Finite element modeling of manufacturing irregularities of porous materials

Finite element model updating of a composite material beam using direct updating method

Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone

Influence of 3D QCT scan protocol on the QCT-based finite element models of human vertebral cancellous bone

The mechanical properties of well-ordered porous materials are related to their geometrical parameters at the mesoscale. Finite element (FE) analysis is a powerful tool to design well-ordered porous materials by analysing the mechanical behaviour. However, FE models are often computationally expensive. This article aims to develop a cost-effective FE model to simulate well-ordered porous metallic materials for orthopaedic applications. Solid and beam FE modelling approaches are compared, using finite size and infinite media models considering cubic unit cell geometry. The model is then applied to compare two unit cell geometries: cubic and diamond. Models having finite size provide similar results than the infinite media model approach for large sample sizes. In addition, these finite size models also capture the influence of the boundary conditions on the mechanical response for small sample sizes. The beam FE modelling approach showed little computational cost and similar results to the solid FE modelling approach. Diamond unit cell geometry appeared to be more suitable for orthopaedic applications than the cubic unit cell geometry.

Damage to civil engineering structures can be identified with a finite element (FE) model updating method using experimental modal data. In such a procedure the uncertain properties (e.g. stiffness distribution) in the FE model are adjusted by minimizing the differences between the measured modal parameters and the numerical (FE) predictions. In civil engineering the differences in eigenfrequencies and mode shapes are minimized, mostly identified from ambient vibrations. Since the modal data are nonlinear functions of the uncertain properties, an iterative sensitivity-based minimization method is used to solve this inverse problem. In order to reduce the number of unknowns, damage functions are used. The FE model updating technique is applied to a prestressed concrete bridge with 3 spans whose girder is damaged by lowering one of the intermediate piers. The damage pattern is identified (localized and quantified) by updating the Young’s and the shear modulus. Introduction Accurate condition assessment of civil engineering structures has become increasingly important. FE model updating provides a very efficient, nondestructive, global damage identification technique. The uncertain properties of the FE model are updated by minimizing the discrepancies between the measured modal data and those computed with the numerical FE model [1, 2]. The damage identification procedure is performed in two updating processes. In the first the initial FE model is tuned to a reference state, i.e. the undamaged structure. In the second process the reference FE model is updated to obtain a model which can reproduce the experimental modal data of the damaged state. The damage is identified by comparing the differences between the reference and the damaged FE model. The technique is applied to the Z24 bridge in Switzerland. It is a prestressed concrete bridge with three spans which is damaged by lowering one of the intermediate piers. A nonlinear least squares problem is solved. The residual vector contains the test/analysis differences of the first 4 bending and/or torsion modes. Frequency residuals as well as mode shape residuals are minimized. Eigenfrequencies contain global, accurate information, whereas mode shapes provide important local, but more noisy information. Therefore, both types of residuals are weighted with an appropriate factor in the residual vector. The updating parameters are both the Young’s and the shear modulus of all the girder elements. The least squares problem is solved with a sensitivity-based Gauss-Newton algorithm. In order to improve the condition of the sensitivity matrix the number of unknown parameters is reduced by using a limited set of damage functions [2]. The girder stiffness distribution is found by combining these damage functions, multiplied with the appropriate factors which are the actual variables of the minimization problem. Only linear damage functions are used, but the method can be extended by including higher order functions. With this approach always a realistic smooth result is obtained. A damage pattern is identified which resembles the observed one. The general updating procedure and the application to the Z24 bridge are presented in the paper. General FE model updating procedure Objective function. In FE model updating an optimization problem is set up in which the differences between the experimental and numerical modal data have to be minimized by adjusting the uncertain model properties [1]. The experimental modal data, i.e. the eigenfrequencies and mode shapes , are obtained from measurements. In civil engineering, the measurements are often obtained in operational conditions (ambient vibrations), which means that the exciting forces (coming from wind, traffic,. . . ) are unknown. As a consequence, an absolute scaling of the mode shapes is missing. Furthermore, only the translation degrees of freedom of the mode shapes can be measured. The minimization of the objective function is stated as a nonlinear least squares problem:

As the average age of the population has increased, the incidence of age-related bone fracture has also increased. While some of the increase of fracture incidence with age is related to loss of bone mass, a significant part of the risk is unexplained and may be caused by changes in intrinsic material properties of the hard tissue. This investigation focused on understanding how changes to the intrinsic damage properties affect bone fragility. We hypothesized that the intrinsic (μm) damage properties of bone tissue strongly and nonlinearly affect mechanical behavior at the apparent (whole tissue, cm) level. The importance of intrinsic properties on the apparent level behavior of trabecular bone tissue was investigated using voxel based finite element analysis. Trabecular bone cores from human T12 vertebrae were scanned using microcomputed tomography (μCT) and the images used to build nonlinear finite element models. Isotropic and initially homogenous material properties were used for all elements. The elastic modulus (E(i)) of individual elements was reduced with a secant damage rule relating only principal tensile tissue strain to modulus damage. Apparent level resistance to fracture as a function of changes in the intrinsic damage properties was measured using the mechanical energy to failure per unit volume (apparent toughness modulus, W(a)) and the apparent yield strength (σ(ay), calculated using the 0.2% offset). Intrinsic damage properties had a profound nonlinear effect on the apparent tissue level mechanical response. Intrinsic level failure occurs prior to apparent yield strength (σ(ay)). Apparent yield strength (σ(ay)) and toughness vary strongly (1200% and 400%, respectively) with relatively small changes in the intrinsic damage behavior. The range of apparent maximum stresses predicted by the models was consistent with those measured experimentally for these trabecular bone cores from the experimental axial compressive loading (experimental: σ(max) = 3.0-4.3 MPa; modeling: σ(max) = 2-16 MPa). This finding differs significantly from previous studies based on nondamaging intrinsic material models. Further observations were that this intrinsic damage model reproduced important experimental apparent level behaviors including softening after peak load, microdamage accumulation before apparent yield (0.2% offset), unload softening, and sensitivity of the apparent level mechanical properties to variability of the intrinsic properties.

Processing of non-random porous ceramic structures via fused deposition process is discussed. structures are characterized experimentally and statistically based on their compressive strength. Finite element modeling is used to understand the effect of stress concentration leading to the strength degradation ofthese brittle elastic solids. Introduction Porous ceramic materials are of significant technological interest due to their applications in molten metal filters, light weight core for sandwich panels, radiant burners, catalyst supports, sensors and bone grafts [1-2]. The porosity may be needed in the structures to reduce the weight of the structure at the non-critical areas, to increase the activity of the ceramics by increasing surface area or to separate the wanted from the unwanted materials during filtering. But in all the cases, a better control of the pore geometry and improvements of the mechanical properties ofthe porous structures are important to improve the reliability ofthe structures. Various processing techniques have been utilized to fabricate porous ceramic materials. Replamineform process was utilized to fabricate porous bioceramic implants to duplicate the macroporous microstructures of corals that have interconnected pores [3]. Porous alumina ceramics have been fabricated using pore former or foaming agent that evolves gases during sintering at elevated temperatures [4]. Porous Hydroxyapatite (HAp) ceramic blocks were also fabricated using HAp slurry mixed with foaming agent followed by sintering at elevated temperature [5]. Shrout et al. and Rittenmyer et al. [6-7] reported fabrication of 3-3 piezocomposites using a mixture of volatilizable plastic spheres and PZT powder, in a process known as BURPS (BURned-out Plastic Spheres). Unfortunately, all of these processes form structures with randotnly arranged pores with a wide variety of sizes and have limited flexibility to control pore volumes and porosity distribution in the final structure. In this paper, we discuss about porous ceramics with non-random pore volumes, shapes and sizes, which have been processed using solid freeform fabrication (SFF) methods. SFF offers tremendous flexibility in varying the porosity parameters which controls the strength ofthese ceramic structures as well. Theoretical and experimental characterization of porous materials is not new and several theories have already been postulated to characterize the mechanical strength of polyct:ystalline porous ceramics. These theories to characterize the mechanical strength can be classified into three broad categories: (1) reduction in cross-section area approach, (2) stress concentration approach and (3) effective flaw size approach. Most of these studies in predicting the porositystrength relationship have been limited to the fitting capability of the equations towards the available experimental data and no attempt has been made to quantitatively access the effects of porosity parameters on the strength degradation ofthe porous ceramic structures.

Quantitative computed tomography-based finite element modeling technique is a promising clinical tool for the prediction of bone strength. However, quantitative computed tomography-based finite element models were created from image datasets with different image voxel sizes. The aim of this study was to investigate whether there is an influence of image voxel size on the finite element models. In all 12 thoracolumbar vertebrae were scanned prior to autopsy (in situ) using two different quantitative computed tomography scan protocols, which resulted in image datasets with two different voxel sizes (0.29 × 0.29 × 1.3 mm(3) vs 0.18 × 0.18 × 0.6 mm(3)). Eight of them were scanned after autopsy (in vitro) and the datasets were reconstructed with two voxel sizes (0.32 × 0.32 × 0.6 mm(3) vs. 0.18 × 0.18 × 0.3 mm(3)). Finite element models with cuboid volume of interest extracted from the vertebral cancellous part were created and inhomogeneous bilinear bone properties were defined. Axial compression was simulated. No effect of voxel size was detected on the apparent bone mineral density for both the in situ and in vitro cases. However, the apparent modulus and yield strength showed significant differences in the two voxel size group pairs (in situ and in vitro). In conclusion, the image voxel size may have to be considered when the finite element voxel modeling technique is used in clinical applications.

Quantitative computed tomography-based finite element analysis (QCT/FEA) has been developed to predict vertebral strength. However, QCT/FEA models may be different with scan resolutions and element sizes. The aim of this study was to explore the effects of scan resolutions and element sizes on QCT/FEA outcomes. Nine bovine vertebral bodies were scanned using the clinical CT scanner and reconstructed from datasets with the two-slice thickness, that is, 0.6 mm (PA resolution) and 1 mm (PB resolution). There were significantly linear correlations between the predicted and measured principal strains (R2 > 0.7, P < 0.0001), and the predicted vertebral strength and stiffness were modestly correlated with the experimental values (R2 > 0.6, P < 0.05). Two different resolutions and six different element sizes were combined in pairs, and finite element (FE) models of bovine vertebral cancellous bones in the 12 cases were obtained. It showed that the mechanical parameters of FE models with the PB resolution were similar to those with the PA resolution. The computational accuracy of FE models with the element sizes of 0.41 × 0.41 × 0.6 mm3 and 0.41 × 0.41 × 1 mm3 was higher by comparing the apparent elastic modulus and yield strength. Therefore, scan resolution and element size should be chosen optimally to improve the accuracy of QCT/FEA.

A new method to determine dynamically equivalent finite element models of aircraft structures from modal test data

In this study, numerical analysis software is used to model the behavior of Tin Slag Polymer Concrete (TSPC) Column under compression. Concrete damage plasticity (CDP) model approach is employed to describe the TSPC property in the finite element (FE) model. FE model is developed based on experimental work data conducted by previous researcher. FE modelling of the TSPC column is performed with purpose to present baseline data for future improvement of the modelling as well as to facilitate future parametric study. The reason is that TSPC is a new material and there was no available previous FE model reported in previous literature as references. The FE model was validated by comparing the simulation results and experimental data for TSPC column under compression. The results indicate that FE model has achieved compressive strength of 37.65 MPa compared with experimental data of 37.62 MPa indicating 0.08% deviation and almost similar location of failure mode. Stress–strain curve indicating that FE model is stiffer than experimental specimen. In conclusion, the stress–strain curve and failure modes for the FE model must be further improved by adjusting CDP parameter in FE model to be able to describe TSPC column specimen accurately. However, the parameters applied can be used as references for future modification on modelling of the TSPC column under compression.KeywordsTSPC columnCompressive behaviorFEConcrete damage plasticityStress–strain curve

Incorporating ligament laxity in a finite element model for the upper cervical spine

ABSTRACTThis paper presents a numerical validation of a thin‐walled beam (TWB) finite element (FE) model of a realistic wind turbine rotor blade. Based on the theory originally developed by Librescu et al. and later extended to suit FE modelling by Phuong, Lee and others, this computationally efficient yet accurate numerical model is capable of capturing most of the features found in large blades including thin‐walled hollow cross section with variable thickness along the section's contour, inner reinforcements, arbitrary material layup and non‐linear anisotropic fibre‐reinforced composites; the present application is, for the time being, restricted to linearity. This one‐dimensional (1D) FE model allows retaining information of different regions of the blade's shell and therefore approximates the behaviour of more complex three‐dimensional (3D) shell or solid FE models more accurately than typical 1D FE beam models. A 9.2 m rotor blade, previously reported in specialized literature, was chosen as a case study to validate the static and dynamic behaviour predicted by a TWB model against an industry‐standard 3D shell model built in a commercial software tool. Given the geometric and material complexities involved, an excellent agreement was found for static deformation curves, as well as a good prediction of the lowest frequency modes in terms of resonance frequencies, mode shapes and frequency response functions; the highest (sixth) frequency mode shows only a fair agreement as expected for an FE model. It is concluded that despite its simplicity, a TWB FE model is sufficiently accurate to serve as a design tool for the recursive analyses required during design and optimization stages of wind turbines using only readily available computational tools. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Curved steel–concrete composite box beams are widely used in urban overpasses and ramp bridges. In contrast to straight composite beams, curved composite box beams exhibit complex mechanical behavior with bending–torsion coupling, including constrained torsion, distortion, and interfacial biaxial slip. The shear-lag effect and curvature variation in the radial direction should be taken into account when the beam is sufficiently wide. Additionally, long-term deflection has been observed in curved composite box beams due to the shrinkage and creep effects of the concrete slab. In this paper, an equilibrium equation for a theoretical model of curved composite box beams is proposed according to the virtual work principle. The finite element method is adopted to obtain the element stiffness matrix and nodal load matrix. The age-adjusted effective modulus method is introduced to address the concrete creep effects. This 26-DOF finite beam element model is able to simulate the constrained torsion, distortion, interfacial biaxial slip, shear lag, and time-dependent effects of curved composite box beams and account for curvature variation in the radial direction. An elaborate finite element model of a typical curved composite box beam is established. The correctness and applicability of the proposed finite beam element model is verified by comparing the results from the proposed beam element model to those from the elaborate finite element model. The proposed beam element model is used to analyze the long-term behavior of curved composite box beams. The analysis shows that significant changes in the displacement, stress and shear-lag coefficient occur in the curved composite beams within the first year of loading, after which the variation tendency becomes gradual. Moreover, increases in the central angle and shear connection stiffness both reduce the change rates of displacement and stress with respect to time.

The main objective of this work is to check the compatibility of Finite element method (FEM) to determine the modal parameters of the rotor system and to compare the results with analytical method. Current work is an attempt to implement different finite element (FE) models for the estimation of modal parameters. Two different order elements from Beam, Axisymmetric and Solid FE models are considered. The analysis is carried out on the rotor system and the accuracy of the results and the computation time of the FE models are estimated. The FE results are compared with the analytical method. It is observed that FE model can be used to simulate even at higher order frequencies, which is a limitation of analytical model. The analysis shows that the FE results closely match with analytical method and also the study summarizes that proper choosing of FE helps in developing rotor models in both a desirable accuracy and efficiency. Finally, a Campbell diagram is generated using the analytical method and FEM. The critical speeds are also calculated from the Campbell diagram. The closeness of the results between the two methods is checked.