Image-based Finite Element Models Research Articles

Investigation on the mechanical properties of epoxy resin with void defects using digital image correlation and image-based finite element method

Fiber-reinforced polymer composite structures are increasingly used as load-bearing components in aerospace and automotive industries. The precise mechanical properties of composites are essential for structural design and analysis. Void defects, which are caused by the curing process of resin matrix, greatly impact the overall performance of composite structures. In this study, a novel image-based finite element modeling algorithm is proposed to acquire the real three-dimensional topography of void defects, including micro X-ray computed tomography scanning, image processing, non-uniform rational B-spline reconstruction and Boolean logic operation. This new algorithm can solve the reconstruction of blurry tomographic slices. Epoxy resin specimens embedded with a low-density expanded polystyrene bead as void defect were fabricated and tested with a digital image correlation system. By using the developed modeling method, the effects of void defect on the ultimate strength, Young's modulus, damage mode and strain field distribution of specimens were analyzed and compared with experimental data. Results revealed that the real geometry of the void defect must be accounted for to obtain the maximum stress accurately.

Two-Scale Tomography Based Finite Element Modeling of Plasticity and Damage in Aluminum Foams.

In this study, finite element (FE) modeling of open-cell aluminum foams in tension was performed based on laboratory X-ray tomography scans of the materials at two different scales. High-resolution stitching tomography of the initial state allowed local intermetallic particles to be distinguished from internal defects in the solid phase of the foam. Lower-resolution scans were used to monitor the deformation and fracture in situ during loading. 3D image-based FE models of the foams were built to simulate the tensile behavior using a new microstructure-informed Gurson–Tvergaard–Needleman model. The new model allows quantitative consideration of the local presence of brittle intermetallic particles in the prediction of damage. It performs well in the discrimination of potential fracture zones in the foam, and can be easily adapted to any type of architectured material where both the global architecture and local microstructural details should be taken into account in the prediction of damage behavior.

X-ray μCT based assessment of thermal cycling induced cracks in non-crimp 3D orthogonal woven composite materials with porosity

This work focuses on X-ray micro-Computed Tomography (μCT) assessment of thermal cycling behavior of a carbon fiber/epoxy matrix composite material reinforced with a non-crimp 3D orthogonal woven preform (3DNCOW) with porosity. Porosity levels and damage mechanisms – i.e. matrix cracking - induced by thermal cycling are characterized by X-ray micro-computed-tomography (μCT). Qualitative and quantitative descriptions of the morphology and the evolution of cracks with thermal cycling are carried out through the analysis of μCT scans of samples at different cycle numbers, with emphasis on the influence of porosity on the damage mechanisms induced by thermal cycling. X-ray μCT image-based Finite Element models are employed to provide rational interpretation to the observed phenomenological scenario.

Three-Dimensional In Situ XCT Characterisation and FE Modelling of Cracking in Concrete

Three-dimensional (3D) characterisation and modelling of cracking in concrete have been always of great importance and interest in civil engineering. In this study, an in situ microscale X-ray computed tomography (XCT) test was carried out to characterise the 3D microscale structure and cracking behaviour under progressive uniaxial compressive loading. The 3D cracking and fracture behaviour including internal crack opening, closing, and bridging were observed through both 2D tomography slices and 3D CT images. Spatial distributions of voids and cracks were obtained to understand the overall cracking process within the specimen. Furthermore, the XCT images of the original configuration of the specimen were processed and used to build microscale realistic 3D finite element (FE) models. Cohesive interface elements were inserted into the FE mesh to capture complicated discrete crack initiation and propagation. An FE simulation of uniaxial compression was conducted and validated by the in situ XCT compression test results, followed by a tension simulation using the same image-based model to investigate the cracking behaviour. The quantitative agreement between the FE simulation and experiment demonstrates that it is a very promising and effective technique to investigate the internal damage and fracture behaviour in multiphasic composites by combining the in situ micro XCT experiment and image-based FE modelling.

Subject-specific finite element modelling of the human foot complex during walking: sensitivity analysis of material properties, boundary and loading conditions

The objective of this study was to develop and validate a subject-specific framework for modelling the human foot. This was achieved by integrating medical image-based finite element modelling, individualised multi-body musculoskeletal modelling and 3D gait measurements. A 3D ankle–foot finite element model comprising all major foot structures was constructed based on MRI of one individual. A multi-body musculoskeletal model and 3D gait measurements for the same subject were used to define loading and boundary conditions. Sensitivity analyses were used to investigate the effects of key modelling parameters on model predictions. Prediction errors of average and peak plantar pressures were below 10% in all ten plantar regions at five key gait events with only one exception (lateral heel, in early stance, error of 14.44%). The sensitivity analyses results suggest that predictions of peak plantar pressures are moderately sensitive to material properties, ground reaction forces and muscle forces, and significantly sensitive to foot orientation. The maximum region-specific percentage change ratios (peak stress percentage change over parameter percentage change) were 1.935–2.258 for ground reaction forces, 1.528–2.727 for plantar flexor muscles and 4.84–11.37 for foot orientations. This strongly suggests that loading and boundary conditions need to be very carefully defined based on personalised measurement data.

Image-based modeling of moisture-induced swelling and stress in 2D textile composite materials using a global-local approach

The present paper focuses on the employment of a global-local approach for the simulation of moisture-induced swelling and stress in a 2D textile carbon fiber/epoxy matrix composite material. The approach is based on the development of a robust image-based finite element model built starting from X-ray microtomography scans of a repetitive unit cell of the textile material: simulations aim at investigating both the global (sample scale) level and the local micromechanical (interfaces between matrix and fibrous tows, matrix inside a tow) level behaviour. Three models at the different cited scales are first built (ply level model, tow level and fiber level model): then a non-concurrent (node-based) approach is used for coupling the models at different scales. The results of numerical simulation of moisture-induced swelling and stress are discussed, with emphasis on the identification of the most critical zones at which maximal stress values are calculated, at different scales.

Direct medical image-based Finite Element modelling for patient-specific simulation of future implants

In patient specific biomedical simulation, the numerical model is usually created after cumbersome, time consuming procedures which often require highly specialized human work and a great amount of man-hours to be carried out. In order to make numerical simulation available for medical practice, it is of primary importance to reduce the cost associated to these procedures by making them automatic. In this paper a method for the automatic creation of Finite Element (FE) models from medical images is presented. This method is based on the use of a hierarchical structure of nested Cartesian grids in which the medical image is immersed. An efficient h-adaptive procedure conforms the FE model to the image characteristics by refining the mesh on the basis of the distribution of elastic properties associated to the pixel values. As a result, a problem with a reasonable number of degrees of freedom is obtained, skipping the geometry creation stage. All the image information is taken into account during the calculation of the element stiffness matrix, therefore it is straightforward to include the material heterogeneity in the simulation. The proposed method is an adapted version of the Cartesian grid Finite Element Method (cgFEM) for the FE analysis of objects defined by images. cgFEM is an immersed boundary method that uses h-adaptive Cartesian meshes non-conforming to the boundary of the object to be analysed.The proposed methodology, used together with the original geometry-based cgFEM, allows prosthesis geometries to be easily introduced in the model providing a useful tool for evaluating the effect of future implants in a preoperative framework. The potential of this kind of technology is presented by mean of an initial implementation in 2D and 3D for linear elasticity problems.

Methodology to Produce Specimen-Specific Models of Vertebrae: Application to Different Species

Image-based continuum-level finite element models have been used for bones to evaluate fracture risk and the biomechanical effects of diseases and therapies, capturing both the geometry and tissue mechanical properties. Although models of vertebrae of various species have been developed, an inter-species comparison has not yet been investigated. The purpose of this study was to derive species-specific modelling methods and compare the accuracy of image-based finite element models of vertebrae across species. Vertebral specimens were harvested from porcine (N = 12), ovine (N = 13) and bovine (N = 14) spines. The specimens were experimentally loaded to failure and apparent stiffness values were derived. Image-based finite element models were generated reproducing the experimental protocol. A linear relationship between the element grayscale and elastic modulus was calibrated for each species matching in vitro and in silico stiffness values, and validated on independent sets of models. The accuracy of these relationships were compared across species. Experimental stiffness values were significantly different across species and specimen-specific models required species-specific linear relationship between image grayscale and elastic modulus. A good agreement between in vitro and in silico values was achieved for all species, reinforcing the generality of the developed methodology.

Image-based correlation between the meso-scale structure and deformation of closed-cell foam

In the correlation between structural parameters and compressive behaviour of cellular materials, previous studies have mostly focused on averaged structural parameters and bulk material properties for different samples. This study focuses on the meso-scale correlation between structure and deformation in a 2D foam sample generated from a computed tomography slice of Alporas™ foam, for which quasi-static compression was simulated using 2D image-based finite element modelling. First, a comprehensive meso-scale structural characterisation of the 2D foam was carried out to determine the size, aspect ratio, orientation and anisotropy of individual cells, as well as the length, straightness, inclination and thickness of individual cell walls. Measurements were then conducted to obtain the axial distributions of local structural parameters averaged laterally to compression axis. Second, the meso-scale deformation was characterised by cell-wall strain, cell area ratio, digital image correlation strain and local compressive engineering strain. According to the results, the through-width sub-regions over an axial length between the average (lower bound) and the maximum (upper bound) of cell size should be used to characterise the meso-scale heterogeneity of the cell structure and deformation. It was found that the first crush band forms in a sub-region where the ratio of cell-wall thickness to cell-wall length is a minimum, in which the collapse deformation is dominated by the plastic bending and buckling of cell walls. Other morphological parameters have secondary effect on the initiation of crush band in the 2D foam. The finding of this study suggests that the measurement of local structural properties is crucial for the identification of the “weakest” region which determines the initiation of collapse and hence the corresponding collapse load of a heterogeneous cellular material.

Biomechanical Study of Vertebral Compression Fracture Using Finite Element Analysis

This research aimed to mechanically analyze vertebral stress concentration in one healthy subject and one subject with osteoporotic first lumbar (L1) vertebral compression fracture by using finite element analysis (FEA). We constructed three-dimensional image-based finite element (FE) models (Th12L2) by using computed tomographic (CT) digital imaging and communications in medicine (DICOM) for each patient and then conducted exercise stress simulations on the spine models. The loadings on the 12th thoracic vertebra (Th12) due to compression, flexion, extension, lateral bending, and axial rotation were examined within the virtual space for both spine models. The healthy and vertebral compression fracture models were then compared based on the application of equivalent vertebral stress. The comparison showed that vertebral stress concentration increased with all stresses in the vertebral compression fracture models. In particular, compression and axial rotation caused remarkable increases in stress concentration in the vertebral compression fracture models. These results suggest that secondary vertebral compression fractures are caused not only by bone fragility but possibly also by the increase in vertebral stress concentration around the site of the initial fracture

Quantitative Assessment of Variation in Poroelastic Properties of Composite Materials Using Micromechanical RVE Models

A poroelastic composite material, containing different material phases and filled with fluids, serves as a model to formulate the overall ablative behaviors of such materials. This article deals with the assessment of variation in nondeterministic poroelastic properties of two-phase composite materials using micromechanical representative volume element (RVE) models. Considering the configuration and arrangement of pores in a matrix phase, various RVEs are modeled and analyzed according to their porosity. In order to quantitatively investigate the effects of microstructure, changes in effective elastic moduli and poroelastic parameters are measured via finite element (FE) analysis. The poroelastic parameters are calculated from the effective elastic moduli and the pore-pressure-induced strains. The reliability of the numerical results is verified through image-based FE models with the actual shape of pores in carbon-phenolic ablative materials. Additionally, the variation of strain energy density is measured, which can possibly be used to evaluate microstress concentrations.

Equine subchondral bone failure threshold under impact compression applied through articular cartilage

Subchondral bone microdamage due to high-impact loading is a key factor leading to post-traumatic knee osteoarthritis. A quantified assessment of the mechanical characteristics of subchondral bone at the tissue-level is essential to study the mechanism of impact-induced microdamage. We combined mechanical impact testing of equine cartilage-bone with µCT image-based finite element models (μFEM) of each specimen to determine subchondral bone (including calcified cartilage: CCSB) elastic tissue modulus and local stresses and strains associated with micro-fractures within the CCSB tissue. The material properties of each specimen-specific μFEM were iteratively adjusted to match the FE-predicted stress-strain curves with experimental results. Isotropic homogeneous material properties for both uncalcified cartilage (UC) and CCSB were assumed. UC large-deformation was simulated using hyperelastic material properties. Final UC shear and CCSB tissue elastic modulus of G=38±20MPa and Et=3.3±0.7GPa were achieved after fit procedure. The results suggested that initial failure in CCSB occurred at local tensile and compressive stresses of 29.47±5.34 MPa and 64.3±21.3MPa, and tensile and compressive strains of 1.12±0.06% and 1.99±0.41%, respectively. Tissue-level material properties can be used in finite element modeling of diarthrodial joints under impact loading, and also in designing artificial cartilage-bone to replace the damaged tissue in the joint. Results can provide an estimate for the threshold of initial failure in subchondral bone tissue due to an impact compression transmitted through the overlying articular cartilage.

A phase-contrast microscopy-based method for modeling the mechanical behavior of mesenchymal stem cells

We present three-dimensional (3D) finite element (FE) models of single, mesenchymal stem cells (MSCs), generated from images obtained by optical phase-contrast microscopy and used to quantify the structural responses of the studied cells to externally applied mechanical loads. Mechanical loading has been shown to affect cell morphology and structure, phenotype, motility and other biological functions. Cells experience mechanical loads naturally, yet under prolonged or sizable loading, damage and cell death may occur, which motivates research regarding the structural behavior of loaded cells. For example, near the weight-bearing boney prominences of the buttocks of immobile persons, tissues may become highly loaded, eventually leading to massive cell death that manifests as pressure ulcers. Cell-specific computational models have previously been developed by our group, allowing simulations of cell deformations under compressive or stretching loads. These models were obtained by reconstructing specific cell structures from series of 2D fluorescence, confocal image-slices, requiring cell-specific fluorescent-staining protocols and costly (confocal) microscopy equipment. Alternative modeling approaches represent cells simply as half-spheres or half-ellipsoids (i.e. idealized geometries), which neglects the curvature details of the cell surfaces associated with changes in concentrations of strains and stresses. Thus, we introduce here for the first time an optical image-based FE modeling, where loads are simulated on reconstructed 3D geometrical cell models from a single 2D, phase-contrast image. Our novel modeling method eliminates the need for confocal imaging and fluorescent staining preparations (both expensive), and makes cell-specific FE modeling affordable and accessible to the biomechanics community. We demonstrate the utility of this cost-effective modeling method by performing simulations of compression of MSCs embedded in a gel.

Inter-lamellar shear resistance confers compressive stiffness in the intervertebral disc: An image-based modelling study on the bovine caudal disc

The intervertebral disc withstands large compressive loads (up to nine times bodyweight in humans) while providing flexibility to the spinal column. At a microstructural level, the outer sheath of the disc (the annulus fibrosus) comprises 12–20 annular layers of alternately crisscrossed collagen fibres embedded in a soft ground matrix. The centre of the disc (the nucleus pulposus) consists of a hydrated gel rich in proteoglycans. The disc is the largest avascular structure in the body and is of much interest biomechanically due to the high societal burden of disc degeneration and back pain. Although the disc has been well characterized at the whole joint scale, it is not clear how the disc tissue microstructure confers its overall mechanical properties. In particular, there have been conflicting reports regarding the level of attachment between adjacent lamellae in the annulus, and the importance of these interfaces to the overall integrity of the disc is unknown. We used a polarized light micrograph of the bovine tail disc in transverse cross-section to develop an image-based finite element model incorporating sliding and separation between layers of the annulus, and subjected the model to axial compressive loading. Validation experiments were also performed on four bovine caudal discs. Interlamellar shear resistance had a strong effect on disc compressive stiffness, with a 40% drop in stiffness when the interface shear resistance was changed from fully bonded to freely sliding. By contrast, interlamellar cohesion had no appreciable effect on overall disc mechanics. We conclude that shear resistance between lamellae confers disc mechanical resistance to compression, and degradation of the interlamellar interface structure may be a precursor to macroscopic disc degeneration.

Transient thermal finite element analysis of CFC–Cu ITER monoblock using X-ray tomography data

The thermal performance of a carbon fibre composite-copper monoblock, a sub-component of a fusion reactor divertor, was investigated by finite element analysis. High-accuracy simulations were created using an emerging technique, image-based finite element modelling, which converts X-ray tomography data into micro-structurally faithful models, capturing details such as manufacturing defects. For validation, a case study was performed where the thermal analysis by laser flash of a carbon fibre composite-copper disc was simulated such that computational and experimental results could be compared directly. Results showed that a high resolution image-based simulation (102 million elements of 32μm width) provided increased accuracy over a low resolution image-based simulation (0.6 million elements of 194μm width) and idealised computer aided design simulations. Using this technique to analyse a monoblock mock-up, it was possible to detect and quantify the effects of debonding regions at the carbon fibre composite-copper interface likely to impact both component performance and expected lifetime. These features would not have been accounted for in idealised computer aided design simulations.

Quantitative characterization of porosity and determination of elastic modulus for sintered micro-silver joints

High resolution serial block-face scanning electron microscopy has been performed on sintered micro-silver pastes that are used as lead replacement joints for die bonding. The size and spatial distributions of the porosity before and after ageing were determined by quantification of the segmented 3D images. The elastic modulus was determined by an image-based finite element model and validated by results obtained from a dynamical resonance method. In agreement with contemporary analytical models on the elastic behaviour of porous materials, the elastic modulus was found to be a function of pore fraction only. Ageing the specimens does not alter the density or Young's modulus.

Multiple-length-scale deformation analysis in a thermoplastic polyurethane.

Thermoplastic polyurethane elastomers enjoy an exceptionally wide range of applications due to their remarkable versatility. These block co-polymers are used here as an example of a structurally inhomogeneous composite containing nano-scale gradients, whose internal strain differs depending on the length scale of consideration. Here we present a combined experimental and modelling approach to the hierarchical characterization of block co-polymer deformation. Synchrotron-based small- and wide-angle X-ray scattering and radiography are used for strain evaluation across the scales. Transmission electron microscopy image-based finite element modelling and fast Fourier transform analysis are used to develop a multi-phase numerical model that achieves agreement with the combined experimental data using a minimal number of adjustable structural parameters. The results highlight the importance of fuzzy interfaces, that is, regions of nanometre-scale structure and property gradients, in determining the mechanical properties of hierarchical composites across the scales.

Assessing the local mechanical environment in medial opening wedge high tibial osteotomy using finite element analysis.

High-tibial osteotomy (HTO) is a surgical technique aimed at shifting load away from one tibiofemoral compartment, in order the reduce pain and progression of osteoarthritis (OA). Various implants have been designed to stabilize the osteotomy and previous studies have been focused on determining primary stability (a global measure) that these designs provide. It has been shown that the local mechanical environment, characterized by bone strains and segment micromotion, is important in understanding healing and these data are not currently available. Finite element (FE) modeling was utilized to assess the local mechanical environment provided by three different fixation plate designs: short plate with spacer, long plate with spacer and long plate without spacer. Image-based FE models of the knee were constructed from healthy individuals (N = 5) with normal knee alignment. An HTO gap was virtually added without changing the knee alignment and HTO implants were inserted. Subsequently, the local mechanical environment, defined by bone compressive strain and wedge micromotion, was assessed. Furthermore, implant stresses were calculated. Values were computed under vertical compression in zero-degree knee extension with loads set at 1 and 2 times the subject-specific body weight (1 BW, 2 BW). All studied HTO implant designs provide an environment for successful healing at 1 BW and 2 BW loading. Implant von Mises stresses (99th percentile) were below 60 MPa in all experiments, below the material yield strength and significantly lower in long spacer plates. Volume fraction of high compressive strain ( > 3000 microstrain) was below 5% in all experiments and no significant difference between implants was detected. Maximum vertical micromotion between bone segments was below 200 μm in all experiments and significantly larger in the implant without a tooth. Differences between plate designs generally became apparent only at 2 BW loading. Results suggest that with compressive loading of 2 BW, long spacer plates experience the lowest implant stresses, and spacer plates (long or short) result in smaller wedge micromotion, potentially beneficial for healing. Values are sensitive to subject bone geometry, highlighting the need for subject-specific modeling. This study demonstrates the benefits of using image-based FE modeling and bone theory to fine-tune HTO implant design.

Strain-rate sensitivity of foam materials: A numerical study using 3D image-based finite element model

Realistic simulations are increasingly demanded to clarify the dynamic behaviour of foam materials, because, on one hand, the significant variability (e.g. 20% scatter band) of foam properties and the lack of reliable dynamic test methods for foams bring particular difficulty to accurately evaluate the strain-rate sensitivity in experiments; while on the other hand numerical models based on idealised cell structures (e.g. Kelvin and Voronoi) may not be sufficiently representative to capture the actual structural effect. To overcome these limitations, the strain-rate sensitivity of the compressive and tensile properties of closed-cell aluminium Alporas foam is investigated in this study by means of meso-scale realistic finite element (FE) simulations. The FE modelling method based on X-ray computed tomography (CT) image is introduced first, as well as its applications to foam materials. Then the compression and tension of Alporas foam at a wide variety of applied nominal strain-rates are simulated using FE model constructed from the actual cell geometry obtained from the CT image. The stain-rate sensitivity of compressive strength (collapse stress) and tensile strength (0.2% offset yield point) are evaluated when considering different cell-wall material properties. The numerical results show that the rate dependence of cell-wall material is the main cause of the strain-rate hardening of the compressive and tensile strengths at low and intermediate strain-rates. When the strain-rate is sufficiently high, shock compression is initiated, which significantly enhances the stress at the loading end and has complicated effect on the stress at the supporting end. The plastic tensile wave effect is evident at high strain-rates, but shock tension cannot develop in Alporas foam due to the softening associated with single fracture process zone occurring in tensile response. In all cases the micro inertia of individual cell walls subjected to localised deformation is found to have negligible effect on the macro strain-rate sensitivity of Alporas foam.

Computationally Efficient Magnetic Resonance Imaging Based Surface Contact Modeling as a Tool to Evaluate Joint Injuries and Outcomes of Surgical Interventions Compared to Finite Element Modeling

Joint injuries and the resulting posttraumatic osteoarthritis (OA) are a significant problem. There is still a need for tools to evaluate joint injuries, their effect on joint mechanics, and the relationship between altered mechanics and OA. Better understanding of injuries and their relationship to OA may aid in the development or refinement of treatment methods. This may be partially achieved by monitoring changes in joint mechanics that are a direct consequence of injury. Techniques such as image-based finite element modeling can provide in vivo joint mechanics data but can also be laborious and computationally expensive. Alternate modeling techniques that can provide similar results in a computationally efficient manner are an attractive prospect. It is likely possible to estimate risk of OA due to injury from surface contact mechanics data alone. The objective of this study was to compare joint contact mechanics from image-based surface contact modeling (SCM) and finite element modeling (FEM) in normal, injured (scapholunate ligament tear), and surgically repaired radiocarpal joints. Since FEM is accepted as the gold standard to evaluate joint contact stresses, our assumption was that results obtained using this method would accurately represent the true value. Magnetic resonance images (MRI) of the normal, injured, and postoperative wrists of three subjects were acquired when relaxed and during functional grasp. Surface and volumetric models of the radiolunate and radioscaphoid articulations were constructed from the relaxed images for SCM and FEM analyses, respectively. Kinematic boundary conditions were acquired from image registration between the relaxed and grasp images. For the SCM technique, a linear contact relationship was used to estimate contact outcomes based on interactions of the rigid articular surfaces in contact. For FEM, a pressure-overclosure relationship was used to estimate outcomes based on deformable body contact interactions. The SCM technique was able to evaluate variations in contact outcomes arising from scapholunate ligament injury and also the effects of surgical repair, with similar accuracy to the FEM gold standard. At least 80% of contact forces, peak contact pressures, mean contact pressures and contact areas from SCM were within 10 N, 0.5 MPa, 0.2 MPa, and 15 mm2, respectively, of the results from FEM, regardless of the state of the wrist. Depending on the application, the MRI-based SCM technique has the potential to provide clinically relevant subject-specific results in a computationally efficient manner compared to FEM.