechanical loads.

An integrated methodology to estimate the effective elastic parameters of amorphous TiO2 nanostructured films, combining SEM images, finite element simulations and homogenization techniques

In this paper, a novel experimental-numerical methodology is outlined, which aims at estimating the homogenized elastic properties of thin nanostructured coatings, utilized in a variety of industrial contexts. Focus is posed on amorphous titanium dioxide (TiO2) films, a few micrometer thick, produced through Pulsed Laser Deposition in the form of columnar elements coating a Silicon flat substrate. The proposed inverse strategy rests on digital images acquired by a Scanning Electron Microscope on coated samples, with a nanometer resolution, and consists of the following steps: (i) within a representative volume element, cavities existing in between the nanostructured columns are identified in the raster images by an automatic edge detection procedure; (ii) information concerning the location of the pore borders are vectorized and passed through a Python script to a commercial finite element code; (iii) the homogenized stiffness matrix is reconstructed on the basis of finite element simulations of such a representative volume subjected to elementary loading conditions, each corresponding to a single component of the effective strain tensor. Diverse mechanical models with periodic boundary conditions have been comparatively assessed, fully three dimensional or under plane conditions, assuming for the TiO2 columns in an amorphous state (as corroborated by Raman spectroscopy) an isotropic behaviour, with a priori known Young’s modulus and Poisson’s ratio. The homogenized elastic moduli and coefficients of TiO2 thin films, at varying the deposition process parameter, are estimated by the novel procedure, resulting in an orthotropic, transversely-isotropic behaviour.

A CFD multi-objective optimization framework to design a wall-type heat recovery and ventilation unit with phase change material

This work applies multi-objective optimization based on a genetic algorithm to design a wall-type heat recovery and ventilation (HRV) unit equipped with a phase change material (PCM) to show the benefits of using this thermal energy storage system in buildings. The initial design – taken from a reference work – consists of an airflow driven by a fan through a copper tube bundle filled with PCM. Starting from this, a thermo-fluid dynamic 3D model is developed to assess the natural convection negligibility inside the PCM. Then, a 2D model is solved with a commercial finite element code and validated. Once the validation is assessed, this model is coupled with MATLAB® to perform the multi-objective optimization procedure. Optimal system configurations (tube diameter, thickness, pitches) and operational variables (fan velocity, cycle time, PCM melt temperature) are achieved on a 3D Pareto surface that collects the non-dominated solutions, i.e., minimizing costs and pressure drop (air side), and maximizing the average storage rate. The 3D Pareto approach enables to find solutions that outperform the initial configuration, i.e., the average storage rate is increased by 28.4%, simultaneously improving the other two objective functions. Finally, two sub-optimal solutions from the 2D fronts are numerically compared to show the difference in the air stream distribution across the new tubes’ arrangement and the PCM melting evolution. The HRV efficiency is enhanced from 37.5% to 44.4%, confirming that the proposed approach provides an economically-feasible solution, while reducing energy consumption and maintaining good indoor air quality.

Numerical and experimental investigations on the mechanical behavior of additively manufactured novel composite materials for biomedical applications

Polymer composites have a great scope which provides improvised mechanical and chemical properties than matrix material. Although most composite materials are relatively strong, they are not sustainable. The sustainability and reusability of the material is significantly affected by the incorporation of non-degradable fillers. Bael bark is a naturally occurring material with numerous medical properties; in this study, Bael bark was dried, synthesized and converted into nano-filler for integrating them in polylactide (PLA) matrix. PLA is a widely used biopolymer in the biomedical sector. The filler and matrix material are both biodegradable; therefore, the resulting composite is also expected to be biodegradable. This study aims to develop a composite comprising Bael bark and PLA, which is a better alternative to PLA in terms of strength and sustainability. Bael bark-reinforced PLA matrices were synthesized with different Bael bark compositions, i.e., 5 wt.%, 10 wt.%, 15 wt.%, and 20 wt.%. Subsequently, the resulting composites were subjected to filament characterization tests such as single fiber tensile test (SFTT), scanning electron microscopy (SEM), and X-ray diffraction (XRD). Notably, all extruded composites exhibited a uniform distribution of filler materials. Tensile, compression, and flexural tests were also conducted on the additively fabricated samples. The tensile strength, compressive strength and Flexural strength of composite specimens were higher than neat PLA material, with increments of 39%, 33.8%, and 33.9%, respectively, for the composite made with 15 wt.% composites. Using a commercial finite element code ABAQUS, numerical simulations were performed on tensile, compression and flexural specimens. The simulation results are in good agreement with the experimental results.