Material Stiffness Variations Research Articles

A multiscale Gaussian expansion method for low-frequency multimodal damping analysis of variable stiffness acoustic black hole beams

To address the issues of slow convergence and poor accuracy in existing dynamics methods caused by non-uniform variable cross-sections and layered material stiffness variations in variable stiffness acoustic black hole structure (VSABH). A multiscale Gaussian expansion method (MSGEM) is proposed in this paper. The structural dimensions are taken into account, and the structural parameters of multiple shape functions are adaptively selected based on stiffness and cross-sectional variation parameters. This results in the formation of shape function groups of various scales, which in turn creates the matrix of multi-scale Gaussian function groups. The feature information of the displacement field is realized to be extracted from multiple scales, and the fitting error of MSGEM to the displacement field of VSABH beam is within 2.02 %. The missing solution of eigenfrequency of Gaussian expansion method is avoided, and the modal vibration patterns are basically matched, which verifies the validity of MSGEM. Meanwhile, the advantages of low-frequency multimodal vibration reduction of VSABH beams are highlighted from several aspects, and the trend of the adjustment of the vibration reduction characteristics of VSABH beams by different parameters is clarified, which provides valuable design guidance for ABH metamaterials oriented to low-frequency vibration reduction.

Dependency of the Accidental Torsion Building Response on Both Live-to-Dead Load Ratio and Material Stiffness Variation

Dependency of the Accidental Torsion Building Response on Both Live-to-Dead Load Ratio and Material Stiffness Variation

Material stiffness optimization for homogenizing contact stress distribution based on particle swarm optimization using elite opposition-based learning mutation

Rapid advances in computer science and material science have made intelligent algorithms promising for solving material design problems. Particle swarm optimization (PSO) algorithm, as a typical swarm intelligence algorithm, is utilized in this paper as the tool to solve the problem of material stiffness optimization for homogenizing the contact stress distribution. In order to achieve an effective and efficient solution, the opposition-based learning (OBL) technique is introduced and combined with PSO to increases its exploration ability. Two mutation strategies, namely, dimension-by-dimension opposition-based learning and multi-dimensional random opposition-based learning mutation strategies, are further proposed to increase the population diversity of PSO. On this basis, algorithms named DEOBL-PSO and MREOBL-PSO are developed. The developed DEOBL-PSO and MREOBL-PSO are then applied to the field of nonlinear contact in engineering, and the specific problem of material stiffness optimization for homogenizing the contact stress distribution is solved. Impressive results are obtained. The contact stress distributing uniformity is substantially improved by material stiffness optimization using DEOBL-PSO and MREOBL-PSO. Additionally, new relation between material stiffness distribution and contact stress distribution is observed, and the effect of the material stiffness variation range on the contact stress distribution is further explored.

Material stiffness variation in mosquito antennae.

The antennae of mosquitoes are model systems for acoustic sensation, in that they obey general principles for sound detection, using both active feedback mechanisms and passive structural adaptations. However, the biomechanical aspect of the antennal structure is much less understood than the mechano-electrical transduction. Using confocal laser scanning microscopy, we measured the fluorescent properties of the antennae of two species of mosquito—Toxorhynchites brevipalpis and Anopheles arabiensis—and, noting that fluorescence is correlated with material stiffness, we found that the structure of the antenna is not a simple beam of homogeneous material, but is in fact a rather more complex structure with spatially distributed discrete changes in material properties. These present as bands or rings of different material in each subunit of the antenna, which repeat along its length. While these structures may simply be required for structural robustness of the antennae, we found that in FEM simulation, these banded structures can strongly affect the resonant frequencies of cantilever-beam systems, and therefore taken together our results suggest that modulating the material properties along the length of the antenna could constitute an additional mechanism for resonant tuning in these species.

Determination of Material Properties and Stiffness Variations of Carbon Nanotube reinforced Multi-Scale Laminated Composite Structures

Determination of Material Properties and Stiffness Variations of Carbon Nanotube reinforced Multi-Scale Laminated Composite Structures

A Temporally Adaptive Material Point Method with Regional Time Stepping

AbstractSpatially and temporally adaptive algorithms can substantially improve the computational efficiency of many numerical schemes in computational mechanics and physics‐based animation. Recently, a crucial need for temporal adaptivity in the Material Point Method (MPM) is emerging due to the potentially substantial variation of material stiffness and velocities in multi‐material scenes. In this work, we propose a novel temporally adaptive symplectic Euler scheme for MPM with regional time stepping (RTS), where different time steps are used in different regions. We design a time stepping scheduler operating at the granularity of small blocks to maintain a natural consistency with the hybrid particle/grid nature of MPM. Our method utilizes the Sparse Paged Grid (SPGrid) data structure and simultaneously offers high efficiency and notable ease of implementation with a practical multi‐threaded particle‐grid transfer strategy. We demonstrate the efficacy of our asynchronous MPM method on various examples including elastic objects, granular media, and fluids.

Numerical and experimental study on free vibration of 3D-printed polymeric functionally graded plates

The paper presents the free vibration analysis of simply supported 3D printed polymeric functionally graded (FG) plates with variation of material stiffness and density along their length. The analytical formulation based on Higher- Order Shear Deformation Theory (HSDT) accounts for both the shear deformation and thickness stretching effect by a sinusoidal variation of the displacement field across the thickness. The problem is then modelled using the finite element (FE) method. The FE solutions are obtained using linear hexahedral solid elements with spatially graded property distribution at different Gauss points, which is implemented by a subroutine (USDFLD) in the ABAQUS FE software. In order to validate the proposed graded FE solutions, experimental tests using Portable Digital Vibrometer (PDV) performed to capture the first natural frequency of designed and manufactured 3D printed polymeric FG plates. It can be concluded that the presented analytical formulation is not only accurate, but also provides for simple prediction of the free vibration of FG plates. Also, the good agreement found between the numerical models and experimental results demonstrates the effectiveness of graded solid elements in the modelling of FG plate vibration.

Bending analysis of functionally graded thick plates with in-plane stiffness variation

In the present paper, functionally graded (FG) materials are presented to investigate the bending analysis of simply supported plates. It is assumed that the material properties of the plate vary through their length according to the power-law form. The displacement field of the present model is selected based on quasi-3D hyperbolic shear deformation theory. By splitting the deflection into bending, shear and stretching parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Governing equations are derived from the principle of virtual displacements. Numerical results for deflections and stresses of powerly graded plates under simply supported boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other shear deformation theories and so it becomes more attractive due to smaller number of unknowns. Some numerical results are provided to examine the effects of the material gradation, shear deformation on the static behavior of FG plates with variation of material stiffness through their length.

Design and mechanical testing of a variable stiffness morphing trailing edge flap

Morphing structures that are both lightweight and conformal to the aerofoil are currently being considered as promising candidates for the next generation of aircraft high-lift systems. Utilizing spatially variable stiffness materials in morphing structures leads to a possible reduction in the actuation energy requirement and also enables geometric control over the deformed shape of the morphing structure, resulting in enhanced aerodynamic and aeroacoustic performance. In this study, a design optimization methodology has been developed to identify the required material stiffness variations of a morphing structure for target optimal deformed shapes. In the optimization scheme, a layer-wise sandwich beam model is used to predict the structural behaviour of the flap with a specific material stiffness variation. Two-dimensional fluid/structure static aeroelastic interaction analysis is performed in the design optimization. Finite element analysis and mechanical tests were also carried out for a chosen optimization result to study the actuation requirements and the capability of control over the deformed shape of the morphing trailing edge. Numerical and experimental results confirm the feasibility of the proposed optimization methodology for identifying the required stiffness variation in the core and also ways of using rapid prototyped honeycomb core to realize the honeycomb core stiffness variations are discussed.

Evaluating the effects of material properties of artificial meniscal implant in the human knee joint using finite element analysis

Artificial meniscal implants may replace severely injured meniscus and restore the normal functionality of the knee joint. Implant material stiffness and shape influence the longevity of implantations. This study, using 3D finite element analysis, aimed to evaluate the effects of material stiffness variations of anatomically shaped artificial meniscal implant in the knee joint. Finite element simulations were conducted on five different cases including intact knee, medial meniscectomized knee, and the knee joint with the meniscal implant with three distinct material stiffness. Cartilage contact pressures, compression stresses, shear stresses, and implant kinematics (medial-lateral and posterior-anterior displacement) were evaluated for an axial compressive load of 1150 N at full extension. Compared to the meniscectomized knee, the knee joint with the meniscal implant induced lower peak cartilage contact pressure and reduced the cartilage regions loaded with contact pressures greater than the peak cartilage contact pressure induced by the intact knee. Results of the current study also demonstrate that cartilage contact pressures and implant displacement are sensitive to the implant material stiffness. The meniscal implant with a stiffness of 11 MPa restores the intact knee contact mechanics, thereby reducing the risk of physiological damage to the articular cartilage.

Tuning friction with composite hierarchical surfaces

Macroscopic friction coefficients observed in experiments are the result of various types of complex multiscale interactions between sliding surfaces. Therefore, there are several ways to modify them depending on the physical phenomena involved. Recently, it has been demonstrated that surface structure, e.g. artificial patterning, can be used to tune frictional properties. In this paper, we show how the global friction coefficients can also be manipulated using composite surfaces with varying roughness or stiffness values, i.e. by combining geometrical features with the modification of local friction coefficients or stiffnesses. We show that a remarkable reduction of static friction can be achieved by introducing hierarchical arrangements of varying local roughness values, or by introducing controlled material stiffness variations.

A finite element study on the cause of vocal fold vertical stiffness variation.

A finite element method based numerical indentation technique was used to quantify the effect of the material stiffness variation and the subglottal convergence angle of the vocal fold on the vertical stiffness difference of the medial surface. It was found that the vertical stiffness difference increased with the increasing subglottal angle, and it tended to saturate beyond a subglottal angle of about 50°. The material stiffness variation could be as important as the subglottal angle depending on the actual material properties.

Spatial variation in mandibular bone elastic modulus and its effect on structural bending stiffness: A test case using the Taï Forest monkeys.

We investigated how heterogeneity in material stiffness affects structural stiffness in the cercopithecid mandibular cortical bone. We assessed (1) whether this effect changes the interpretation of interspecific structural stiffness variation across four primate species, (2) whether the heterogeneity is random, and (3) whether heterogeneity mitigates bending stress in the jaw associated with food processing. The sample consisted of Taï Forest, Cote d'Ivoire, monkeys: Cercocebus atys, Piliocolobus badius, Colobus polykomos, and Cercopithecus diana. Vickers indentation hardness samples estimated elastic moduli throughout the cortical bone area of each coronal section of postcanine corpus. For each section, we calculated maximum area moment of inertia, Imax (structural mechanical property), under three models of material heterogeneity, as well as spatial autocorrelation statistics (Moran's I, IMORAN ). When the model considered material stiffness variation and spatial patterning, Imax decreased and individual ranks based on structural stiffness changed. Rank changes were not significant across models. All specimens showed positive (nonrandom) spatial autocorrelation. Differences in IMORAN were not significant among species, and there were no discernable patterns of autocorrelation within species. Across species, significant local IMORAN was often attributed to proximity of low moduli in the alveolar process and high moduli in the basal process. While our sample did not demonstrate species differences in the degree of spatial autocorrelation of elastic moduli, there may be mechanical effects of heterogeneity (relative strength and rigidity) that do distinguish at the species or subfamilial level (i.e., colobines vs. cercopithecines). The potential connections of heterogeneity to diet and/or taxonomy remain to be discovered.

Quantify patient-specific coronary material property and its impact on stress/strain calculations using in vivo IVUS data and 3D FSI models: a pilot study.

Computational models have been used to calculate plaque stress and strain for plaque progression and rupture investigations. An intravascular ultrasound (IVUS)-based modeling approach is proposed to quantify in vivo vessel material properties for more accurate stress/strain calculations. In vivo Cine IVUS and VH-IVUS coronary plaque data were acquired from one patient with informed consent obtained. Cine IVUS data and 3D thin-slice models with axial stretch were used to determine patient-specific vessel material properties. Twenty full 3D fluid-structure interaction models with ex vivo and in vivo material properties and various axial and circumferential shrink combinations were constructed to investigate the material stiffness impact on stress/strain calculations. The approximate circumferential Young's modulus over stretch ratio interval [1.0, 1.1] for an ex vivo human plaque sample and two slices (S6 and S18) from our IVUS data were 1631, 641, and 346kPa, respectively. Average lumen stress/strain values from models using ex vivo, S6 and S18 materials with 5% axial shrink and proper circumferential shrink were 72.76, 81.37, 101.84kPa and 0.0668, 0.1046, and 0.1489, respectively. The average cap strain values from S18 material models were 150-180% higher than those from the ex vivo material models. The corresponding percentages for the average cap stress values were 50-75%. Dropping axial and circumferential shrink consideration led to stress and strain over-estimations. In vivo vessel material properties may be considerably softer than those from ex vivo data. Material stiffness variations may cause 50-75% stress and 150-180% strain variations.

Material stiffness parameters as potential predictors of presence of left ventricle myocardial infarction: 3D echo-based computational modeling study.

BackgroundVentricle material properties are difficult to obtain under in vivo conditions and are not readily available in the current literature. It is also desirable to have an initial determination if a patient had an infarction based on echo data before more expensive examinations are recommended. A noninvasive echo-based modeling approach and a predictive method were introduced to determine left ventricle material parameters and differentiate patients with recent myocardial infarction (MI) from those without.MethodsEcho data were obtained from 10 patients, 5 with MI (Infarct Group) and 5 without (Non-Infarcted Group). Echo-based patient-specific computational left ventricle (LV) models were constructed to quantify LV material properties. All patients were treated equally in the modeling process without using MI information. Systolic and diastolic material parameter values in the Mooney-Rivlin models were adjusted to match echo volume data. The equivalent Young’s modulus (YM) values were obtained for each material stress–strain curve by linear fitting for easy comparison. Predictive logistic regression analysis was used to identify the best parameters for infract prediction.ResultsThe LV end-systole material stiffness (ES-YMf) was the best single predictor among the 12 individual parameters with an area under the receiver operating characteristic (ROC) curve of 0.9841. LV wall thickness (WT), material stiffness in fiber direction at end-systole (ES-YMf) and material stiffness variation (∆YMf) had positive correlations with LV ejection fraction with correlation coefficients r = 0.8125, 0.9495 and 0.9619, respectively. The best combination of parameters WT + ∆YMf was the best over-all predictor with an area under the ROC curve of 0.9951.ConclusionComputational modeling and material stiffness parameters may be used as a potential tool to suggest if a patient had infarction based on echo data. Large-scale clinical studies are needed to validate these preliminary findings.

Analytical solutions for elastic deformation of functionally graded thick plates with in-plane stiffness variation using higher order shear deformation theory

Abstract This paper presents the deformation solution of functionally graded (FG) plates with variation of material stiffness through their length using higher order shear deformation theory (HSDT) including stretching effects. The present theory accounts for both the shear deformation and thickness stretching effect by a sinusoidal variation of the displacement field across the thickness. Equations of motion are derived from Hamilton's principle, and the relevant governing equations of elasticity are solved with a power law distribution of material property (material stiffness) to derive the analytical solution of the deflection of the FG plate. The problem is then modelled using the finite element method (FEM). The resultant analytical solutions are verified against the finite element (FE) solutions. The FE solutions are obtained using linear hexahedral solid elements with spatially graded property distribution (at different Gauss points), which is implemented by a user material subroutine (UMAT) in the ABAQUS FE software. It can be concluded that the present exact formulation is not only accurate, but also simple in predicting the bending of FG plates. Also, this study can be applied to find the optimum material distribution to produce controlled-stiffness distribution in FG plates corresponding to prescribed characteristics. Moreover, the good agreement found between the exact solution and the numerical simulation demonstrates the effectiveness of graded solid elements in the modelling of FG plate deflection under bending.

Infarcted Left Ventricles Have Stiffer Material Properties and Lower Stiffness Variation: Three-Dimensional Echo-Based Modeling to Quantify In Vivo Ventricle Material Properties.

Methods to quantify ventricle material properties noninvasively using in vivo data are of great important in clinical applications. An ultrasound echo-based computational modeling approach was proposed to quantify left ventricle (LV) material properties, curvature, and stress/strain conditions and find differences between normal LV and LV with infarct. Echo image data were acquired from five patients with myocardial infarction (I-Group) and five healthy volunteers as control (H-Group). Finite element models were constructed to obtain ventricle stress and strain conditions. Material stiffening and softening were used to model ventricle active contraction and relaxation. Systolic and diastolic material parameter values were obtained by adjusting the models to match echo volume data. Young's modulus (YM) value was obtained for each material stress-strain curve for easy comparison. LV wall thickness, circumferential and longitudinal curvatures (C- and L-curvature), material parameter values, and stress/strain values were recorded for analysis. Using the mean value of H-Group as the base value, at end-diastole, I-Group mean YM value for the fiber direction stress-strain curve was 54% stiffer than that of H-Group (136.24 kPa versus 88.68 kPa). At end-systole, the mean YM values from the two groups were similar (175.84 kPa versus 200.2 kPa). More interestingly, H-Group end-systole mean YM was 126% higher that its end-diastole value, while I-Group end-systole mean YM was only 29% higher that its end-diastole value. This indicated that H-Group had much greater systole-diastole material stiffness variations. At beginning-of-ejection (BE), LV ejection fraction (LVEF) showed positive correlation with C-curvature, stress, and strain, and negative correlation with LV volume, respectively. At beginning-of-filling (BF), LVEF showed positive correlation with C-curvature and strain, but negative correlation with stress and LV volume, respectively. Using averaged values of two groups at BE, I-Group stress, strain, and wall thickness were 32%, 29%, and 18% lower (thinner), respectively, compared to those of H-Group. L-curvature from I-Group was 61% higher than that from H-Group. Difference in C-curvature between the two groups was not statistically significant. Our results indicated that our modeling approach has the potential to determine in vivo ventricle material properties, which in turn could lead to methods to infer presence of infarct from LV contractibility and material stiffness variations. Quantitative differences in LV volume, curvatures, stress, strain, and wall thickness between the two groups were provided.

Using 3D Echo-based Modeling to Quantify in Vivo Ventricle Material Properties: A Multi-patient Study

Methods to quantify ventricle material properties noninvasively using in vivo data are of great importance in clinical applications. Echo image data were acquired from ten people, five patients with myocardial infarction (Group 1) and five healthy volunteers as control (Group 2). 3D finite element models were constructed to obtain ventricle stress and strain conditions. Material stiffening and softening were used to model ventricle active contraction and relaxation. Our results indicated that Group 2 had much greater systole-diastole material stiffness variations. This initial study indicated that our modeling approach has the potential to determine in vivo ventricle material properties, which in turn could lead to methods to infer presence of infarct from LV contractibility and material stiffness variations.

Age-related variations in the biomechanical properties of human sclera

This study examined age-related changes in biomechanical behaviour in the anterior, equatorial and posterior regions of the human sclera (white of the eye). Circumferential strip specimens were extracted from areas close to the limbus, equator and posterior pole in 45 donor scleras ranging in age between 51 and 84 years. The strips were subjected to cycles of uniaxial tension loading at a strain rate of 8% per minute while monitoring their load-deformation behaviour. All specimens demonstrated nonlinear behaviour with an initially low tangent modulus (a measure of material stiffness) increasing under higher stresses. The average ratios between the tangent modulus at a high stress of 1MPa and that at a low stress of 0.05MPa were 11.2±1.7, 12.0±1.7 and 12.4±1.5 for anterior, equatorial and posterior specimens, respectively. Stiffening was observed with age in all regions, but it was statistically significant only in the anterior region (P<0.01). Anterior specimens showed the largest stiffness growth with advancing age in both the initial, matrix regulated phase of behaviour (0.32MPa/decade), and the final, collagen regulated phase (3.97MPa/decade), followed by equatorial (0.27 and 2.15MPa/decade) then posterior specimens (0.14 and 0.26MPa/decade). The stress–strain behaviour of scleral tissue exhibits increasing stiffness with higher age. In addition to a regional variation of material stiffness, the rate of stiffness growth with age also varies between regions.

Using contracting band to improve right ventricle ejection fraction for patients with repaired tetralogy of Fallot: A modeling study using patient-specific CMR-based 2-layer anisotropic models of human right and left ventricles

Patients with repaired tetralogy of Fallot account for most cases of late-onset right ventricle failure. The current surgical approach, which includes pulmonary valve replacement/insertion, has yielded mixed results. A new surgical option of placing an elastic band in the right ventricle is proposed to improve right ventricular cardiac function as measured by the ejection fraction. A total of 20 computational right ventricular/left ventricular/patch/band combination models using cardiac magnetic resonance imaging from a patient with tetralogy of Fallot were constructed to investigate the effect of band material stiffness variations, band length, and active contraction. These models included 4 different band material properties, 3 band length, 3 active contracting band materials, and models with patch and scar replaced by contracting tissue. Our results indicated that the band insertion, combined with active band contraction and tissue regeneration techniques that restore right ventricular myocardium, has the potential to improve right ventricular ejection fraction by 7.5% (41.63% ejection fraction from the best active band model to more than 34.10% ejection fraction from baseline passive band model) and 4.2% (41.63% from the best active band model compared with cardiac magnetic resonance imaging-measured ejection fraction of 37.45%). The cardiac magnetic resonance imaging-based right ventricular/left ventricular/patch/band model provides a proof of concept for using elastic bands to improve right ventricular cardiac function. Band insertion, combined with myocardium regeneration techniques and right ventricular remodeling surgical procedures, has the potential to improve ventricular function in patients with repaired tetralogy of Fallot and other similar forms of right ventricular dysfunction after surgery. Additional investigations using invitro experiments, animal models, and, finally, patient studies are warranted.