Finite Element Model Calibration Research Articles

Neural network surrogate and projected gradient descent for fast and reliable finite element model calibration: A case study on an intervertebral disc.

Accurate calibration of finite element (FE) models is essential across various biomechanical applications, including human intervertebral discs (IVDs), to ensure their reliability and use in diagnosing and planning treatments. However, traditional calibration methods are computationally intensive, requiring iterative, derivative-free optimization algorithms that often take days to converge. This study addresses these challenges by introducing a novel, efficient, and effective calibration method demonstrated on a human L4-L5 IVD FE model as a case study using a neural network (NN) surrogate. The NN surrogate predicts simulation outcomes with high accuracy, outperforming other machine learning models, and significantly reduces the computational cost associated with traditional FE simulations. Next, a Projected Gradient Descent (PGD) approach guided by gradients of the NN surrogate is proposed to efficiently calibrate FE models. Our method explicitly enforces feasibility with a projection step, thus maintaining material bounds throughout the optimization process. The proposed method is evaluated against state-of-the-art Genetic Algorithm (GA) and inverse model baselines on synthetic and in vitro experimental datasets. Our approach demonstrates superior performance on synthetic data, achieving a Mean Absolute Error (MAE) of 0.06 compared to the baselines' MAE of 0.18 and 0.54, respectively. On experimental specimens, our method outperforms the baseline in 5 out of 6 cases. While our approach requires initial dataset generation and surrogate training, these steps are performed only once, and the actual calibration takes under three seconds. In contrast, traditional calibration time scales linearly with the number of specimens, taking up to 8 days in the worst-case. Such efficiency paves the way for applying more complex FE models, potentially extending beyond IVDs, and enabling accurate patient-specific simulations.

Structural response of precast reinforced concrete structure with emulative moment connections under internal column loss scenarios

Depending on the design, the connections of precast concrete (PC) structures can be susceptible to severe damage under large deformation. Consequently, PC structures may behave differently from cast-in-situ reinforced concrete (RC) structures under column loss scenarios. This study focuses on a class of PC structures that utilize splice sleeves (SSs) to assemble the precast components with integrated beam-column connections (IBCCs). This PC design can alleviate rebar congestion issues and minimize the need for post-cast concrete in the connection regions during assembly. The IBCCs are typically designed to mimic the behavior of corresponding RC connections under service loading conditions. However, the extent of structural emulation under column loss scenarios is not immediately clear. In this paper, the collapse behavior of PC structures with IBCCs under an internal column removal scenario is thoroughly assessed using experimental investigations and numerical analyses. Three PC subassemblages and one RC subassemblage are tested experimentally to provide experimental data for the calibration and validation of finite element (FE) models. The collapse behavior of full-span PC and RC subassemblages are next compared numerically under the internal column loss scenario, with an accompanying investigation on the influence of horizontal SSs. It is found that the PC subassemblages exhibit emulative collapse behavior as the RC subassemblage under internal column loss scenarios, provided that the horizontal SSs are located beyond the beam plastic region under the internal column loss scenario. To achieve the latter, a minimum distance of 0.15 L (L is clear beam span before column removal) is recommended for the positioning of horizontal SSs under the internal column loss scenario. Finally, it is shown that the fracture load and corresponding displacement can be enhanced with the incorporation of high ductility rebars.

Calibration and surrogate model-based sensitivity analysis of crystal plasticity finite element models

Crystal plasticity models are powerful tools for predicting the deformation behaviour of polycrystalline materials accounting for underlying grain morphology and texture. These models typically have a large number of parameters, an understanding of which is required to effectively calibrate and apply the model. This study presents a structured framework for the global sensitivity analysis of the effect of crystal plasticity parameters on model outputs. Due to the computational cost of evaluating crystal plasticity models multiple times within a finite element framework, a Gaussian process regression surrogate was constructed and used to conduct the sensitivity analysis. Influential parameters from the sensitivity analysis were carried forward for calibration using both a local Nelder-Mead and global differential evolution optimisation algorithm. The results show that the surrogate based global sensitivity analysis is able to efficiently identify influential crystal plasticity parameters and parameter combinations. Comparison of the Nelder-Mead and differential evolution algorithms demonstrated that only the differential evolution algorithm was able to reliably find the global optimum due to the presence of local minima in the calibration objective function. However, the performance of the differential evolution algorithm was dependent on the optimisation hyperparameters selected.

Finite Element Model Calibration with Surrogate Model-Based Bayesian Updating: A Case Study of Motor FEM Model

This paper introduces an advanced methodology for the calibration of Finite Element Models (FEM) utilizing a surrogate model-based Bayesian updating framework. The approach is exemplified through a case study on motor design, where precise FEM calibration is essential for predicting and optimizing motor performance. Traditional calibration techniques are often computationally expensive due to the iterative nature of the simulation process. To mitigate this, the proposed method integrates surrogate models to approximate FEM simulations, significantly reducing the computational burden without sacrificing accuracy. Bayesian updating is then employed to iteratively refine the surrogate model by incorporating new data, thereby enhancing prediction accuracy. This dual approach not only accelerates the calibration process but also ensures a high level of precision, making it highly suitable for complex engineering applications requiring both efficiency and reliability. The case study underscores the effectiveness of this methodology, demonstrating its potential to streamline the design process in motor development and other FEM-dependent engineering fields. The findings suggest that the surrogate model-based Bayesian updating approach achieves robust calibration with significantly fewer simulations, thereby optimizing both time and computational resources.

Thermally anisotropic building envelope for thermal management: finite element model calibration using field evaluation data

ABSTRACT The thermally anisotropic building envelope (TABE) is an active building envelope that redistributes thermal loads in response to weather conditions and building energy demand. Conductive layers throughout the TABE distribute low-grade heat among hydronic loops, altering heat flow direction and intensity. Finite element models of TABE roof and wall panels were developed and calibrated using field evaluation data. The calibration results showed that heat flux differences between the experimental data and finite element models averaged −0.42% and 3.57%, with a maximum mean square error of 1.78 and 3.96 for roof and wall panels, respectively. A reduction in heat flux from the environment to the building living space over the entire testing period (weeks in July/August) was found to be 85% for roof panels and 335% (load reversed) for wall panels. These results indicate TABE can effectively harness low-grade thermal energy sources to achieve high energy efficiency and promote demand-side management.

Mechanical properties of Acropora cervicornis aragonite skeleton by using multiscale models based on micro-CT data

Corals, crucial for ocean ecosystems, face threats such as ocean acidification from global warming and pollution, which weaken their skeletons. This study focuses on Acropora cervicornis, known for its hard but fragile structure, requiring strength and flexibility to withstand the forces from climate-driven atmospheric events. An experiment using uniaxial mechanical loading from the initial stage to complete failure at a very low strain rate (1.2821 × 10−5 s−1) was conducted to ascertain the mechanical properties of corals. The geometric properties and Young's modulus were analysed based on various levels of micro-architectural details from micro-CT data, with resolution values influencing the measurements. The highest resolution model showed a Young's modulus approaching 22.265 GPa and porosity at 40.448%. Calibration of finite element models incorporating micro-architectural details enabled a precise comparison of parameter effects and more accurate results, highlighting the significance of resolution in modelling coral mechanical properties.

Behaviour and design of cold-formed high-strength steel built-up beams

The adoption of high-strength steel in the construction sector can provide potential advantages, such as supporting large-scale structures with small cross-sectional sizes leading to decreased self-weight and improved space availability. In this paper, detailed numerical investigations are presented to investigate the nonlinear behaviour of cold-formed high-strength steel (HSS) built-up beams subjected to in-plane flexure along with their bending moment capacities, deformed shapes, and moment-curvature curves. Finite element (FE) models incorporating the initial geometric imperfections of cold-formed sections and material nonlinearities were established and validated against the experiments presented in the literature by comparing the moment-curvature curves, deformed shape, and ultimate bending moment capacities. Following validation, the calibrated FE models were utilized to perform extensive parametric studies to generate further numerical data by varying three different parameters: cross-sectional yield strengths (S700, S900 and S1100), geometries (such that the local slenderness, λl values varied from 1.07 to 4.65) and cold-formed steel (CFS) sheet thicknesses (1.0, 1.5, 2.0, and 2.5 mm). The specimens considered in the present study were restrained to inhibit lateral-torsional buckling and demonstrated failure owing to local buckling. The applicability of the design principles for predicting bending capabilities was assessed using numerical data in accordance with direct strength method (DSM) of AISI codal provisions and continuous strength method (CSM). The obtained numerical results demonstrated that the existing standards lack precise design procedures for cold-formed HSS built-up members and additional research is still required to provide accurate design procedures. Therefore, an improved rational extension of DSM of AISI codal provisions and CSM is recommended to predict the ultimate bending moment resistance.

Member capacity of cold-rolled aluminium alloy channel columns - part I: Experimental investigation

Cold-rolled aluminium alloy sections have been recently introduced in Australia as newly developed thin-walled products. To fabricate these sections, the roll-forming process used in cold-formed steel production has been employed, which has proven to be more cost-effective than the conventional extrusion process. This paper describes a series of compression tests to investigate member buckling behaviour and ultimate strengths of cold-rolled aluminium alloy 5052-36 channel columns. Twenty-eight specimens of three commercially available sections (C10030, C25025 and C40030) were tested at the University of Sydney. Two configurations of end boundary conditions were specially designed to capture flexural, flexural-torsional and local-global interaction buckling failure modes. Prior to testing, initial geometric imperfections were measured using a laser scanning method, and flat/corner coupons were tested to determine compressive and tensile strengths of the aluminium alloy material. The experimental results are compared with ultimate column strength predictions by current Australian/New Zealand, North American and European design specifications for aluminium structures. Additionally, the test results provide data for calibration of finite element models of cold-rolled aluminium structural members for use in parametric and similar studies. A companion paper describes such parametric study and the derivation of new design guidelines for member buckling of cold-rolled aluminium channel columns based on the numerical parametric data and the experimental data presented herein.

Analyzing the Mechanical Response of a Calibrated Finite Element Model for Flexible Pavement with Embedded Dynamic Wireless Power Transfer Technology

Analyzing the Mechanical Response of a Calibrated Finite Element Model for Flexible Pavement with Embedded Dynamic Wireless Power Transfer Technology

Stability bearing capacity of equal-leg angle steel columns with end connection joints

This study investigated the stability bearing capacity of Q355 equal-leg angle steel columns with end connection joints for transmission towers and proposed a new design method for stable bearing capacity. A total of 39 structural tests were conducted considering the connection joints. The test results, including the failure modes and load-response histories, were reported. The numerical simulations were conducted and validated using multiple comparisons. An extensive parametric study based on a calibrated finite-element model was conducted to investigate several influential parameters. The critical elastic buckling load of a three-span continuous beam with rigid or elastic supports was derived, and the relationship between the effective length coefficients and the support stiffness was obtained. Based on the experimental and numerical simulation results, a stable bearing capacity design method applicable to equal-leg angle steel columns with end connection joints was proposed. It is shown that the proposed design method improves the consistency and reliability of the prediction of the ultimate strength.

Southbank Place development: tunnel movement predictions and monitoring performance

The Southbank Place project comprised the redevelopment of the UK headquarters of the Shell Company (formerly known as the Shell Centre) in the Waterloo area of London. The project included the demolition of all structures within the site except for the iconic tower building, local extension of the existing basement and the construction of eight new mixed-use buildings. London Underground's (LU) Bakerloo Line and Northern Line running tunnels pass beneath the site. The excavation of the basement and construction of the Shell Centre in the late 1950s caused movements of the underlying Bakerloo Line tunnels that were much larger than expected. The monitoring of these tunnels between 1958 and 1995 has provided a classic case history for the behaviour of London Clay. The proposed redevelopment offered an opportunity to analyse and monitor the behaviour of LU tunnels over a period of 60 years and two phases of significant construction. This paper presents a back-analysis of the historical monitoring of the Bakerloo Line tunnels and the calibration of a sophisticated finite-element model. The model was subsequently used to predict the impact of the redevelopment on the tunnels as part of the assurance procedure with LU.

Calibration of finite element model of bridge with pier retrofitted using Fe-SMA strips

Calibration of finite element model of bridge with pier retrofitted using Fe-SMA strips

Sensitivity and reliability assessment of buckling restrained braces using machine learning assisted-simulation

Buckling Restrained Braces (BRBs) play an essential role in seismic protection due to their remarkable energy dissipation capacity, ductility, and stiffness. This paper represents the first thorough evaluation of the reliability and uncertainty of BRBs, accounting for various sources of uncertainty and varied conditions, such as different gap sizes, friction coefficients between the encasing and the steel core, and other geometric and mechanical properties of the connecting parts. This paper introduces an innovative application of an integrated probabilistic approach that combined Finite Element (FE) modeling, Artificial Neural Networks (ANN), and Monte Carlo simulation to characterize the seismic behavior of BRBs. Experimental results from literature is used to validate the FE model constructed using ABAQUS. This validated model is then integrated into a Low-rank Tensor Approximation process to yield variance-based sensitivity measures for the considered variables. The most influential variables identified in this process along with the calibrated FE model is utilized to conduct a reliability assessment through an ANN-assisted Monte Carlo simulation. This analysis is conducted to quantify the reliability level of the investigated BRBs as a function of the gap size and establish the resistance factors necessary to maintain the reliability level above prescribed thresholds. It was found that the highest reliability can be achieved at a small gap size equal to half the radius of gyration of the main steel core, requiring a resistance factor of 0.9. For gap sizes higher than this value, a resistance factor ranging between 0.70 and 0.85 is needed.

Research on the Construction of a Finite Element Model and Parameter Calibration for Industrial Hemp Stalks

Finite element numerical simulations provide a visual and quantitative approach to studying the interaction between rigid mechanical components and flexible agricultural crops. This method is an important tool for the design of modern agricultural production equipment. Obtaining accurate material model parameters for crops is a prerequisite for ensuring the reliability and accuracy of numerical simulations. To address the issue of unclear mechanical constitutive model parameters for industrial hemp stalks, this study utilized the theory of composite materials to establish a mechanical constitutive relationship model for industrial hemp stalks. Compression, tensile, and bending tests on different components of the stalk were conducted, using a computer-controlled universal testing machine, to obtain their elastic parameters. Combined with the measured basic material parameters and contact parameters of industrial hemp stalks, a finite-element numerical simulation model of industrial hemp stalks was established. By conducting Plackett–Burman and central composite experiments, it was determined that among the six measured parameters, the anisotropic plane Poisson’s ratio of the phloem and the isotropic plane Poisson’s ratio of the xylem have a significant influence on the maximum bending force of the stalk. Parameter optimization was carried out, using the relative error of the maximum bending force as the optimization objective, resulting in an anisotropic plane Poisson’s ratio of 0.054 for the phloem and an isotropic plane Poisson’s ratio of 0.28 for the xylem of industrial hemp stalks. To validate the accuracy and reliability of the optimized parameters, a numerical simulation was conducted and compared with the physical experiments. The simulated value obtained was 405.81 N while the actual measured value was 392.55 N. The error between the simulated and measured values was only 3.4%, confirming the effectiveness of the model. The precise parameters for the mechanical characteristics of industrial hemp stalk material obtained in this study can provide a parameter basis for future research on the numerical simulation of mechanized industrial hemp harvesting and retting.

Parameter optimization in a finite element mandibular fracture fixation model using the design of experiments approach

Only a few mandibular bone finite element (FE) models have been validated in literature, making it difficult to assess the credibility of the models. In a comparative study between FE models and biomechanical experiments using a synthetic polyamide 12 (PA12) mandible model, we investigate how material properties and boundary conditions affect the FE model's accuracy using the design of experiments approach.Multiple FE parameters, such as contact definitions and the materials' elastic and plastic deformation characteristics, were systematically analyzed for an intact mandibular model and transferred to the fracture fixation model. In a second step, the contact definitions for the titanium screw and implant (S–I), implant and PA12 mandible (I-M), and interfragmentary (IF) PA12 segments were optimized. Comparing simulated deformations (from 0 to −5 mm) and reaction forces (from 10 to 1′415 N) with experimental results showed a strong sensitivity to FE mechanical properties and contact definitions. The results suggest that using the bonded definition for the screw-implant contact of the fracture plate is ineffective. The contact friction parameter set with the highest agreement was identified: titanium screw and implant μ = 0.2, implant and PA12 mandible μ = 0.2, interfragmentary PA12 mandible μ = 0.1. The simulated reaction force (RMSE = 26.60 N) and surface displacement data (RMSE = 0.19 mm) of the FE analysis showed a strong agreement with the experimental biomechanical data. The results were generated through parameter optimization which means that our findings need to be validated in the event of a new dataset with deviating anatomy.Conclusively, the predictive capability of the FE model can be improved by FE model calibration through experimental testing. Validated preoperative quasi-static FE analysis could allow engineers and surgeons to accurately estimate how the implant's choice and placement suit the patient's biomechanical needs.

Block shear and tear-out in bolted connections as limited by curling

In the literature, the block shear and tear-out phenomena and strengths of cold-formed steel bolted connections have been well understood and thoroughly investigated. However, the strength of these failure modes in the bolted connections between thin and thick plates may be governed by the effect of out of plane curling of the thin plate, and this phenomenon has not been studied in detail yet. It is apparent that the curling not only affects the shear strength but also changes the behaviour of the bolted connections. In particular, the design shear strength of the bolted connections remains unchanged with high ductility even though the end distance between the bolt holes and the free edge is becoming larger. An experimental program on the block shear and tear-out behaviour of bolted connections was performed at the University of Sydney in order to provide a better understanding on the effect of the curling. A total of 48 tests including thicknesses of thin plates (1.0 mm, 1.2 mm and 1.9 mm) and 10 mm thick plates was conducted at the University of Sydney with three configurations of bolted connections in conjunction with two different hole diameters (9 mm and 14 mm) and various end distances as the main variables. Three different failure modes being block shear, tear-out and curling were observed in the tests. In addition, different material properties of the cold-formed sheet steels (i.e., G300, G450, G500 and G550) were also considered in this program to create a large database for the investigation. Consequently, a design equation for block shear and tear-out strength accounting for the curling effect is proposed in this paper. It provides a better correlation with the experimental results than those predicted in the current Australian and New Zealand Standard (AS/NZS 4600) and the North American Specification for cold-formed steel structures (AISI S100). In addition, a calibrated Finite Element Model (FEM) was subsequently developed using the commercial finite element program ABAQUS to verify against the test results. The reliable data set of the FEM models is further utilised to extend the data range in a parametric study and is finally used for the verification procedure of the proposed formula over a wider range of data.

Model-informed deep learning strategy with vision measurement for damage identification of truss structures

Structural damage identification approaches can be divided into two categories, i.e. data-driven approaches via statistical pattern recognition and model-based approaches via finite element (FE) model updating. These two approaches have their own merits, and their main shortcomings can be remedied by each other’s merits. Therefore, this study proposed a deep learning-based damage identification strategy involving both data-driven and model-based approaches, termed as model-informed deep learning (MIDL)-based strategy. This strategy first proposes a vision-based displacement estimation approach to extract structural displacement responses from video data. This approach reduces the displacement drift induced by conventional optical flow approaches and improves the tracking accuracy of feature points. Then, a calibrated FE model is built to construct data sets with different damage levels via FE model updating and time-history analysis. Following this, a one-dimensional convolutional neural network (1D CNN) is established to detect and localize structural damage by using direct displacement responses. Finally, FE model updating is performed again to quantify structural damage level with constrained targets. A truss structure is further used to evaluate the accuracy of the proposed strategy experimentally. Results illustrate that the proposed MIDL strategy, which uses time series to localize the structural damage, achieves a global location accuracy of 86.09% and avoids the feature extraction process. Meanwhile, with the known damage location, the efficiency and accuracy of structural damage quantification via rerunning model updating can also be significantly improved. In addition, the displacements estimated by the proposed approach have a good match with ground truth values with error standard deviations of less than 0.3 mm.

Modelling Strategies for the Updating of Infilled RC Building FEMs Considering the Construction Phases

This paper deals with modelling strategies for the updating of Finite Element Models (FEMs) of infilled Reinforced Concrete (RC) frame buildings. As is known, this building typology is the most adopted worldwide for residential houses and strategic buildings, such as hospitals, schools, police stations, etc. The importance of achieving trustworthy numerical models for these kinds of structures, especially the latter ones, is clear. The updating procedure mainly consists in changing the geometrical and mechanical material properties of models until pre-determined convergence criteria are verified, the latter based on the comparison between numerical and experimental outcomes. In this work, the modelling strategies that can be adopted to refine FEMs of infilled RC buildings are treated in-depth, starting from the simple model usually developed for design purposes. Modelling techniques relevant to the geometry, the mechanical properties, the mass, and the restraint conditions of the model are discussed. Moreover, the approaches that can be adopted to calibrate numerical models during the construction process are addressed as well. Then, an application of the proposed strategies is provided with reference to a real building that was investigated during its construction. The proposed modelling strategies proved to be effective in the model updating of the considered building and provide useful support for the calibration of FEMs of this building typology in general.

8-MW wind turbine tower computational shell buckling benchmark. Part 2: Detailed reference solution

An assessment of the elastic–plastic buckling limit state for multi-strake wind turbine support towers poses a particular challenge for the modern finite element analyst, who must competently navigate numerous modelling choices related to the tug-of-war between meshing and computational cost, the use of solvers that are robust to highly nonlinear behaviour, the potential for multiple near-simultaneously critical failure locations, the complex issue of imperfection sensitivity and finally the interpretation of the data into a safe and economic design.This paper presents a detailed reference solution to the computational buckling analysis of a standardised benchmark problem of an 8-MW multi-strake wind turbine support tower. Both linear and nonlinear analyses are performed, including advanced GMNIA with several different models of geometric imperfections. The crucial issue of interpreting the imperfection amplitude in a way that is compliant with the new prEN 1993-1-6 is discussed in detail. The solution presented herein is intended for use by analysts in both industry and academia for training, verification and calibration of finite element models and is intended to initiate a public repository of such computational solutions for metal civil engineering shell structures.This paper is the second of a pair. The first paper [37] presents a synthesis of 29 submissions to an international round-robin exercise performed on the same benchmark problem.

Evaluation of Spliced UHM CFRP Strip Panels for Strengthening Steel Beams

Short ultrahigh-modulus (UHM) carbon fiber–reinforced polymer (CFRP) strip panels connected through a finger joint configuration offer a convenient modular method for strengthening steel girders. Three-dimensional nonlinear finite-element (FE) analysis was conducted to characterize the interfacial and flexural behavior of strip panels. The calibrated FE model provides an efficient and economical method of evaluating different parameters related to the material properties and strengthening configuration of the UHM CFRP strip panels, for which experimental data are not available. Analysis implemented robust features, including debonding of CFRP using a mixed-mode bond–slip model, CFRP rupture, steel yielding, and concrete slab crushing. Predictions were calibrated and validated against experimental results from double lap shear tests and flexural tests of steel beams and steel–concrete composite beams. The FE model was used to investigate the effects of finger joint location, joint length, and laminate thickness. Strip panels with 300-mm-long finger joints and thicknesses of up to 2 mm equaled the strength of a continuous laminate with the same CFRP area. Both failed by CFRP rupture. At greater thicknesses, debonding occurred at lower ultimate loads than for a continuous laminate. The finger joint splice was also compared to the traditional splice plate method. The splice plate length required to achieve the same level of load transfer was longer than the finger joint length when the connection was in the maximum moment region. For a given CFRP thickness and splice plate length (or finger joint length), strip panels with finger joints provide greater load-carrying capacity.