Elastic Modulus Distribution Research Articles

Does group velocity always reflect elastic modulus in shear wave elastography?

.Dynamic elastography is an attractive method to evaluate tissue biomechanical properties. Recently, it was extended from US- and MR-based modalities to optical ones, such as optical coherence tomography for three-dimensional (3-D) imaging of propagating mechanical waves in subsurface regions of soft tissues, such as the eye. The measured group velocity is often used to convert wave speed maps into 3-D images of the elastic modulus distribution based on the assumption of bulk shear waves. However, the specific geometry of OCE measurements in bounded materials such as the cornea and skin calls into question elasticity reconstruction assuming a simple relationship between group velocity and shear modulus. We show that in layered media the bulk shear wave assumption results in highly underestimated shear modulus reconstructions and significant structural artifacts in modulus images. We urge the OCE community to be careful in using the group velocity to evaluate tissue elasticity and to focus on developing robust reconstruction methods to accurately reconstruct images of the shear elastic modulus in bounded media.

Evaluation Method of Mechanical Properties of Living NSCLC Cells Based on Nano-indentation

Background:In AFM study of cell mechanical properties, the apparent elastic modulus of a cell is affected by many factors, especially the AFM tip geometry, indentation site of the cell, the application of the mathematical model and testing conditions.Background:In AFM study of cell mechanical properties, the apparent elastic modulus of a cell is affected by many factors, especially the AFM tip geometry, indentation site of the cell, the application of the mathematical model and testing conditions.Methods:In this study, indentation experiments of living cells under different conditions were performed aiming to build an accurate evaluation system of mechanical properties of lung cancer cells based on AFM. Comparisons of the effects of spherical and pyramid AFM tips, Hertz model of semiinfinite and finite thickness, cell nuclear and cytoplasmic indentation regions on the cell apparent elastic modulus were accomplished.Methods:In this study, indentation experiments of living cells under different conditions were performed aiming to build an accurate evaluation system of mechanical properties of lung cancer cells based on AFM. Comparisons of the effects of spherical and pyramid AFM tips, Hertz model of semiinfinite and finite thickness, cell nuclear and cytoplasmic indentation regions on the cell apparent elastic modulus were accomplished.Results:Compared with the calculated results by spherical tip, the elastic modulus distribution of non-small lung cancer cells (NSCLC) by pyramid tip was observed to be similar while the absolute values increased obviously, which were more than twice the numerical values by the spherical tip (p<0.05). The apparent elastic modulus values were the overvalued cause of the underestimation of the contact region in pyramidal tip measurement. Two different indentations over nucleus or lamellipodium of NCI-H520 cell and NCI-H1299 cell were analyzed. Consequently, the exact elastic modulus over the nucleus area can be calculated accurately using the semi-infinite Hertz model while the finite thickness Hertz model should be used for elasticity assessment of cell lamellipodium with a small thickness.Results:Compared with the calculated results by spherical tip, the elastic modulus distribution of non-small lung cancer cells (NSCLC) by pyramid tip was observed to be similar while the absolute values increased obviously, which were more than twice the numerical values by the spherical tip (p<0.05). The apparent elastic modulus values were the overvalued cause of the underestimation of the contact region in pyramidal tip measurement. Two different indentations over nucleus or lamellipodium of NCI-H520 cell and NCI-H1299 cell were analyzed. Consequently, the exact elastic modulus over the nucleus area can be calculated accurately using the semi-infinite Hertz model while the finite thickness Hertz model should be used for elasticity assessment of cell lamellipodium with a small thickness.Conclusion:This evaluation system provides technological support for accurate evaluation of viscoelastic properties of living cancer cells.Conclusion:This evaluation system provides technological support for accurate evaluation of viscoelastic properties of living cancer cells.

Analysis of Plastic Properties of Fe-Based Coatings at Different Annealing Temperatures by Nanoindentation

Fe-based alloys were deposited on 1045 steel by plasma cladding technique and the specimens were annealed at different temperatures. Instrumented indentation technique was adopted to investigate the plastic properties of the coatings, especially the stress-strain relations, critical yield stress and the strain hardening exponent. The results show that the elastic recovery in nanoindentation is less than 20% for all coatings and proves an obvious existence of plastic deformation in the coatings. It is found in the stress-strain curves that the annealing process makes the distribution of elastic modulus among the whole coating more uniformly. With the penetration depth increasing, the initial plastic deformation value gradually decreased which is more obvious for coatings annealing at high temperatures. In addition, the strain hardening exponent of the as-cladding coating and coatings annealed at 500°C keeps steady around 0.15 while the corresponding values of coatings annealed at 600°C and 700°C increased sharply with the penetration depth increasing and the maximum value is up to 0.32.

Pre-strain effect on twist springback of a 3D P-channel in deep drawing

Abstract With the widely use of high-strength steel sheets in the automotive industry, the twist springback phenomenon of the steel sheets under multi-step forming conditions has received extensive attention. In this work, the Dual Phase steel DP500 is taken as the research object to investigate the complex non-linear elastoplastic behaviors and twist springback under two-step loading paths. The large specimen with a pre-strain of 4% true strain in rolling direction is carried out on a large tensile testing machine, and several specific blanks are extracted from it at different directions for a subsequent P-channel forming. The influence of twist springback associated with the pre-strain is analyzed. The finite element model based on the non-linear elastic model and the homogeneous anisotropic hardening model (HAH) is also established for the springback prediction and stress analysis. The results indicate that the pre-strain has a considerable impact on the twist springback. The non-linear strain path changes resulted from pre-straining not only influence the residual stress but also affect the elastic modulus distribution.

Thermoacoustic elastography: recovery of bulk elastic modulus of heterogeneous media using tomographically measured thermoacoustic measurements.

Tissue mechanical parameters such as elasticity are of great significance for the assessment of biological histopathological and physiological characteristics. Here, we propose a new approach called thermoacoustic elastography (TAE) for imaging tissue elastic modulus. Central to TAE is an image reconstruction algorithm that allows the recovery of both microwave energy loss and elastic modulus distributions. The algorithm is first evaluated using simulated data under various practical scenarios, including a varied range of microwave energy loss and elastic modulus between the heterogeneity and background region, different noise levels, and multiple targets. The feasibility of the proposed TAE was then validated by imaging the elastic modulus distribution of agar phantoms with various elastic modulus and microwave energy loss. The results from both the simulated and phantom experiments show that the recovered elastic modulus by TAE agree well with the exact values, having an average error of less than 12.74%. The findings from this study suggest that TAE provides a new addition to the family of elasticity imaging and may have broad application prospects, such as cirrhosis and atherosclerosis detection.

Degradation of mechanical properties of CA mortar caused by calcium leaching

Abstract Calcium leaching is an important durability problem for cement asphalt (CA) mortar used in ballastless slab track. In this paper, calcium leaching in CA mortar was accelerated by immersing in 6 mol/L ammonium nitrate solution. The leaching kinetics and related changes in mechanical behavior and microstructure of CA mortar were studied. Results showed that calcium leaching followed the Fick’s law. The calcium leaching led to the formation of three distinct zones in term of local calcium content in the direction of radius of the specimen. Due to the leaching of calcium hydroxide and the progressive decalcification of C S H, the three zones had different chemical compositions. The compressive mechanical behavior was modeled by a compression damage model derived from Weibull distribution. The degradation damage model was established on the distribution of local elastic modulus. The combination of these two models can well predict the compressive behavior of partially leached CA mortar.

Novel inverse finite-element formulation for reconstruction of relative local stiffness in heterogeneous extra-cellular matrix and traction forces on active cells

Accurately resolving the traction forces on active cells in 3D extra-cellular matrix (ECM) is crucial to understanding stress homeostasis in cellularized ECM systems and the resulting collective cellular behavior. The majority of 3D traction force microscopy techniques, which compute the stress distribution in ECM as well as cellular traction forces from experimentally measured deformation field in the ECM using dispersed tracing particles or fluorescently-tagged matrix proteins, have assumed a spatially homogeneous ECM with constant material properties at every location in the system. Recent studies have shown that ECM can exhibit significant heterogeneity due to the disordered nature of collagen network as well as cell remodeling. In this paper, we develop a novel inverse finite-element formulation for accurately resolving the cellular traction forces by explicitly reconstructing the relative local elastic modulus values of the heterogeneous ECM containing an arbitrary shaped cell from a measured displacement field in the ECM. Our formulation does not require any a priori knowledge of the boundary conditions, and simultaneously results in the distribution of the heterogeneous modulus values and stress field in the ECM, as well as the traction forces on the cell, given experimentally measured average modulus of the ECM. We first validate our procedure in artifical model cell-ECM systems, and then employ the procedure to compute the distribution of elastic modulus in a heterogeneous type-I collagen gel as well as the traction force on a rounded breast cancer cell in the gel, based on the deformation field data obtained via 3D reflectance force microscopy. Our results indicate that the majority part of the cell is in a tensile state, while a local region on the cell is in a tri-axial compressive state, indicating the possible development of a local protrusion in this region. This is further verified by tracking the subsequent evolution of the cell morphology.

Geophysical Monitoring of Moisture‐Induced Landslides: A Review

AbstractGeophysical monitoring of landslides can provide insights into spatial and temporal variations of subsurface properties associated with slope failure. Recent improvements in equipment, data analysis, and field operations have led to a significant increase in the use of such techniques in monitoring. Geophysical methods complement intrusive approaches, which sample only a very small proportion of the subsurface, and walk‐over or remotely sensed data, which principally provide information only at the ground surface. In particular, recent studies show that advances in geophysical instrumentation, data processing, modeling, and interpretation in the context of landslide monitoring are significantly improving the characterization of hillslope hydrology and soil and rock hydrology and strength and their dynamics over time. This review appraises the state of the art of geophysical monitoring, as applied to moisture‐induced landslides. Here we focus on technical and practical uses of time‐lapse methods in geophysics applied to monitoring moisture‐induced landslide. The case studies identified in this review show that several geophysical techniques are currently used in the monitoring of subsurface landslide processes. These geophysical contributions to monitoring and predicting the evolution of landslide processes are currently underrealized. Hence, the further integration of multiple‐parametric and geotechnically coupled geophysical monitoring systems has considerable potential. The complementary nature of certain methods to map the distribution of subsurface moisture and elastic moduli will greatly increase the predictive and monitoring capacity of early warning systems in moisture‐induced landslide settings.

Influence of soil characteristics on natural frequency-based bridge scour detection

The concept of detecting scour severity by analyzing the change in the Predominant Natural Frequency (PNF) of a bridge pier has been gaining increasing interest in recent years. Previous studies primarily focus on this topic using less cohesive soils such as highly erodible sands, whereas no discussions have been reported on the influence of soil characteristics, especially those of cohesive soils, on the PNF. This missing knowledge gap is critical for this application as cohesive soils are an essential part of the soil-pier interaction to determine PNFs. This study aims to fill this knowledge gap by investigating three issues that are related to soil characteristics: 1) the effect of soil types on the PNF variation; 2) the questionable issue regarding the pier diameter effect for soil-pier dynamic modeling using the Vesic analytical expression; and 3) contradictory statements in the existing studies regarding the influence of the soil’s elastic modulus on the PNF variation. For the purpose, a series of lab-scale tests is first conducted, and a Winkler-based numerical model is then developed and validated against the experimental results to investigate the effect of soil characteristics on the PNFs measured from systems with cohesive soils and those with less cohesive soils. We found that the soil characteristics affect the PNF by providing a different lateral stiffness to the soil-pier interaction. The strength of the soil-pier interaction mainly depends on the lateral stiffness of each type of soils. In-depth discussions are also made to clarify the pier diameter effect on the predicted PNFs from both less cohesive and cohesive soils. It was clarified that the distribution of the soil’s elastic modulus determines whether the pier diameter effect needs to be considered using the Vesic analytical expression. Further simulations are finally conducted with more complex and realistic field soil conditions to mediate the contradictory statements regarding the influence of the soil’s elastic modulus. The simulation results indicated that the soil’s elastic modulus significantly influences the PNFs. The PNF variations differ under different elastic moduli of soils and distributions of elastic moduli with soil depths.

Damage progression in thermal barrier coating systems during thermal cycling: A nano-mechanical assessment

This paper studies how the nano-mechanical properties of thermal barrier coatings (TBCs) vary during thermal cycling, as a way to shed new light on their failure mechanisms. In particular, high-throughput nanoindentation revealed the evolution of hardness and elastic modulus distributions of plasma-sprayed yttria-stabilized zirconia (YSZ) top layers. The evolution of fracture toughness of the YSZ layers and the thermally grown oxide (TGO) formed onto the vacuum plasma-sprayed NiCoCrAlY bond coat were investigated by nanoindentation micro-pillar splitting.The TGO fracture toughness increases up to ≈2.5–3.5 MPa√m at the early stages of thermal cycling, followed by a rapid decrease to ≈2.0 MPa√m after a critical TGO thickness of ≈5 μm is reached. Consequently, interface damage is initially limited to short cracks within the YSZ material. As TGO thickness exceeds the critical threshold, multiple cracks originate within the TGO and join through the YSZ to form long delamination cracks. Joining is favoured by a simultaneous loss in YSZ strength, testified by a decrease in the nanomechanical properties (hardness, elastic modulus) of both high- and low-porosity top coats. This is due to microstructural changes occurring because of the continuous interplay between sintering and thermal shock cracking in the YSZ layers.

Characterization Method of ITZ in Concrete and Measurement of Nominal Compressive Elastic Modulus Based on SEM and DIC

With the combination of scanning electron microscope (SEM) and digital image correlation (DIC), the mechanical properties of interfacial transition zone (ITZ) in concrete are experimentally studied. The experimental compression tests are performed on cuboid samples whose half part is aggregate and the other part is mortar. The morphology of the ITZ is captured by SEM under compressive load, and from the recorded images the deformation of the ITZ is analyzed. After that, the distribution of the nominal compressive elastic modulus of the ITZ is obtained along the distance from the aggregate to the mortar, which can be used to characterize the size of the ITZ with the strain contour. A conclusion can be draw that the area where the nominal compressive elastic modulus is obviously less than that of the aggregate and mortar can be defined as the ITZ. In this paper, the area 30~130 μm away from the aggregate can be regarded as the ITZ, where the average nominal compressive elastic modulus is about 695.1580 MPa. With increasing distance from the aggregate boundary, the nominal compressive elastic modulus of the ITZ decreases first and then increases, and at the sides close to the aggregate and mortar, the nominal compressive elastic modulus of the ITZ gradually tends to that of the two materials. Finally, the relationship between the average nominal compressive elastic modulus and the distance from the aggregate boundary can be fitted by two order polynomial function, which can be used to describe the mechanical properties of the ITZ.

Sound Transmission-Based Elastography Imaging

Elastography is of great interest in biomechanics and medical imaging due to its nondestructive capability of mapping elasticity of tissues. The elastography framework relies on external excitations which actuate deformation inside an object. The internal response is then acquired and analyzed to map the distribution of elastic moduli. In this paper, with no need of measuring any internal responses, an integrated elastography method is developed which only requires the transmitted responses of applied sound waves. During the process, the tomography image (e.g., CT or MRI) and the applied waves are integrated into a computational model. Following a procedure of inverse analysis, the elasticity of all phases in the object is reconstructed when the computational transmission of waves matches with the measured transmission. The numerical simulation on brain tissues and a demonstration on silicon rubber phantom are conducted to validate the proposed method. Both cases demonstrate that the integrated method successfully predicts the real elasticity of samples. The verification measurements on the phantom further show that the predicted elastic moduli agree well with the experimental results of uniaxial compression testing.

Do the normal compression lines of cemented and uncemented geomaterials run parallel or converge to each other after yielding?

Whether the normal compression lines (NCLs) of cemented and uncemented materials run parallel or converge to each other after yielding is a fundamental yet controversial issue in the study of compression behaviour of geomaterials. An effort is made here to clarify the question by means of the distinct element method (DEM) combined with available experimental observations. In the DEM simulations, the effects of cement content, void ratio, bond elastic modulus, bond strength and bond distribution on the compression curves are considered. In addition, the microscopic mechanical responses, including bond breakage events, deviatoric fabric and stress shared by bonded part or unbonded part, are investigated. The DEM simulations show that the NCLs for all the cemented specimens run parallel with the NCL for the uncemented specimen within the range of stresses adopted in the study, which is not influenced by the aforementioned factors. Through comparing the DEM results in this study, previous 3D DEM data and experimental observations, it can be preliminarily concluded that the interactions between cement breakage and particle crushing determine the convergence or non-convergence of NCLs. The NCLs of the cemented and uncemented sands run parallel for the strong-particle case, while those tend to converge for the fragile-particle case.

Numerical simulation of the mechanical properties of a carbon‐fiber‐reinforced hollow glass microsphere–epoxy syntactic foam

ABSTRACTThe addition of carbon fibers has a great influence on the mechanical properties of hollow glass microsphere (HGM)–epoxy syntactic foam. Thus, to elucidate the reinforcement mechanism, the numerical simulation of HGM‐ and carbon‐fiber‐filled epoxy matrixes was carried out. The effect of the orientation of carbon fibers on the elastic modulus and stress distribution was studied. The effect of the elastic modulus of the matrix on the change of force was also studied. We noted that the orientation of carbon fibers affected the elastic modulus of the matrix, and when the carbon fibers were distributed in the direction of force, the elastic modulus of the matrix reached its maximum. The maximum stress of HGMs decreased with increasing matrix elastic modulus, and the mechanical properties of the syntactic foam increased with increasing elastic modulus of the matrix. When the carbon fibers were distributed in the direction of the force, the enhancement effect was the best. Because the carbon fibers had a higher elastic modulus than the matrix, the degree of compressive deformation of the carbon fibers was smaller than that of the matrix. During compression, carbon fibers were pulled out and consumed a lot of energy. Thus, the mechanical properties of the syntactic foam were improved. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47083.

Fourier‐series‐based virtual fields method combining with moiré interferometry for characterising elastic modulus distribution of laser repaired GH4169

AbstractLaser cladding is an effective technology for repairing damaged components with high efficiency and low cost. Characterisation for the mechanical properties of the repaired structure is of great importance to evaluate its reliability. In this study, the mechanical properties of laser repaired GH4169 are investigated by Fourier‐series‐based virtual fields method and moiré interferometry. The elastic modulus distribution of the whole structure is identified to understand the mechanical performance of the repaired zone and base material. A uniaxial tensile test is performed and the full‐field deformation is measured by moiré interferometry. With the measured strain field, the distribution of modulus in repaired structures can be calculated. In addition, simulation experiments of moiré interferometry are conducted to optimise the parameters of Fourier‐series‐based virtual fields method to improve the accuracy of the proposed method. On the basis of these results, experiments on the repaired GH4169 material are performed and the variation of modulus in the whole structure is identified. The results verify that the proposed method is effective for characterising modulus distribution of the laser repaired structures, and will have a good prospect for further application.

Microstructure and Micromechanical Properties of Mg Microtubes Prepared by Laser Dieless Drawing

The paper presents microscale experimental investigation performed on microtubes that were prepared with a novel laser dieless drawing (LDD) technique from difficult-to-work AZ31 magnesium alloy (nominally 3wt.%Al-1wt.%Zn-0.3wt.%Mn-Mg balanced). A microstructure analysis was performed via various microscopic techniques. Mechanical response of individual grains with various orientations was tested using instrumental nanoindentation and the results were compared with the microstructure. Distributions of elastic modulus, hardness and visco-elastic properties were analyzed. In addition, microtubes were also characterized in terms of their surface roughness and morphology based on different modes of surface treatment. The grain size is practically not changed when LDD is applied after extrusion showing low thermal and straining effect of the process. Local mapping of mechanical properties does not show weak spots and imply feasibility of the novel production technology.

An Inverse Method for Optimizing Elastic Properties Considering Multiple Loading Conditions and Displacement Criteria

Significant research effort has been devoted to topology optimization (TO) of two- and three-dimensional structural elements subject to various design and loading criteria. While the field of TO has been tremendously successful over the years, literature focusing on the optimization of spatially varying elastic material properties in structures subject to multiple loading states is scarce. In this article, we contribute to the state of the art in material optimization by proposing a numerical regime for optimizing the distribution of the elastic modulus in structural elements subject to multiple loading conditions and design displacement criteria. Such displacement criteria (target displacement fields prescribed by the designer) may result from factors related to structural codes, occupant comfort, proximity of adjacent structures, etc. In this work, we utilize an inverse problem based framework for optimizing the elastic modulus distribution considering N target displacements and imposed forces. This approach is formulated in a straight-forward manner such that it may be applied in a broad suite of design problems with unique geometries, loading conditions, and displacement criteria. To test the approach, a suite of optimization problems are solved to demonstrate solutions considering N = 2 for different geometries and boundary conditions.

Defect nucleation modelling

The purpose of this article is to compare concepts of defect nucleation based on bifurcation of equilibrium solution and on damage modelling. The nucleation criterion is defined as a bifurcation of the equilibrium solutions of the perfect body and of the imperfect one when the size of the defect vanishes. The defect is considered as a small volume which evolves as a damaged zone. To study the influence of geometry of the defect on the critical loading governing its initiation, we consider the particular cases of a linear elastic composite sphere and of a linear elastic composite cylinder, for which the equilibrium solutions are known when the radial distribution of elastic bulk modulus is given simultaneously with a uniform shear modulus. The initial defect is a small sphere or a small cylinder, respectively, it can be a cavity or a kernel made with an elastic material with lower mechanical properties.

Characterization of the mechanical properties of a claystone by nano-indentation and homogenization

Based on the analyses of mineralogical compositions by X-ray diffraction and microstructure by optical microscopy, the Young’ modulus and hardness of a claystone were characterized by the nano-indentation technique and homogenization method. Three distinct microstructural zones are identified in the claystone: clay matrix, a composite matrix of clay and small mineral grains and imbedded quartz grains. The elastic modulus and hardness of different zones were determined by nano-indentation testing. Based on the statistical analysis of nano-indentation results, the spatial mappings and frequency distributions of elastic modulus and hardness of the different zones were obtained. The elastic moduli of main constituent phases of the claystone are then estimated from the nano-indentation tests. These values were further used for the determination of the macroscopic elastic modulus of the claystone using two different homogenization schemes: the dilute scheme and Mori–Tanaka scheme. The predicted values by the homogenization schemes are compared with experimental data obtained from conventional uniaxial compression tests.

On the identification of earlywood and latewood radial elastic modulus ofPinus pinasterby digital image correlation: A parametric analysis

This work addresses the reconstruction of strain gradient fields at the wood growth ring scale from full-field deformation measurements provided by digital image correlation. Moreover, the spatial distribution of the earlywood and latewood radial modulus of elasticity is assessed. Meso-scale tensile tests are carried out on Pinus pinaster Ait. wooden specimens oriented in the radial–tangential plane under quasi-static loading conditions. A parametric analysis of the two-dimensional digital image correlation extrinsic and intrinsic setting parameters is performed, in a balance between spatial resolution and resolution. It is shown that the parametric module is an effective way to quantitatively support the choice of digital image correlation parameters in the presence of the high deformation gradient fields generated by the structure–property relationships at the scale of observation. Under the assumption of a uniaxial tensile stress state, the spatial distribution of the radial elastic modulus across the growth rings is obtained. It is observed that the ratio of the radial modulus of elasticity between latewood and earlywood tissues can vary significantly as a function of the digital image correlation parameters. It is pointed out, however, that a convergence value can be systematically established. Effectively, earlywood and latewood stress–strain curves are obtained and elastic properties are determined assuming the converged digital image correlation setting parameters.