FE Calculation Research Articles

A cluster-based incremental potential approach for reduced order homogenization of bones.

We develop a cluster-based model order reduction (called C-pRBMOR) approach for efficient homogenization of bones, compatible with a large variety of generalized standard material (GSM) models. To this end, the pRBMOR approach based on a mixed incremental potential formulation is extended to a clustered version for a significantly improved computational efficiency. The microscopic modeling of bones falls into a mixed incremental class of the GSM framework, originating from two potentials. An offline phase of the C-pRBMOR approach includes both a clustering analysis spatially decomposing the micro-domain within an RVE and a space-time decomposition of the microscopic plastic strain fields. A comparative study on two different clustering approaches and two algorithms for mode identification is additionally conducted. For an online analysis, a cluster-enhanced version of evolution equations for the reduced variables is derived from an effective incremental variational formulation, rendering a very small set of nonlinear equations to be numerically solved. Several numerical examples show the effectiveness of the C-pRBMOR approach. A striking acceleration rate beyond 104 against conventional FE computations and that beyond 103 against the original pRBMOR approach are observed.

Reduced order homogenization of composites with strength difference effects in elastoplasticity coupled to damage

This paper addresses reduced order homogenization of composites with strength difference (SD) effects in elastoplasticity coupled to damage, while containing several well-known plasticity criteria as special cases. We extend two approaches for this purpose: 1. nonuniform transformation field analysis (NTFA by Michel and Suquet, 2003) and 2. a recent variant called cluster-based NTFA (CNTFA by Ri et al., 2021), and conduct a comparative study on them. For the NTFA approach, a space–time decomposition is done separately for volumetric and deviatoric inelastic strain fields. A coupled model is derived for the present case to govern the evolution of resulting reduced variables. For the CNTFA approach, a clustering analysis is additionally performed for a spatial decomposition of the micro-domain. Unlike the NTFA, the online analysis is formulated as a unified minimization problem, which does not require a major adaptation for the present case. For both approaches, localization rules are deduced from the superposition principle and then homogenized to obtain the effective responses. FE-based implementation is presented in detail for both approaches. Numerical results show that both approaches provide a striking acceleration rate against conventional FE computations. The CNTFA predictions are more accurate than the NTFA ones by involving clustered microscopic fields in the online analysis, thus resulting into a slightly increased memory requirement.

Multiscale Thermodynamics-Informed Neural Networks (MuTINN) towards fast and frugal inelastic computation of woven composite structures

The complex behavior of inelastic woven composites stems primarily from their inherent heterogeneity. Achieving accurate predictions of their linear and nonlinear responses, while considering their microstructures, appears feasible through the application of multi-scale modeling approaches. However, effectively incorporating these methodologies into real-scale applications, particularly within FE2 analyses, remains challenging due to the significant computational requirements they entail. To overcome this issue, while considering the scale effects, this study introduces an alternative approach based on Artificial Neural Networks (ANNs) to perform a macroscopic surrogate model of composites. This model, referred to as Multiscale Thermodynamics Informed Neural Networks (MuTINN), is founded on thermodynamic principles and introduces specific quantities of interest that serve as internal state variables at the macroscopic level. This captures efficiently the state and evolution laws governing the history-dependent behavior of these composites while retaining the thermodynamic admissibility and the physical interpretability of their overall responses. Moreover, to facilitate its numerical implementation within a FE code, a Meta-UMat has been developed, streamlining the application of multiscale FE×MuTINN approach for composite structure computations. The prediction capabilities of the proposed approach is demonstrated across the material scales, exemplified through diverse instances of woven composite structures. These applications account for anisotropic yarn damage and an elastoplastic polymer matrix behavior. The numerical results and the related comparison with experimental findings and FE computations demonstrate remarkable consistency across a wide range of non-proportional loading paths. This promises a potential solution to alleviate the computational challenges associated with multiscale simulations of large-scale composite structures.

A novel anchor method for large tonnage CFRP cable: Anchorage design and full-scale experiment

This study introduces a novel three-segment CFRP cable anchorage to address stress concentration challenges in CFRP cable anchors. The anchorage features a continuously varying inner cone angle along the anchor length to prevent excessive radial stress on the CFRP cable. The radial stress distribution is theoretically analyzed, followed by a numerical simulation design using the Tsai-Wu failure criterion and the anchor system's equivalent stiffness as evaluation indices. The results demonstrate a 47.06 % and 45.73 % reduction in the radial stress peak of the novel anchorage compared to the inner cone and inner cone + straight cylinder anchorage, respectively. Importantly, beyond an anchor length 23 times the equivalent diameter of the CFRP tendon, increasing length has a marginal impact on anchor efficiency but diminishes equivalent stiffness. Positive effects are observed by increasing the inner cone segment proportion and adjusting the inner cone angle within the 2° to 4° range. Conversely, increasing the bonding medium thickness reduces anchor efficiency and equivalent stiffness. Experimental verification indicates the anchor system achieving 99.83 % anchor efficiency. Moreover, the axial strain of CFRP tendons in the anchor zone exhibits a linear trend along the anchor length, with test stresses at corresponding positions consistent with FE calculation results.

Tikhonov Regularization for the Fully Coupled Integral Method of Incremental Hole-Drilling

BackgroundThe unit pulse integral method is used extensively with the incremental hole-drilling residual stress measurement technique. The ASTM E837 standard, which applies only to isotropic materials, recommends the use of Tikhonov regularization to reduce instability when many depth increments are used. In its current formulation, Tikhonov regularization requires the decoupling of stress, as is possible for isotropic materials. The fully coupled integral method is needed for residual stress determination in layered composite laminates and is currently employed without Tikhonov regularization. This causes greater sensitivity to measurement errors and consequently large stress uncertainties. An approximate method of applying Tikhonov regularization exists for biaxial composites, but is not applicable to more complex laminates.ObjectiveExtend Tikhonov regularization to the fully coupled integral method to improve residual stress determination in composite laminates.MethodsThis work investigates the use of the approximate and fully coupled regularization approaches in an angle ply composite laminate of [+45/-45/0/90]s construction. Experimental validation in a [0/+45/90/-45]s laminate is also presented where the regularized fully coupled integral method is compared to the series expansion method that includes all in-plane stress and strain directions simultaneously in a least-squares solution.ResultsThe regularized integral method produces comparable results to those of series expansion while requiring twelve times less FE computation to calculate the compliances. The optimal degree of regularization is also more convenient to determine than the optimal combination of series order required by series expansion.ConclusionsThe new method is easily applied and should find wide application in the measurement of residual stresses in composite laminates.

Stability design of a geosynthetic reinforced rock cuttings wall

Rocks excavation with tunnel boring machines induces a lot of cuttings. This granular material needs to be stored. When reinforced by geosynthetics, significant tensile stresses can be obtained in the resulting composite structure which allows to build steep slopes. A real case study of a reinforced rock cuttings wall is presented in this paper. To study accurately this complex problem, two calculation methods were used: a limit equilibrium (using the Bishop criteria), classically used for these kinds of stability problems and two-dimensional finite element calculations. These two methods are different and give different results. The FE calculation is the more representative and the more conservative method for such designs when considering the studied case.

Mixed-mode crack growth analysis using a cyclic plasticity model

The effects of two singularity fields, namely, the HRR solution and modified form of the nonlinear kinematic hardening (NKH) solution, on the pure mode I and mixed mode I/II fatigue crack propagation were investigated. Experiments and computations were performed on compact tension shear (CTS) specimens of P2M steel, aluminium 7050, and Ti-6Al-4V with different monotonic and cyclic elastic–plastic properties. The analysis of the experimental data on the crack growth rate for all tested materials is given in terms of plastic stress intensity factors (SIFs) according to the HRR and NKH models. The elastic–plastic crack tip fields were obtained by FE computation as a function of the position along the curvilinear crack path for the monotonic condition and the first several cycles of fatigue deformation considering the Bauschinger effect. As a complement to the FE modelling, digital image correlation (DIC) measurements of the displacement and strain fields around the crack tip in the CTS specimens were performed. This study aimed to obtain more detailed information on the local cyclic strain ahead of the mixed mode crack tip by using DIC. From the sensitivity analysis, it was established that the DIC value depended significantly on the location along the crack direction of the pair of points selected before and behind the crack tip. In this study, acceleration or retardation of the crack growth rate in terms of the NKH plastic SIF with respect to the HRR model was observed because of the coupling effect of the mode mixity and cyclic plastic properties of the tested P2M steel, aluminium 7050, and Ti-6Al-4V.

Practice Design of Ship Thin Section Considering Prevention of Welding-Induced Buckling

_ The lightweight fabrication of thin-walled cabin sections is popular for advanced ships, and the dimensional tolerance generated by welding buckling significantly influences the fabrication accuracy and schedule with poststraightening. A typical thin section employed in the superstructure of a high-tech passenger ship is considered the research object. Conventional fabrication procedures and welding conditions were examined beforehand with combined thermal elastic-plastic and elastic FE computations based on the theory of welding inherent deformation, while welding buckling was represented with identical behavior compared with fabrication observation. Actually, there are usually two methods to prevent welding buckling with advanced fabrication. Stiffeners with optimized geometrical features and excellent elasticity moduli were assembled to enhance the rigidity of the ship thin section, and less welding inherent deformation with advanced welding methods can be employed to reduce mechanical loading. Computational results show that either less in-plane welding inherent strain or higher structural rigidity can reduce the magnitude of welding-induced buckling, and avoid the generation of welding-induced buckling during the lightweight fabrication. Keywords ship thin section; welding buckling; FE computation; welding driving force; structural rigidity

JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science

This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented with pure Python while scalable to efficiently solve problems with moderate to large sizes. For example, in a 3D tensile loading problem with 7.7 million degrees of freedom, JAX-FEM with GPU achieves around 10× acceleration compared to a commercial FEM code depending on platform. Beyond efficiently solving forward problems, JAX-FEM employs the automatic differentiation technique so that inverse problems are solved in a fully automatic manner without the need to manually derive sensitivities. Examples of 3D topology optimization of nonlinear materials are shown to achieve optimal compliance. Finally, JAX-FEM is an integrated platform for machine learning-aided computational mechanics. We show an example of data-driven multi-scale computations of a composite material where JAX-FEM provides an all-in-one solution from microscopic data generation and model training to macroscopic FE computations. The source code of the library and these examples are shared with the community to facilitate computational mechanics research. Program summaryProgram Title: JAX-FEMCPC Library link to program files:https://doi.org/10.17632/hgwshjbcw6.1Developer's repository link:https://github.com/tianjuxue/jax-am/tree/main/jax_am/femLicensing provisions: GPLv3Programming language: PythonNature of problem: Implementation of the finite element method (FEM) with several appealing features that classic FEM software typically does not have: realized with pure Python; running on CPU/GPU; differentiable for solving PDE-constrained optimization problems; seamless integration with machine learning.Solution method: Our framework JAX-FEM is based on Google JAX, a high-performance numerical computing library with automatic differentiation features and supporting both CPU/GPU. Unlike classic FEM software written in Fortran or C/C++, JAX-FEM is implemented with pure Python and can easily be installed as a Python package. We demonstrate our software by solving problems including forward PDE prediction, inverse design/optimization, and data-driven analysis.

Characterization and model‐based mechanical analysis of moisture gradients in PA 6

AbstractIn this contribution, a numerical calculation environment for the determination of the moisture absorption of polyamide 6 (PA 6) is developed. The focus in this context is on modeling and evaluating the influence of locally varying water concentrations and existing moisture gradients on the mechanical properties of the material. Defined moisture distributions are set by specific conditioning processes and compared to the results of an FE calculation environment. The developed numerical method combines a mass diffusion with a subsequent structural‐mechanical simulation. The first includes a transient analysis of moisture absorption and the resulting swelling processes and residual stresses. The water concentration and residual stress distributions determined within this calculation are implemented as initial conditions in the structural mechanics FE analysis. The experimental setup of the three‐point bending test is considered in this case. The evaluation of the moisture‐induced influence on the mechanical behavior of the considered PA 6 is performed using a linear elastic modeling approach. The validation and evaluation of the calculation quality is carried out for the sorption and swelling calculation as well as for the FE model by means of experimental test data. The calculation methodology presented in this work provides a novel and even more accurate approach for the design of plastic components which are exposed to the influence of environmental humidity or direct water contact in their application.

Buckling resistance of a metal column in a corrugated sheet silo-experiments and non-linear stability calculations

The results of experimental and numerical tests of a single corrugated sheet silo column’s buckling resistance are presented in this study. The experiments were performed in a real silo with and without bulk solid (wheat). A very positive impact of the bulk solid on the column buckling resistance occurred. The experimental results were first compared to the buckling resistance calculated by Eurocode 3 formulae. The comparison revealed that code formulae were overly conservative for the empty and pre-filled silo. The experiments were next simulated using the finite element method (FEM) with initial geometric imperfections, based on geodetic measurements or linear bifurcation analyses. The bulk solid’s behaviour was described by two different linear elastic approaches. For real geometric imperfections, the FE computations and experimental findings were in good agreement (particularly for an empty silo). For the pre-filled silo with the code elasticity of the bulk solid and the geodetic amplitude of geometric imperfection of the empty silo, the numerical buckling resistance was too low as compared to the experimental outcomes. In addition, the model tests were performed for a single column with a corrugated sheet at the laboratory scale.

Multiparametric modeling of composite materials based on non-intrusive PGD informed by multiscale analyses: Application for real-time stiffness prediction of woven composites

In this paper, a multiparametric solution of the stiffness properties of woven composites involving several microstructure parameters is performed. For this purpose, non-intrusive PGD-based methods are employed. From offline pre-computed solutions generated through a full-field multiscale modeling, the proposed method approximates the multidimensional solution as a sum of products of one-dimensional functions each depending on a single variable. The present work aims at providing an accurate approximation of this multiparametric solution with lower computational cost for dataset generation. Thus, a comparative analysis of three non-intrusive PGD formulations (SSL, s-PGD and ANOVA-PGD) is carried out. The obtained results reveal and demonstrate that the ANOVA-PGD model works well for approximating the stiffness properties over the entire parameter space, i.e., along its boundary as well as inside it, by using only few pre-computed high-fidelity solutions. Finally, a GUI application is developed to exploit this multiparametric solution by incorporating other composite weave architectures. This application could be easily used by engineers and composite designers, to deduce, in real-time, the macroscopic properties of woven composite for a given set of microstructural parameters by simply varying the cursors and without any microstructure generation and meshing nor FE computations using periodic homogenization.

Buckling distortion investigation during thin plates butt welding with considering clamping influence

Welding induced buckling is generally considered as the most complicated type of out-of-plane welding distortion during thin plate section fabrication, which will significantly influence the fabrication accuracy and cost. Thin plates of 3 mm thickness with dissimilar materials were experimentally butt welded together beforehand, while clamping constraint by fixture jig and additional plate was employed. After cooling down and clamping release, out-of-plane welding distortions were measured, and characteristic of welding buckling behavior can be observed. Advanced thermal elastic plastic (TEP) FE computation with solid elements models of examined butt-welded joints were then carried out. Welding induced buckling can be represented without considering clamping constraint, while much larger difference between computed results and measurement data was obtained. When the influence of clamping constraint employed during welding experiment was considered, good agreement for both deformed tendency and magnitude of out-of-plane welding distortion can be represented. With the clarification of mechanism based on the comparison of longitudinal residual stress, plastic strain as well as shrinkage force, clamping can significantly reduce magnitude of out-of-plane welding distortion, which still could not avoid the occurrence of welding induced buckling, as well as the change of deformed shape pattern.

Strengthening and SHM system installation on RC slab using non-linear FE analysis

Re-life of aged load-bearing structures may be more efficient and economical than complete re-building. Nowadays, the strengthening of an RC structure can be designed using non-linear FE analysis, taking a realistic structural behaviour into account. Within the current article, this process is demonstrated in connection with the strengthening of a monolithic RC slab. The slab must be strengthened due to a change of function which increases live load. To ensure satisfactory operation in SLS for increased load, the flexural strengthening of the slab by CFRP strips and bonded steel plates was considered. Static verification of the slab for original and increased loads is performed by linear FE analysis. The load-bearing capacities of the original and the strengthened slabs are also determined by non-linear FE calculation. A comparative analysis of the results highlights the effectiveness of different strengthening methods in increasing the stiffness and SLS capacity of the slab. To perform real-time monitoring of the slab in question, an SHM system is also suggested with the installation of three different types of sensors. This system increases the safety of operation and reduces future maintenance and strengthening costs.

Mitigation of welding induced buckling with transient thermal tension and its application for accurate fabrication of offshore cabin structure

Offshore cabin structure is usually fabricated by welding with 6–8 mm steel plates as lightweight application, and welding distortion is inevitable generated to influence its dimensional accuracy. In particular, welding induced buckling will occur under conventional welding procedure due to the geometric feature of cabin structure. Typical fillet welded joints in considered cabin structure were numerically examined beforehand, while thermal and mechanical behaviors were represented with non-linear thermal elastic plastic FE computation. Then, welding inherent deformation was proposed as driving force for welding distortion prediction, which can be evaluated by integration of residual plastic strain for each typical welded joint. Since transient thermal tension is applied during fillet welding with numerical investigation, self-constraint supported by base materials on welding line will become weak. Thus, less plastic strain is generated during welding process, and magnitude of welding inherent deformation will be significantly reduced. Elastic FE computation with welding inherent deformation as mechanical load was carried out to predict out-of-plane welding distortion of considered cabin structure, while cases of conventional welding and welding with transient thermal tension were examined. Better fabrication accuracy can be obtained with application of transient thermal tension due to less welding inherent deformation.

Slopes Analyses - Case Study, Slope Stability of Bypass Project

The scope of this study was to compare various stability evaluation methods. Accordingly, most common LE approaches were compared with the advanced LE (M‐P) method. Similarly, the differences in FOS computed from LE and FE analyses were compared based on a simple slope considering various load cases. In addition, two real slopes in a case study were analysed for the recorded minimum‐maximum GWT, pseudo‐static and dynamic conditions. Moreover, the stability evaluations of these slopes were based on both LE (M‐P) and FE (PLAXIS) calculation approaches, which both utilized shear strength parameters from advanced triaxle tests. Similarly, Mohr‐Coulomb model was applied in both approaches. The following conclusions are hence derived based on the reported work on both idealized and real slopes. To fulfil one of the aims of the study, the LE based methods are compared based on the factor of safety (FOS) obtained for various load combinations. The comparison is mainly based on simplified slope geometry and assumed input parameters. Among the LE methods, the Bishop simplified (BS), Janbu simplified (JS) and Janbu GPS methods are compared with the Morgenstern‐Price method (M‐PM). These LE methods are well established for many years, and thus some of them are still commonly used in practice for stability analysis. Moreover, the M‐PM has been compared with results from the FE analyses. Compared with theFE (PLAXIS) analyses, the LE (M‐PM) analyses may estimate 5 – 14percent higher FOS, depending on the conditions of a dry slope and a fully saturated slope with hydrostatic pore pressure distributions. For fully saturated conditions in the slope, inaccurate computation of stresses in LE methods may have resulted in larger difference in the computed FOS. Since, the FE software is based on stress‐strain relationship, stress redistributions are surely better computed even for a complicated problem. This has been found one of the advantages in FE simulations. A parameter study shows that the application of a positive dilatancy angle in FE analysis can significantly improve the FOS (4 ‐ 10percent). On contrast, the shear surface optimization in LE (M‐PM in SLOPE/W) analysis results in lower FOS, and thus minimizing the difference in FOS compared with FE analysis

Evaluation of Behaviour of Plan Curved Structure Supported by Arch

New type of plan curved structure has been developed within the research of arch footbridges at Faculty of Civil Engineering of Brno University of Technology. Structural arrangement came out of study of behaviour of plan curved upper deck arch structures of various radii of curvature. The design method of such structures with ideal shape of arch was the outcome of the research. Results of numerical analysis were verified on physical model in scale 1:10, which has been built and tested. The model has been mounted with gauges – 41 strain gauges at various positions on concrete and steel part of the structure and 5 deflection sensors. Then the structure has been subjected to loads in various positions corresponding with load positions of variable loads in calculation model. The paper describes evaluation of measurement of stresses and deformations of physical model of plan curved structure supported by an arch. Obtained values of stresses and deformations were compared with values derived from FE calculation model.

A multiscale four-layer finite element model to predict the effects of collagen fibers on skin behavior under tension.

Human skin is a complex multilayered multiscale material that exhibits nonlinear and anisotropic mechanical behavior. It has been reported that its macroscopic behavior in terms of progression of wrinkles induced by aging is strongly dependent on its microscopic composition in terms of collagen fibers in the dermis layer. In the present work, a multiscale four-layer 2D finite element model of the skin was developed and implemented in Matlab code. The focus here was to investigate the effects of dermal collagen on the macroscopic mechanical behavior of the skin. The skin was modeled by a continuum model composed of four layers: the Stratum Corneum, the epidermis, the dermis, and the hypodermis. The geometry of the different layers of the skin was represented in a 2D model with their respective thicknesses and material properties taken from literature data. The macroscopic behavior of the dermis was modeled with a nonlinear multiscale approach based on a multiscale elastic model of collagen structure going from cross-linked molecules to the collagen fiber, combined with a Mori-Tanaka homogenization scheme. The model includes the nonlinear elasticity of the collagen fiber density, the fiber radius, the undulation, and the fiber orientation. An axial tension was applied incrementally to the lateral surfaces of the skin model. A parametric study was performed in order to investigate the effect of the collagen constituents on the macroscopic skin mechanical behavior in terms of the predicted macroscopic stress-strain curve of the skin. The results of the FE computations under uniaxial tension showed that the different layers undergo different strains, leading to a difference in the transversal deformation at the top surface. In addition, the parametric study revealed a strong correlation between macroscopic skin elasticity and its collagen structure.

Intelligent approach based on FEM simulations and soft computing techniques for filling system design optimisation in sand casting processes

This paper reports an intelligent approach for modeling and optimisation of filling system design (FSD) in the case of sand casting process of aluminium alloy. In order to achieve this purpose, physics-based process modeling using finite element method (FEM) has been integrated with artificial neural networks (ANN) and genetic algorithm (GA) soft computing techniques. A three-dimensional FE model of the studied process has been developed and validated, using experimental literature data, to predict two melt flow behaviour (MFB) indexes named ingate velocity and jet high. Two feed-forward back-propagation ANN-based process models were developed and optimised to establish the relationship between the FSD input parameters and each studied MFB index. Both ANN models were trained, tested and tuned by using database generated from FE computations. It was found that both ANN models could independently predict, with a high accuracy, the values of the ingate velocity and the jet high for training and test data. The developed ANN models were coupled with an evolutionary GA to select the optimal FSD for each one. The validity of the found solutions was tested by comparing ANN-GA prediction with FE computation for both studied MFB indexes. It was found that error between predicted and simulated values does not exceed 5.61% and 6.31% respectively for the ingate velocity and the jet high, which proves that the proposed approach is reliable and robust for FSD optimisation.

Mechanical behavior of thin-walled steel under hard contact with rigid seabed rock: Theoretical contact approach and nonlinear FE calculation

Abstract This work aims to investigate the mechanical behavior of steel-plated structures under a raking incident and to quantify the effect of the mesh size in nonlinear finite element (NLFE) analysis. To conveniently comprehend nonlinear phenomena, i.e., the grounding which takes place in this work, a series of theoretical contact formulations was defined. In the main analysis, raking, which is a part of the grounding scenario, was strictly assumed as contact between a tanker, which was assumed to have thin-walled steel, and a seabed rock in the form of a solid obstruction. Designed raking scenarios were calculated using the FE method by using the nonlinear phenomena of the material behavior in the calculation. The findings of this work indicated that the possibility of expanding the recommended mesh size in FE simulation should be evaluated by quantifying the behavior of structural responses, such as energy, the force damage pattern, and acceleration, subjected to a variety of applied meshing techniques. The results concluded that a notable difference occurred when the mesh size was more than 132 mm (ratio 11 based on the plate dimension in this work), and this size is strictly recommended to be used for calculation of the element length-to-thickness (ELT) ratio. Assessment in time simulation showed that applying larger mesh sizes will reduce the simulation time but increase the maximum values of the crashworthiness parameters, i.e., energy, force, acceleration, and displacement.