Fiber Orientation Tensor Research Articles

Group-random algorithm to generate representative volume element models for composites

One of the most commonly used methods for characterizing the mechanical properties of discontinuous fiber reinforced composites (DFRC) is to establish a Representative Volume Element (RVE) model and perform finite element (FE) analysis. However, FE analysis on RVE models established by traditional sampling algorithms is often computationally expensive due to the large size of RVE that is required to be statistically representative of the composite. To address this issue, this paper proposes a new approach for constructing RVE models with more accurate description of fiber orientation, aiming to make the FE modelling more efficient by using an RVE with small size. When establishing RVE models with given target fiber orientation tensor, it is very challenging to accurately capture the orientation of fibers. In order to mitigate the error between the orientation tensor reconstructed by fibers generated in the RVE and the target orientation tensor, a group-random algorithm is proposed in the current work to generate RVE models. Unlike the traditional algorithm, in which fibers are sampled one by one in the RVE, the group-random algorithm samples a group of four fibers at one time in order to eliminate the error of the off-diagonal components of the reconstructed orientation tensor in the principal coordinate system. Then a modification tensor is further introduced to mitigate the error of the diagonal components of the reconstructed orientation tensor. Simulation results show that the orientation tensor error could be significantly reduced by the group-random algorithm even for the RVE with low number of fibers. The merits of the group-random algorithm are also witnessed by the stability and accuracy of predicting the elastic constants of composite materials through RVE modeling. It is thus concluded that the major advantage of this work is to provide an alternatively feasible strategy to substantially improve computational efficiency of RVE modelling.

The use of digital thread for reconstruction of local fiber orientation in a compression molded pin bracket via deep learning

A deep convolutional neural network (DCNN) was used for microstructure reconstruction using artificial intelligence (MR-AI) by predicting local average fiber orientation distributions (FOD) in a 3D prepreg platelet molded composite (PPMC) pin bracket. To train the MR-AI model, surface strain fields from residual stresses simulated in PPMC plates were used as the input to the DCNN. A training dataset included PPMC plates with various degrees of global fiber alignment, based on the information obtained from high-fidelity flow simulation of a pin bracket. The MR-AI model was then deployed to analyze FOD in the 3D pin bracket by conducting thermo-elastic residual stress analysis. Initially, the MR-AI model was established entirely on the synthetic simulation data. Then, a μCT scan of a physically molded pin bracket was used to create a finite element model that provided data for additional validation of the DCNN model. For the μCT scan finite element pin bracket the MR-AI model predicted the distribution of fiber orientation tensor components with MAE of 0.10 indicating a global prediction error of 10 %. For the flow simulated pin bracket, the MR-AI model predicted the distribution of fiber orientation tensor components with a global prediction error of 11 %. The MR-AI model showed the ability to predict regions of varying alignment in the base and flange of the pin bracket. The proposed MR-AI methodology allows for rapid prediction of FOD in geometrically complex parts and offers a promising path to detecting unique fiber orientation states in molded components.

Multi-Objectives Optimization of Plastic Injection Molding Process Parameters Based on Numerical DNN-GA-MCS Strategy.

An intelligent optimization technique has been presented to enhance the multiple structural performance of PA6-20CF carbon fiber-reinforced polymer (CFRP) plastic injection molding (PIM) products. This approach integrates a deep neural network (DNN), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Monte Carlo simulation (MCS), collectively referred to as the DNN-GA-MCS strategy. The main objective is to ascertain complex process parameters while elucidating the intrinsic relationships between processing methods and material properties. To realize this, a numerical study on the PIM structural performance of an automotive front engine hood panel was conducted, considering fiber orientation tensor (FOT), warpage, and equivalent plastic strain (PEEQ). The mold temperature, melt temperature, packing pressure, packing time, injection time, cooling temperature, and cooling time were employed as design variables. Subsequently, multiple objective optimizations of the molding process parameters were employed by GA. The utilization of Z-score normalization metrics provided a robust framework for evaluating the comprehensive objective function. The numerical target response in PIM is extremely intricate, but the stability offered by the DNN-GA-MCS strategy ensures precision for accurate results. The enhancement effect of global and local multi-objectives on the molded polymer-metal hybrid (PMH) front hood panel was verified, and the numerical results showed that this strategy can quickly and accurately select the optimal process parameter settings. Compared with the training set mean value, the objectives were increased by 8.63%, 6.61%, and 9.75%, respectively. Compared to the full AA 5083 hood panel scenario, our design reduces weight by 16.67%, and achievements of 92.54%, 93.75%, and 106.85% were obtained in lateral, longitudinal, and torsional strain energy, respectively. In summary, our proposed methodology demonstrates considerable potential in improving the, highlighting its significant impact on the optimization of structural performance.

Predicting the fiber orientation of injection molded components and the geometry influence with neural networks

The injection molding simulation of short fiber reinforced plastics (SFRP) is time consuming. However, until now it is necessary for predicting the local fiber orientation, to optimize the molding process and to predict the mechanical behavior of the material. This research presents the capabilities of artificial neural networks (NN) in predicting fiber orientation tensor (FOT) during injection molding processes, with a focus on enhancing computational efficiency compared to traditional simulation methods. Three NN architectures are compared based on simulated injection molded plates, with the goal of predicting the effect of the plate geometry on the local fiber orientation. Results indicate that NN outperform the baseline assumption of aligned fibers and demonstrate significant potential for accurate FOT prediction. The computational efficiency of NN, especially during the prediction phase, showcases a reduction in processing time by a factor of 104 compared to traditional simulation methods. This research lays a foundation for further exploration into the feasibility of NN in partly replacing time-consuming simulations for practical applications in injection molding processes.

On the effectiveness of deep material networks for the multi-scale virtual characterization of short fiber-reinforced thermoplastics under highly nonlinear load cases

A key challenge for the virtual characterization of components manufactured using short fiber-reinforced thermoplastics (SFRTs) is the inherent anisotropy which stems from the manufacturing process. To address this, a multi-scale approach is necessary, leveraging deep material networks (DMNs) as a micromechanical surrogate, for a one-stop solution when simulating SFRTs under highly nonlinear long-term load cases like creep and fatigue. Therefore, we extend the a priori fiber orientation tensor interpolation for quasi-static loading (Liu et al. in Intelligent multi-scale simulation based on process-guided composite database. arXiv:2003.09491, 2020; Gajek et al. in Comput Methods Appl Mech Eng 384:113,952, 2021; Meyer et al. in Compos Part B Eng 110,380, 2022) using DMNs with a posteriori approach. We also use the trained DMN framework to simulate the stiffness degradation under fatigue loading with a linear fatigue-damage law for the matrix. We evaluate the effectiveness of the interpolation approach for a variety of load classes using a dedicated fully coupled plasticity and creep model for the polymer matrix. The proposed methodology is validated through comparison with composite experiments, revealing the limitations of the linear fatigue-damage law. Therefore, we introduce a new power-law fatigue-damage model for the matrix in the micro-scale, leveraging the quasi-model-free nature of the DMN, i.e., it models the microstructure independent of the material models attached to the constituents of the microstructure. The DMN framework is shown to effectively extend material models and inversely identify model parameters based on composite experiments for all possible orientation states and variety of material models.

Topology Optimization and Efficiency Evaluation of Short-Fiber-Reinforced Composite Structures Considering Anisotropy

The current study aims to develop a methodology for obtaining topology-optimal structures made of short fiber-reinforced polymers. Each iteration of topology optimization involves two consecutive steps: the first is a simulation of the injection molding process for obtaining the fiber orientation tensor, and the second is a structural analysis with anisotropic material properties. Accounting for the molding process during the internal iterations of topology optimization makes it possible to enhance the weight efficiency of structures—a crucial aspect, especially in aerospace. Anisotropy is considered through the fiber orientation tensor, which is modeled by solving the plastic molding equations for non-Newtonian fluids and then introduced as a variable in the stiffness matrix during the structural analysis. Structural analysis using a linear anisotropic material model was employed within the topology optimization. For verification, a non-linear elasto-plastic material model was used based on an exponential-and-linear hardening law. The evaluation of weight efficiency in structures composed of short-reinforced composite materials using a dimensionless criterion is addressed. Experimental verification was performed to confirm the validity of the developed methodology. The evidence illustrates that considering anisotropy leads to stiffer structures, and structural elements should be oriented in the direction of maximal stiffness. The load-carrying factor is expressed in terms of failure criteria. The presented multidisciplinary methodology can be used to improve the quality of the design of structures made of short fiber-reinforced composites (SFRC), where high stiffness, high strength, and minimum mass are the primary required structural characteristics.

On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains

Fiber orientation tensors (FOT) are widely used to approximate statistical orientation distributions of fibers within fiber-reinforced polymers. The design process of components made of such fiber-reinforced composites is usually accompanied by a virtual process chain. In this virtual process chain, process-induced FOT are computed in a flow simulation and transferred to the structural simulation. Within the structural simulation, effective macroscopic properties are identified based on the averaged information contained in the FOT. Solving the field equations in flow simulations as well as homogenization of effective stiffnesses necessitates the application of a closure scheme, computing higher-order statistical moments based on assumptions. Additionally, non-congruent spatial discretizations require an intermediate mapping operation. This mapping operation is required, if the discretization, i.e., mesh, of the flow simulation differs from the discretization of the structural simulation. The main objective of this work is to give an answer to the question: Does the sequence of closure and mapping influence the achieved results? It will turn out, that the order influences the result, raising the consecutive question: Which order is beneficial? Both questions are addressed by deriving a quantification of the closure-related uncertainty. The two possible sequences, mapping followed by closure and closure followed by mapping, yield strongly different results, with the magnitude of the deviation even exceeding the magnitude of a reference result. Graphical consideration reveals that for both transversely isotropic and planar FOT-input, invalid results occur if the mapping takes place prior to closure. This issue is retrieved by orientation averaging stiffness tensors. As a by-product, we explicitly define for the first time the admissible parameter space of orthotropic fourth-order fiber orientation tensors and define a distance measure in this parameter space.

Generalized micromechanical formulation of fiber orientation tensor evolution equations

Fiber orientation tensors are widely used to efficiently describe the fiber orientation evolution of anisotropic fiber suspensions during mold-filling. Real viscous fiber suspensions show fiber-induced anisotropic behavior. It is an open question how to correctly account for the anisotropic microstructure of fiber suspensions in general in the evolution equation of the fiber orientation tensors. In this study, a generalized evolution equation for the fiber orientation tensor of arbitrary even order is formulated, which takes into account the microstructural anisotropy of the fiber suspension. This formulation is based on a linear homogenization approach which allows the application of arbitrary mean-field models. The derived interaction term, representing the anisotropic environment of a single fiber, is discussed as a micromechanical convergence criterion of the underlying integral operator. It is shown and discussed in detail how the special cases of the Jeffery equation and the Folgar–Tucker equation follow from this general formulation. In addition, the generalized evolution equation is specified for selected mean-field models. In this context, an equation is presented to describe the evolution of the fiber orientation tensor depending on the spatial distribution of the fibers. For simple shear flow, all models describing the orientation dynamics are numerically investigated and compared. The results for the second-order orientation tensor as well as for a single fiber show that the well-known periodic behavior is present and strongly depends on the volume fraction and the chosen mean-field model. Considering the spatial distribution of the fibers has a significant effect on the orientation evolution and strongly affects the periodic reorientation.

On fully symmetric implicit closure approximations for fiber orientation tensors

On fully symmetric implicit closure approximations for fiber orientation tensors

Three‐dimensional polymer composite flow simulation and associated fiber orientation prediction for large area extrusion deposition additive manufacturing

AbstractMaterial flow and associated fiber orientation are among the most important features in Large Area extrusion deposition Additive Manufacturing (LAAM) of short fiber‐filled composites. Endeavors have been done in 2D flow models, where significant knowledge is achieved in explaining the material anisotropy of the deposited composite parts. Nevertheless, 2D flow models are limited by a couple of assumptions that lose significant characters of the deposition flow. This study is one of the first few that employ a 3D flow model which focuses on the quasi‐steady state of the polymer composite melt flow within the nozzle and the subsequent 90‐degree turning deposition onto the material substrate. The material flow is assumed as a highly viscous Newtonian flow. The fiber orientation is evaluated using the advanced pARD‐RSC fiber orientation tensor evaluation model, via the one‐way weakly‐coupled flow/orientation analysis formulation. Computed results show the fiber orientation state on the entire cross‐section of a deposited bead, which yields a clear view of how the material anisotropy is affected by the locally varied fiber orientation. The 3D‐flow prediction proves that the transverse directional fiber alignments are in high degree of similarity as compared to the over‐predicted results from the simplified 2D planar flows. In addition, the 3D‐model results exhibit a more favorable agreement with the reported experimental data than that yielded by the conventional 2D models.

Single and Multiple Gate Design Optimization Algorithm for Improving the Effectiveness of Fiber Reinforcement in the Thermoplastic Injection Molding Process.

Fiber reinforcement orientation in thermoplastic injection-molded components is both a strength as well as a weak point of this largely employed manufacturing process. Optimizing the fiber orientation distribution (FOD) considering the shape of the part and the applied loading conditions allows for enhancing the mechanical performances of the produced parts. Henceforth, this research proposes an algorithm to identify the best injection gate (IG) location/s starting from a 3D model and a user-defined load case. The procedure is composed of a first Visual Basic Architecture (VBA) code that automatically sets and runs Finite Volume Method (FVM) simulations to find the correlation between the fiber orientation tensor (FOT) and the IG locations considering single and multiple gates combinations up to three points. A second VBA code elaborates the results and builds a dataset considering the user-defined loading and constraint conditions, allowing the assignment of a score to each IG solution. Three geometrical components of increasing complexity were considered for a total of 1080 FVM simulations and a total computational time of ~390 h. The search for the best IG location has been further expanded by training a Machine Learning (ML) model based on the Gradient Boosting (GB) algorithm. The training database (DB) is based on FVM simulations and was expanded until a satisfactory prediction accuracy higher than 90% was achieved. The enhancement of the local FOD on the critical regions of three components was verified and showed an average improvement of 26.9% in the stiffness granted by a high directionality of the fibers along the load path. Finite element method (FEM) simulations and laboratory experiments on an industrial pump housing, injection-molded with a polyamide-66 reinforced with 30% of short glass fibers (PA66-30GF) material were also carried out to validate the FVM-FEM simulation frame and showed a 16.4% local stiffness improvement in comparison to the currently employed IG solution.

Implementation and comparison of algebraic and machine learning based tensor interpolation methods applied to fiber orientation tensor fields obtained from CT images

Fiber orientation tensors (FOT) are used as a compact form of representing the mechanically important quantity of fiber orientation in fiber reinforced composites. While they can be obtained via image processing methods from micro computed tomography scans (μCT), the specimen size needs to be sufficiently small for adequate resolution – especially in the case of carbon fibers. In order to avoid massive workload by scans and image evaluation when determining full-field FOT distributions for a plaque or a part, e.g., for comparison with process simulations, the possibilities of a direct interpolation of a few measured FOT at specific support points were opened in this paper. Hence, three different tensor interpolation methods were implemented and compared qualitatively with the help of visualization through tensor glyphs and quantitatively by calculating originally measured tensors at support points and evaluating the deviations. The methods compared in this work include two algebraic approaches, firstly, a Euclidean component averaging and secondly, a decomposition approach based on separate invariant and quaternion weighting, as well as an artificial intelligence (AI)-based method using an artificial neural network (ANN). While the decomposition method showed the best results visually, quantitatively the component averaging method and the neural network behaved better (that is for the type of quantitative error assessment used in this paper) with mean absolute errors of 0.105 and 0.114 when calculating previously measured tensors and comparing the components. With each method providing different advantages, the use for further application as well as necessary improvement is discussed. The authors would like to highlight the novelty of the methods being used with small and CT-based tensor datasets.

Improved Mean Value‐Amplitude Method for Determination of Orientation‐Dependent Modulus of Short Fiber‐Reinforced Thermoplastics

Short fiber‐reinforced thermoplastics such as 30% by weight glass fiber‐reinforced polyamide 46 (PA46GF30) are considered as substitute material for lightweight metallic parts. Despite the short fiber length, a distinct fiber orientation caused by local shear flow conditions during injection molding is obtained. This results in anisotropic material properties, which should be considered in the design phase of a component. Material properties are obtained by mechanical testing, e.g., tensile tests of specimens. These specimens have their own inherent microstructure consisting of different layers with different fiber orientations. The recently proposed mean value‐amplitude method enables the correlation of the Young's modulus to the eigenvalues of the fiber orientation tensor. The study presented herein applies a physically based improvement of the mean value‐amplitude method by consideration of the real fiber length. The results are very accurate for the description of the anisotropic material behavior and can be implemented in simulation tools for component design very easily.

ガラス短繊維強化PPS樹脂の繊維配向分布を考慮したマイクロメカニックスに基づくX線応力評価

The stress in polyphenylene sulfide (PPS) resin reinforced by glass fibers of 26 mass% was measured by the diffraction method using synchrotron with energy of 18 keV. The stress in the matrix was determined by the sin2ψ method with iso-inclination optics of transmitted X-ray diffractions. Tensile coupon specimens were cut from the skin-layer of injection molded plates in three directions, parallel, perpendicular and 45°, to the molding direction. The matrix stresses in the loading and transverse directions of specimens were measured under several uniaxial applied stresses. They changed proportionally to the applied stress. The proportional constants of the matrix stresses to the applied stress were determined, and named the stress-partitioning coefficients. The elastic constant and the matrix stress of the composite were calculated theoretically using micromechanics for two cases of fiber orientation: unidirectional (UD) and varied orientation distribution (VD). Fiber orientation tensor was determined from microscopic measurement of the cross-sectional shape distribution of fibers. Compared with the calculation based on UD fiber orientation, the analytical values based on micromechanics considering the variation in fiber orientation are closer to experimental values of elastic constants and stress-partitioning coefficients.

Variety of Planar Fourth‐Order Fiber Orientation Tensors and Implications on Effective Elastic Stiffnesses

AbstractIn this contribution, selected results from [1–3] are presented in a compact and simplified way. In addition, the variety of fiber orientation tensors is used to determine a maximum deviation of the direction‐dependent Young's modulus, which can arise if only second‐order directional information is included in a specific meanfield homogenization. Focusing on the special case of planar fiber distributions, the variety of fiber orientation tensors identified in [1] is considered as a design space. This design space is completely explored for the orientation‐averaging homogenization following [4], fixed material parameters and fixed fiber volume content. The possible directional dependence of the resulting effective stiffnesses is graphically presented using polar plots of the direction‐dependent Young's modulus. These polar plots are arranged on two‐dimensional slices within the parameter space of planar fourth‐order fiber orientation tensors. This gives a complete representation of the influence of the orientation tensor on the anisotropic stiffness tensor. Consequences of closure approximations, i.e., restriction to second‐order directional information, are demonstrated and motivate measurement of fourth‐order fiber orientation tensors.

Influence of flow–fiber coupling during mold-filling on the stress field in short-fiber reinforced composites

The anisotropic elastic properties of injection molded composites are fundamentally coupled to the flow of the fiber suspension during mold-filling. Regarding the modeling of mold-filling processes, both a decoupled and a flow–fiber coupled approach are possible. In the latter, the fiber-induced viscous anisotropy is considered in the computation of the flow field. This in turn influences the evolution of the fiber orientation compared to the decoupled case. This study investigates how flow–fiber coupling in mold-filling simulation affects the stress field in the solid composite under load based on the final elastic properties after fluid–solid transition. Furthermore, the effects of Newtonian and non-Newtonian polymer matrix behavior are investigated and compared. The entire process is modeled micromechanically unified based on mean-field homogenization, both for the fiber suspension and for the solid composite. Different numerical stabilization methods of the mold-filling simulation are discussed in detail. Short glass fibers with a typical aspect ratio of 20 and a volume fraction of 20% are considered, embedded in polypropylene matrix material. The results show that the flow–fiber coupling has a large effect on the fiber orientation tensor in the range of over ± 30% with respect to the decoupled simulation. As a consequence, the flow–fiber coupling affects the stress field in the solid composite under load in the range of over ± 10%. In addition, the predictions based on a non-Newtonian modeling of the matrix fluid differ significantly from the Newtonian setup and thus the necessity to consider the shear-thinning behavior is justified in a quantifiable manner.

Effect of fibre orientation on the light scattering during laser transmission welding

During laser welding of thermoplastic (LTW) composites reinforced with short fibres, a divergence of the laser beam is observed due to internal refraction of the beam at each matrix–fibre interface. This phenomenon leads to scattering of the laser beam in this heterogeneous medium, resulting in reduction of energy reaching the weld interface. This work presents a numerical study of the effect of fibre orientation in fibre-reinforced composites during the laser transmission welding simulation. A three dimensional (3D) numerical structure is generated to take into account the real microstructure of a composite material reinforced with short fibres. The information of fibre volume fraction, fibre length distribution and fibre orientation distribution is extracted from injection moulding simulations. Fibre orientation distribution function is extracted from fibre orientation tensors. An algorithm is implemented to trace rays propagating through composite material at two scales: microscopic and macroscopic. This algorithm uses optical properties of the composite material to simulate laser beam reflection and refraction in a complex structure. Laser beam scatter at the weld interface is simulated in 3D geometries with various fibre orientation distributions. The effect of fibre orientation on the light scattering phenomenon of laser is compared for different cases of fibre orientation. The simulation results are validated experimentally.

Influence of fiber breakage on flow behavior in fiber length- and orientation-dependent injection molding simulations

• Orientation dependent fiber breakage modeling approach • Fiber length and orientation dependent flow modeling • Coupling of transient fiber breakage modeling and fiber dependent viscosity and flow modeling Injection molding is one of the most important processes for manufacturing discontinuous fiber reinforced polymers (FRPs). The matrix of FRPs shows a transient chemo-thermomechanical behavior and the fibers create anisotropy influencing physical properties. Hence, FRPs are complex materials, but also likely used in volume production. In this work, the fiber-induced anisotropic behavior during mold filling is modelled with an anisotropic fourth order viscosity tensor. The viscosity tensor takes second and fourth order fiber orientation tensor, fiber length and non-Newtonian matrix viscosity into account. In this way, the macroscopic simulation captures the influence of the flow field on the fiber re-orientation and vice versa. The fiber orientation tensor is used to determine reference fibers in every element for calculation of hydrodynamic forces. This information is used in a novel fiber breakage model, based on buckling of fibers in Jeffery's orbit. The result is a macroscopic molding simulation with not only transient fiber orientation distribution, but also fiber length distribution. Due to the anisotropic viscosity tensor, the predicted fiber breakage influences the material's viscosity and flow behavior, which is also visible in the simulated cavity pressure. The results are validated with injection molding experiments, performed with a glass fiber reinforced phenolic compound, showing good agreement.

Predicting the elasto-plastic response of short fiber reinforced composites using a computationally efficient multi-scale framework based on physical matrix properties

Predicting the nonlinear mechanical response of short fiber reinforced composites (SFRCs) is a crucial and challenging task. In this paper, a computationally efficient multi-scale strategy is proposed to predict the anisotropic elasto-plastic behavior of SFRCs using the intrinsic mechanical behavior of the pure polymer and fibers without the requirements for reverse engineering. In doing so, different simple unit cells are first examined to find the one that can adequately describe the nonlinear mechanical response of SFRCs' representative volume elements (RVE) with aligned fibers. Considering the effects of packing configuration, fiber aspect ratio, volume fraction and material properties, the performance of different unit cells is investigated. Then, the homogenized mechanical responses of unit cells are linked to Hill's anisotropic plasticity model to correlate the mechanical response of the suggested unit cell to the continuum domain. Using the pseudo-grain approach and a numerical orientation averaging framework, the effects of fiber misalignment are taken into account. A multi-step homogenization strategy is also employed to consider the variation of fiber orientation tensor and volume fraction through the thickness. Finally, the validity and robustness of the proposed multi-scale strategy are extensively investigated based on the RVE-generated results and the available experimental observations.

Experimental Investigation and Applicability of Multi-Stage Simulations in the Case of a Thick-Walled Injection-Moulded Composite

The structure and mechanical properties of an injection-moulded short glass fibre (GF)-reinforced polymer composite were analysed through simulation methods. Fibre orientation, which evolves during the production of a thick-walled automotive part, was determined with an injection moulding simulation. Next, using the material model for the injected product, the force that resulted from the given deformation was determined with finite element software. To validate the simulation results, the examined products were manufactured with 30% reinforced GF, and then measurements were carried out. The validation of the fibre orientation tensor was achieved with optical microscope images, while the validation of the finite element, which analysed the flexural tests, was carried out through a comparison of flexural rigidity. The aim of the project was to verify the reliability of multi-stage finite element software. According to the results, in the case of a thick-walled GF-reinforced product, it was demonstrated that the integration of a different finite element software could be used reliably.