Inhomogeneous Material Properties Research Articles

Verified and validated finite element analyses of humeri

Background: Although ~200,000 emergency room visits per year in the US alone are associated with fractures of the proximal humerus, only limited studies exist on their mechanical response. We hypothesise that for the proximal humeri (a) the mechanical response can be well predicted by using inhomogeneous isotropic material properties, (b) the relation between bone elastic modulus and ash density (E(ρash)) is similar for the humerus and the femur, and may be general for long bones, and (c) it is possible to replicate a proximal humerus fracture in vitro by applying uniaxial compression on humerus׳ head at a prescribed angle. Methods: Four fresh frozen proximal humeri were CT-scanned, instrumented by strain-gauges and loaded at three inclination angles. Thereafter head displacement was applied to obtain a fracture. CT-based high order (p-) finite element (FE) and classical (h-) FE analyses were performed that mimic the experiments and predicted strains were compared to the experimental observations. Results: The E(ρash) relationship appropriate for the femur is equally appropriate for the humeri: predicted strains in the elastic range showed an excellent agreement with experimental observations with a linear regression slope of m=1.09 and a coefficient of regression R2=0.98. p-FE and h-FE results were similar for the linear elastic response. Although fractures of the proximal humeri were realised in the in vitro experiments, the contact FE analyses (FEA) were unsuccessful in representing properly the experimental boundary conditions. Discussion: The three hypotheses were confirmed and the linear elastic response of the proximal humerus, attributed to a stage at which the cortex bone is intact, was well predicted by the FEA. Due to a large post-elastic behaviour following the cortex fracture, a new non-linear constitutive model for proximal humerus needs to be incorporated into the FEA to well represent proximal humerus fractures. Thereafter, more in vitro experiments are to be performed, under boundary conditions that may be well represented by the FEA, to allow a reliable simulation of the fracture process.

Digital Plasmonic Absorption Modulator Exploiting Epsilon-Near-Zero in Transparent Conducting Oxides

Optical switches operated around ε-near-zero (ENZ) of transparent conducting oxides (TCOs) are analyzed. A digital optical switching behavior is derived that is quite different from earlier predictions. The digital modulation characteristic originates from the fact that the nonlinear switching is, to a large extent, performed in the ENZ layer. The ENZ layer, however, arises from carrier accumulation in the TCO and is confined to a relatively thin layer with a characteristic dimension that does not change upon applying a higher voltage. An accurate treatment of this inhomogeneous layer is vital to reliably predict modulation characteristics. Such nonlinear accumulation processes and inhomogeneous material properties require refined simulations, which is why we apply an iterative solver based on a high-order finite-element method. More precisely, we solve the nonlinear stationary quantum hydrodynamic model to derive the carrier concentration upon applying an electrical field across the modulator. The result is then directly coupled to Maxwell's equation, which shows a strong local enhancement of the electromagnetic fields in the ENZ layer. In an exemplary implementation, we forecast the feasibility of 6 μm long TCO absorption modulators with on-state losses of 2.8 dB and extinction ratios above 10 dB.

弾塑性有限要素解析によるき裂を有する構造物の耐荷重評価（ステンレス鋼平板および管の耐荷重予測方法の検討）

A procedure for obtaining the load carrying capacity of cracked components of ductile material conducting by an elastic-plastic finite element analysis (FEA) was discussed. First, tensile tests using stainless steel plate specimens with through wall or part-through wall crack were performed. The deformation and strain were measured by the digital image correlation technique. Ductile crack initiation behavior was also observed. The tests was simulated by the elastic-plastic FEA. It was shown that the maximum load obtained by the FEA was about 1.15 times that obtained by the tests. The FEA using the stress-strain curve estimated by the K-fit method, in which the curve is estimated using the yield and ultimate strengths, agreed well that obtained using the curve by the tensile test. The FEA was also performed for simulating four point bending tests of cracked stainless steel pipes. Since the drop in applied load caused by ductile crack penetration of wall thickness was difficult to simulate, the stress penetration criterion was newly proposed. It was shown that the load for crack penetration could be predicted by the stress penetration criterion. Finally, the procedure for performing the FEA using the K-fit method and the stress penetration criterion was discussed for applying fitness-for-service assessments. The procedure allows deriving the load carrying capacity of cracked components which has a complex geometry or has inhomogeneous material properties such as welding portion.

Fracture Toughness of Explosively Welded Al/Ti Layered Material in Cryogenic Conditions

In the paper results of comparative analysis of the fracture toughness of explosively welded Al/Ti composite determined for the ambient temperature and for the cryogenic conditions were presented. Testing of mechanical properties of inhomogeneous materials very often presents a lot of difficulties connected with the experimental procedures as well as with the interpretation of study results. It is also in the case of layered Al/Ti material, for which cracking history has different nature for both layers: aluminium and titanium alloy. However, from the viewpoint of practical application, the knowledge of ‘global’ material properties is important. Due to differences of properties of both materials constituting the Al/Ti bimetal, it is hard to talk about determination of material property, which is plane strain fracture toughness K1C. In such case more adequate is fracture toughness KQ value, which can refers to the system of two materials. In investigations compact tension (CT) specimens were used. For specimens used in the tests the ratio of width to thickness W/B was 4. The initial pre-cracks were made by cyclic axial loading of specimens. The experimental tests were made with the use of the axial servohydraulic test system equipped with an original cryogenic chamber. During the tests all parts including specimen, clevis grips, extensometer were immersed in liquid nitrogen. The influence of cryogenic temperature on the fracture toughness was observed as a result of the tests.

Singularity analysis for a V-notch with angularly inhomogeneous elastic properties

Stress singularity of a V-notch with angularly inhomogeneous elasticity is studied in this work. The characteristic differential equations with respect to the orders of the stress singularity for the V-notch problem are derived by using of asymptotic expansion technique. The boundary conditions on the two radial edges of the V-notch are then expressed by the combination of the orders of the stress singularity and the characteristic angular functions. With the manipulation, the problem is transformed into solving the characteristic ordinary differential equations with variable coefficients under the corresponding boundary conditions, which are solved by the interpolating matrix method developed by us before. The method and treatments presented are suitable for the singularity analyses of the V-notches with any angularly inhomogeneous material properties under the plane and anti-plane loading. As examples, the singularities of the V-notches with three differential types of angularly variable elasticity moduli are evaluated and compared for their orders of the stress singularity.

Prediction of facial deformation after complete denture prosthesis using BP neural network

With the accelerated aging of world population, complete denture prosthesis plays an increasingly important role in mouth rehabilitation. In addition to recovering stomatognathic system function, restoring the appearance of a third of the area under the face has become a great challenge in complete denture prosthesis. This study analyzes the interactive relationship between the appearance of a third of the area under the face and complete denture, and proposes a new method to predict facial deformation after complete denture prosthesis. Firstly, to improve computational efficiency, the feature template is constructed to replace the deformed facial region. Secondly, a forecast model of elastic deformation is constructed using BP neural network and predicts elastic deformation amount because of the inhomogeneous, anisotropic and nonlinear material properties of soft tissue. Finally, a new feature template is calculated using deformation amount, and the deformation of preoperative model is simulated using Laplacian deformation technique. The average error rates of different hidden layer nodes in the neural network are analysed. Deformation and postoperative models are superimposed for match analysis. Experimental results show that this method can predict facial soft tissue deformation quickly and accurately.

An approach to prediction of microstructure formation near friction surfaces at large plastic strains

The paper develops an approach to formulation of constitutive equations for predicting the microstructure formation in a thin material layer near surfaces with high friction stresses in material forming processes. The approach is based on the use of the strain rate intensity factor. An equation relating the layer thickness to the strain rate intensity factor is proposed. A similarity condition that provides the same layer thickness at appropriate friction surface points in full-scale and model experiments is derived. The condition implies that the degree of strain inhomogeneity and hence the degree of inhomogeneity of material properties depends on the scale factor. As an example, compression of a thin layer between parallel plates is considered. Assuming validity of the proposed equation, a relationship is established between the parameters of compression and the layer thickness with essentially changed microstructure.

High-speed laser-assisted cutting of strong transparent materials using picosecond Bessel beams

We report single-pass cutting of strong transparent glass materials of 700 μm thickness with a speed up to 270 mm/s using single-shot nanostructuring technique exploiting picosecond, zero-order Bessel beams at laser wavelength of 1030 nm. Particularly, we present results of a systematic study of cutting of tempered glass which has high resistance to thermal and mechanical shocks due to the inhomogeneous material properties along its thickness, and homogeneous glass that identify a unique focusing geometry and a finite pitch dependency, for which cutting with high quality and high reproducibility can be achieved. These results represent a significant advancement in the field of high-speed cutting of technologically important transparent materials.

TU‐F‐CAMPUS‐J‐02: Mooney‐Rivlin Biomechanical Modeling of Lung with Inhomogeneous Material Property

Purpose:The Mooney‐Rivlin material with hyperelastic strain energy has been proposed for realistic biomechanical modeling of lung. In this study, the lung is modeled as an inhomogeneous Mooney‐Rivlin material with the incompressibility factors being optimized to improve the tumor center of mass (TCM) motion simulation accuracy during respiration.Method:ITK‐SNAP was used to segment lungs of eight lung cancer patients from the 4D‐CT images and tetrahedral volume meshes of the lungs in phase 50% were created by using adaptive mesh generation toolkit. The interphase deformation vector fields (DVFs) are calculated by demons deformable registration algorithm and the barycentric coordinate system of tetrahedral elements is obtained from the resulted DVFs. Mooney‐Rivlin hyperelastic material is used to model the lung volume. Each element is considered unique where the incompressibility factor (k‐factor) for each element is assumed to be proportional to the magnitude of normalized DVF. The incompressibility factor for each element was optimized by minimizing the tumor center of mass motion simulation error.Results:If lung is considered as a homogenous material in Mooney‐Rivlin modeling, the average TCM motion simulation error is 2.26 mm. By considering inhomogeneous properties of lung in the proposed strategy, the average TCM motion simulation error is reduced to 2.04 mm.Conclusions:We proposed a method for assigning the inhomogeneous biomechanical material in the Mooney‐Rivlin model of lung based on the lung regional deformation vector fields. Inhomogeneous material property of lung improves the simulation accuracy.

Mesoscale simulation of the solidification process in injection moulded parts

Abstract Due to their wide range of applications and their complex material properties, it is desirable to be able to predict the behaviour of injection moulded parts with the help of simulation tools. For semi-crystalline materials, this can only take place with considerable accuracy if the inhomogeneous material properties are taken into account. Because of this, it is necessary to calculate the microstructure of the solidified melt and to incorporate these findings in the simulation. We present an integrative, multiscale simulation approach in which the manufacturing process is calculated on a macroscale and the solidification process on a mesoscale. A multiphase filling and cooling simulation is done to calculate temperature and velocity fields, which are used as boundary conditions for the calculation of the spherulite distribution in the part. We present the used nucleation and growth model and shortly describe the parallelisation approach of the mesoscale simulation.

On the computation of the Hashin–Shtrikman bounds for transversely isotropic two-phase linear elastic fibre-reinforced composites

Although various forms for the Hashin–Shtrikman bounds on the effective elastic properties of inhomogeneous materials have been written down over the last few decades, it is often unclear how to construct and compute such bounds when the material is not of simple type (e.g. isotropic spheres inside an isotropic host phase). Here, we show how to construct, in a straightforward manner, the Hashin–Shtrikman bounds for generally transversely isotropic two-phase particulate composites where the inclusion phase is spheroidal, and its distribution is governed by spheroidal statistics. Note that this case covers a multitude of composites used in applications by taking various limits of the spheroid, including both layered media and long unidirectional composites. Of specific interest in this case is the fact that the corresponding Eshelby and Hill tensors can be derived analytically. That the shape of the inclusions and their distribution can be specified independently is of great utility in composite design. We exhibit the implementation of the computations with several examples.

Flexural Behavior of HPFRCC Members with Inhomogeneous Material Properties.

In this paper, the flexural behavior of High-performance Fiber-Reinforced Cementitious Composite (HPFRCC) has been investigated, especially focusing on the localization of cracks, which significantly governs the flexural behavior of HPFRCC members. From four points bending tests with HPFRCC members, it was observed that almost evenly distributed cracks formed gradually, followed by a localized crack that determined the failure of the members. In order to investigate the effect of a localized crack on the flexural behavior of HPFRCC members, an analytical procedure has been developed with the consideration of intrinsic inhomogeneous material properties of HPFRCC such as cracking and ultimate tensile strengths. From the comparison, while the predictions with homogeneous material properties overestimated flexural strength and ductility of HPFRCC members, it was found that the analysis results considering localization effect with inhomogeneous material properties showed good agreement with the test results, not only the flexural strength and ductility but also the crack widths. The test results and the developed analysis procedure presented in this paper can be usefully applied for the prediction of flexural behaviors of HPFRCC members by considering the effect of localized cracking behavior.

Preventing lodging in bioenergy crops: a biomechanical analysis of maize stalks suggests a new approach.

The hypothetical ideal for maize (Zea mays) bioenergy production would be a no-waste plant: high-yielding, with silage that is easily digestible for conversion to biofuel. However, increased digestibility is typically associated with low structural strength and a propensity for lodging. The solution to this dilemma may lie in our ability to optimize maize morphology using tools from structural engineering. To investigate how material (tissue) and geometric (morphological) factors influence stalk strength, detailed structural models of the maize stalk were created using finite-element software. Model geometry was obtained from high-resolution x-ray computed tomography (CT) scans, and scan intensity information was integrated into the models to infer inhomogeneous material properties. A sensitivity analysis was performed by systematically varying material properties over broad ranges, and by modifying stalk geometry. Computational models exhibited realistic stress and deformation patterns. In agreement with natural failure patterns, maximum stresses were predicted near the node. Maximum stresses were observed to be much more sensitive to changes in dimensions of the stalk cross section than they were to changes in material properties of stalk components. The average sensitivity to geometry was found to be more than 10-fold higher than the average sensitivity to material properties. These results suggest a new strategy for the breeding and development of bioenergy maize varieties in which tissue weaknesses are counterbalanced by relatively small increases (e.g. 5%) in stalk diameter that reduce structural stresses.

Creating femtosecond-laser-hyperdoped silicon with a homogeneous doping profile

Femtosecond-laser hyperdoping of sulfur in silicon typically produces a concentration gradient that results in undesirable inhomogeneous material properties. Using a mathematical model of the doping process, we design a fabrication method consisting of a sequence of laser pulses with varying sulfur concentrations in the atmosphere, which produces hyperdoped silicon with a uniform concentration depth profile. Our measurements of the evolution of the concentration profiles with each laser pulse are consistent with our mathematical model of the doping mechanism, based on classical heat and solute diffusion coupled to the far-from-equilibrium dopant incorporation. The use of optimization methods opens an avenue for creating controllable hyperdoped materials on demand.

FE Simulation and Full-field Strain Measurements to Evaluate the Necking Phenomena

During airbag production, many parts are obtained by plastic deformation such as the lid of the gas generator. Since the airbag gas generator is a significant vehicle safety part, several pressure tests have been developed in order to prove the reliability of this product. A ductile fracture problem initialized by a localization of the deformation is observed along the blending radius. In order to understand the mechanical processes involved in the forming operation, a numerical and experimental study was developed. A tensile test specimen extracted from the sheet of study, undergoes elastic deformation that is followed by a transition to plastic deformation. Although during this stage of the test the deformation is stable, the strains begin to localize within a relatively broad zone known as diffuse necking. The stable deformation, with continuously rising load, is followed by the instability whereby a local neck or shear band is produced due to strong localization of deformation. The localization is explainable by the inhomogeneity in macroscopic material properties in the specimen. The necking behavior is a vital precursor to the final failure. A Digital Image Correlation (DIC) method is used in 2D and 3D to evaluate the necking and localization of deformation, which shows clearly the two stage of necking phenomena. Moreover, a numerical modeling was developed of tensile test under ABAQUS commercial software. In this model we use Gurson Tvergaard Needleman (GTN) ductile model of damage to predict the necking phenomenon. Furthermore the results from FE simulations are compared with experimental results from uniaxial tensile tests. Finally we develop the numerical model of the lid of the gas generator obtained by forming process.

3D scanning SAXS: A novel method for the assessment of bone ultrastructure orientation

The arrangement and orientation of the ultrastructure plays an important role for the mechanical properties of inhomogeneous and anisotropic materials, such as polymers, wood, or bone. However, there is a lack of techniques to spatially resolve and quantify the material's ultrastructure orientation in a macroscopic context. In this study, a new method is presented, which allows deriving the ultrastructural 3D orientation in a quantitative and spatially resolved manner. The proposed 3D scanning small-angle X-ray scattering (3D sSAXS) method was demonstrated on a thin trabecular bone specimen of a human vertebra. A micro-focus X-ray beam from a synchrotron radiation source was used to raster scan the sample for different rotation angles. Furthermore, a mathematical framework was developed, validated and employed to describe the relation between the SAXS data for the different rotation angles and the local 3D orientation and degree of orientation (DO) of the bone ultrastructure. The resulting local 3D orientation was visualized by a 3D orientation map using vector fields. Finally, by applying the proposed 3D scanning SAXS method on consecutive bone sections, a 3D map of the local orientation of a complete trabecular element could be reconstructed for the first time. The obtained 3D orientation map provided information on the bone ultrastructure organization and revealed links between trabecular bone microarchitecture and local bone ultrastructure. More specifically, we observed that trabecular bone ultrastructure is organized in orientation domains of tens of micrometers in size. In addition, it was observed that domains with a high DO were more likely to be found near the surface of the trabecular structure, and domains with lower DO (or transition zones) were located in-between the domains with high DO. The method reproducibility was validated by comparing the results obtained when scanning the sample under different sample tilt angles. 3D orientation maps such as the ones created using 3D scanning SAXS will help to quantify and understand structure–function relationships between bone ultrastructure and bone mechanics. Beyond that, the proposed method can also be used in other research fields such as material sciences, with the aim to locally determine the 3D orientation of material components.

Microscopically inhomogeneous electronic and material properties arising during thermal and plasma CVD of graphene

Graphene layers were prepared on copper substrates by thermal chemical vapor deposition (CVD) and microwave (MW) plasma CVD processes. Atomic force microscopy in topography, phase imaging, and conductivity detection (C-AFM) as well as Raman micro-spectroscopy are employed to analyze the graphene layers on a microscopic scale in an as-deposited state on copper. By correlating these data we identify microscopic inhomogeneities (on a micrometer and nanometer scale) in material and electrical properties of both types of graphene. The inhomogeneities are attributed to (i) large but defects including flakes of plasma CVD graphene and (ii) high quality but small flakes of thermal CVD graphene. Moreover, the plasma CVD graphene contains large density of non-conductive openings (0.1–1 μm in size) where no graphene is detected. The obtained data explain two orders of magnitude lower electrical conductivity of the plasma CVD graphene measured macroscopically after substrate transfer. Implications for optimizing the graphene growth processes are discussed.

Zone wise local characterization of welds using digital image correlation technique

The process of welding is associated with high and varying thermal gradients across the weld, resulting in inhomogeneous material properties surrounding the weldment. A proper understanding of the varying mechanical properties of the weld and surrounding materials is important in designing and modelling of components with weld. In the present study the characterization of different zones such as fusion zone, heat affected zones and unaffected base material of a deposited weld is carried out using digital image correlation (DIC) technique. A methodology using the micrographic observation and image processing is proposed for accurate identification of various weld zones. The response of welded samples in the elastic and plastic region is compared with the virgin sample. Full range stress–strain curves are obtained for each zone using the whole field strain measurement involving DIC. The parameters investigated are Young׳s modulus, Poisson׳s ratio, yield stress, strain hardening exponent and strength coefficient. A study regarding the variation of properties with respect to varying weld currents of 100A, 130A and 150A is carried out. The Vickers microhardness measurement is also conducted to obtain the variation in hardness across weldment. Fusion zone of all the welded samples have reported lower Young׳s modulus and higher yield strength compared to virgin samples. The Vickers hardness values obtained for fusion and heat affected zones are in line with the yield stress variation obtained zone wise.

Superscatterer Illusions Without Using Complementary Media

Research has suggested that it is possible to create a superscatterer using complementary media, which is however very difficult to realize, and hence such a superscatterer has not been verified by experiments. An easier way to realize superscatterer illusions with abundant functionality based on transformation optics is proposed here, in which only anisotropic and inhomogeneous media with positive components are required. By enclosing a metallic object within the superscatterer illusion device, the scattering signature of the object equals that of an enlarged metallic object with a pre‐controlled scaling factor and multiple dielectric objects with pre‐designed material properties. The proposal is demonstrated by numerical simulations and finally verified by experiments of an elaborately designed proof‐of‐concept sample made of 6408 gradually varying meta‐atoms. A new strategy, combining compact electric‐ and magnetic‐resonance particles, is proposed to fulfill the complicated inhomogeneous and anisotropic material properties.

Interaction of bursts in exponentially graded materials characterized by parametric plots

The nonlinear interaction of tone bursts in functionally graded materials with strongly variable properties is studied resorting to the five constant nonlinear theory of elasticity in the 1D setting. The problem is solved numerically for an exponentially graded material. The influence of the material properties variation on the bursts profiles evolution is traced on the boundaries of the sample. A special case of the bursts interaction by which oscillations evoked by counterpropagating bursts disappear in the homogeneous material is proposed as a reference case for the problem of nondestructive material characterization. The deviation from this special case caused by inhomogeneity in material properties is analyzed by parametric plots. Obtained results may be used by qualitative nondestructive determination of the inhomogeneity in material properties.