Three-dimensional Strain Distribution Research Articles

Full-Field Strain Measurements of the Muscle-Tendon Junction Using X-ray Computed Tomography and Digital Volume Correlation.

We report, for the first time, the full-field 3D strain distribution of the muscle-tendon junction (MTJ). Understanding the strain distribution at the junction is crucial for the treatment of injuries and to predict tear formation at this location. Three-dimensional full-field strain distribution of mouse MTJ was measured using X-ray computer tomography (XCT) combined with digital volume correlation (DVC) with the aim of understanding the mechanical behavior of the junction under tensile loading. The interface between the Achilles tendon and the gastrocnemius muscle was harvested from adult mice and stained using 1% phosphotungstic acid in 70% ethanol. In situ XCT combined with DVC was used to image and compute strain distribution at the MTJ under a tensile load (2.4 N). High strain measuring 120,000 µε, 160,000 µε, and 120,000 µε for the first principal stain (εp1), shear strain (γ), and von Mises strain (εVM), respectively, was measured at the MTJ and these values reduced into the body of the muscle or into the tendon. Strain is concentrated at the MTJ, which is at risk of being damaged in activities associated with excessive physical activity.

Reconstruction of three-dimensional strain field in an asymmetrical curved core–shell hetero-nanowire

Crystal orientation and strain mapping of an individual curved and asymmetrical core–shell hetero-nanowire (NW) is performed based on transmission electron microscopy. It relies on a comprehensive analysis of scanning nanobeam electron diffraction data obtained for 1.3 nm electron probe size. The proposed approach also handles the problem of appearing twinning defects on diffraction patterns and allows for the investigation of materials with high defect densities. Based on the experimental maps and their comparison with finite element simulations, the entire core–shell geometry including full three-dimensional strain distribution within the curved core–shell NW are obtained. Our approach represents, therefore, a low-dose quasi-tomography of the strain field within a nanoobject using only a single zone axis diffraction experiment. Our approach is applicable also for electron beam-sensitive materials for which performing conventional tomography is a difficult task.

Three-dimensional Observation and Strain Distribution Measurement in Oxide-Based CMC

Three-dimensional Observation and Strain Distribution Measurement in Oxide-Based CMC

Bragg coherent diffraction imaging allowing simultaneous retrieval of three-dimensional shape and strain distribution for 40–500 nm particles

We report the improvement of an apparatus for Bragg coherent X-ray diffraction imaging (Bragg-CDI) at BL22XU in SPring-8 to expand the applicable particle size and the application of the Bragg-CDI technique for Pd and ferroelectric barium titanate (BaTiO3) fine crystals with particle sizes of 40–500 nm. Preparing a vacuum environment around the sample enabled us to obtain the high-contrast diffraction pattern of a 40 nm particle. The reconstructed three-dimensional image showed the outer shape, size, and internal phase (strain) for a single particle. A single 500 nm BaTiO3 particle showed a straight and sharp antiphase-boundary shape, whereas smaller BaTiO3 particles showed different phase boundary shapes. The present Bragg-CDI apparatus, thus, allows the observation of the outer shape, size, and inner phase distribution for a single particle with a size of 40–500 nm.

A novel approach to evaluate the effects of artificial bone focal lesion on the three-dimensional strain distributionswithin the vertebral body.

The spine is the first site for incidence of bone metastasis. Thus, the vertebrae have a high potential risk of being weakened by metastatic tissues. The evaluation of strength of the bone affected by the presence of metastases is fundamental to assess the fracture risk. This work proposes a robust method to evaluate the variations of strain distributions due to artificial lesions within the vertebral body, based on in situ mechanical testing and digital volume correlation. Five porcine vertebrae were tested in compression up to 6500N inside a micro computed tomography scanner. For each specimen, images were acquired before and after the application of the load, before and after the introduction of the artificial lesions. Principal strains were computed within the bone by means of digital volume correlation (DVC). All intact specimens showed a consistent strain distribution, with peak minimum principal strain in the range -1.8% to -0.7% in the middle of the vertebra, demonstrating the robustness of the method. Similar distributions of strains were found for the intact vertebrae in the different regions. The artificial lesion generally doubled the strain in the middle portion of the specimen, probably due to stress concentrations close to the defect. In conclusion, a robust method to evaluate the redistribution of the strain due to artificial lesions within the vertebral body was developed and will be used in the future to improve current clinical assessment of fracture risk in metastatic spines.

Method for Calculating Plastic Deformation of High Resolution and Large Contact Area

AbstractIn a rolling contact, the tribological properties in terms of friction, wear, and fatigue are significantly influenced by the surface roughness. Due to solid contact of the surfaces in the contact area, the roughness and thus also the tribological properties change during the service life of the contact. The initial load leads to major changes of the tribological properties figured out by Brecher et al. (2019, “Influence of the Metalworking Fluid on the Micropitting Wear of Gears,” Wear, 61(434–435), p. 202996). Prediction of the initial changes in topography in the contact area is necessary for specific optimization of rolling contacts. Especially for dry rolling–sliding contact, the roughness of the surfaces is crucial for the lifetime, which is part of the investigations within the DFG priority program 2074 (357505886). In this work, an elastic-plastic contact algorithm for calculating plastic deformation for dry contact of rough surfaces with large contact area and high resolution is presented. Due to the nonlinearity behavior associated with plastic deformation, the plastic contact algorithm is based on an iterative approach. An optimized meshing strategy is implemented to calculate the elastic pressure distribution on the surface. Corresponding to the two-dimensional pressure distribution, the three-dimensional stress distribution allows the consideration of residual stresses and interactions of the microscopic peaks of the rough surface. Furthermore, the three-dimensional plastic strain distribution allows the application of an analytical approach to represent the plastic deformation of the surface. Finally, the solution of a plastic contact calculation with an exemplary topography measured on a real rough surface is presented.

Strain-life estimation of the last stage blade in steam turbine during low volume flow conditions

Based on the elastic-plastic analysis, the local strain-life of the last stage of steam turbine under the low volume flow conditions is predicted. Considering the unsteady flow steam force and local high temperature of blade, the three-dimensional transient flow field, strain distribution and stress distribution of the last stage blade are calculated by the two-way fluid structure interaction method. Under low volume flow conditions, the temperature of blade tip increases with the decrease of volume flow. In addition, the self-excited unsteady frequency of rotor -stator clearance vortex is obtained at 90% span. According to the distribution of maximum equivalent stress on the rotor blade surface, three dangerous points are identified, which are located at the blade tip of the pressure surface (DP1), 90% span of the suction surface (DP2) and the trailing edge at the blade root of the pressure surface (DP3). With the decrease of volume flow, the equivalent stress and strain range of dangerous points increase, so the strain- life of dangerous points decreases. Among them, the strain-life of DP2 is the shortest at case3 condition. The strain response frequency of DP2 is consistent with the self-excited unsteady frequency of rotor -stator clearance vortex, which proves that it is necessary to consider the unsteady steam flow force in strain-life calculation. This study provides theoretical guidance for the safe operation time of the steam turbine under low volume flow conditions.

Strain Distribution Analysis of Two Perpendicular Planes in SUS310S Austenitic Stainless Steel Using Digital Image Correlation

We performed a strain distribution analysis of two perpendicular planes in SUS310S austenitic stainless steel using digital image correlation (DIC). Strain bands in both the rolling direction, (RD)-transverse direction and RD-normal direction planes, were connected at an edge, and the formation of a strain plane surrounded by the strain bands in each plane was confirmed. Furthermore, we found that the three-dimensional strain distribution can be inferred by analyzing the strain distribution of two perpendicular planes using DIC. The finite element method (FEM) was used to verify the formation of macro and micro strain bands. The FEM analysis also revealed that the connection of micro strain bands led to the formation of macro strain bands. The angle of macro strain bands to tensile loading direction was dependent on preferential deformation site distribution. In contrast, the angle of micro strain bands was mainly determined by preferential deformation site distribution when the angle of preferential deformation site to tensile loading direction was <50° and by maximum shear stress when it was >50°. From these results, we concluded that (i) the angle of the macro strain bands observed by DIC to tensile loading direction was mainly determined by the preferential deformation site distribution; and (ii) the angle of the micro strain bands was determined by both the preferential deformation site distribution and maximum shear stress.

Sub-trabecular strain evolution in human trabecular bone

To comprehend the most detrimental characteristics behind bone fractures, it is key to understand the material and tissue level strain limits and their relation to failure sites. The aim of this study was to investigate the three-dimensional strain distribution and its evolution during loading at the sub-trabecular level in trabecular bone tissue. Human cadaver trabecular bone samples were compressed in situ until failure, while imaging with high-resolution synchrotron radiation X-ray tomography. Digital volume correlation was used to determine the strains inside the trabeculae. Regions without emerging damage were compared to those about to crack. Local strains in close vicinity of developing cracks were higher than previously reported for a whole trabecular structure and similar to those reported for single isolated trabeculae. Early literature on bone fracture strain thresholds at the tissue level seem to underestimate the maximum strain magnitudes in trabecular bone. Furthermore, we found lower strain levels and a reduced ability to capture detailed crack-paths with increased image voxel size. This highlights the dependence between the observed strain levels and the voxel size and that high-resolution is needed to investigate behavior of individual trabeculae. Furthermore, low trabecular thickness appears to be one predictor of developing cracks. In summary, this study investigated the local strains in whole trabecular structure at sub-trabecular resolution in human bone and confirmed the high strain magnitudes reported for single trabeculae under loading and, importantly extends its translation to the whole trabecular structure.

Full-field strain of regenerated bone tissue in a femoral fracture model.

The mechanical behaviour of regenerated bone tissue during fracture healing is key in determining its ability to withstand physiological loads. However, the strain distribution in the newly formed tissue and how this influences the way a fracture heals it is still unclear. X-ray Computed Tomography (XCT) has been extensively used to assess the progress of mineralised tissues in regeneration and when combined with in situ mechanics and digital volume correlation (DVC) has been proven a powerful tool to understand the mechanical behaviour and full-field three-dimensional (3D) strain distribution in bone. The purpose of this study is therefore to use in situ XCT mechanics and DVC to investigate the strain distribution and load-bearing capacity in a regenerating fracture in the diaphyseal bone, using a rodent femoral fracture model stabilised by external fixation. Rat femurs with 1 mm and 2 mm osteotomy gaps were tested under in situ XCT step-wise compression in the apparent elastic region. High strain was present in the newly formed bone (εp1 and εp3 reaching 29000 µε and -43000 µε, respectively), with a wide variation and inhomogeneity of the 3D strain distribution in the regenerating tissues of the fracture gap, which is directly related to the presence of unmineralised tissue observed in histological images. The outcomes of this study will contribute in understanding natural regenerative ability of bone and its mechanical behaviour under loading.

Room temperature giant magnetostriction in single-crystal nickel nanowires

Magnetostriction is the emergence of a mechanical deformation induced by an external magnetic field. The conversion of magnetic energy into mechanical energy via magnetostriction at the nanoscale is the basis of many electromechanical systems such as sensors, transducers, actuators, and energy harvesters. However, cryogenic temperatures and large magnetic fields are often required to drive the magnetostriction in such systems, rendering this approach energetically inefficient and impractical for room-temperature device applications. Here, we report the experimental observation of giant magnetostriction in single-crystal nickel nanowires at room temperature. We determined the average values of the magnetostrictive constants of a Ni nanowire from the shifts of the measured diffraction patterns using the 002 and 111 Bragg reflections. At an applied magnetic field of 600 Oe, the magnetostrictive constants have values of λ100 = −0.161% and λ111 = −0.067%, two orders of magnitude larger than those in bulk nickel. Using Bragg coherent diffraction imaging (BCDI), we obtained the three-dimensional strain distribution inside the Ni nanowire, revealing nucleation of local strain fields at two different values of the external magnetic field. Our analysis indicates that the enhancement of the magnetostriction coefficients is mainly due to the increases in the shape, surface-induced, and stress-induced anisotropies, which facilitate magnetization along the nanowire axis and increase the total magnetoelastic energy of the system.

Effects of three-dimensional strain distribution on the performance of GaN-based light-emitting diodes on patterned sapphire substrates

Depth-resolved confocal Raman and micro photoluminescence (PL) are adopted to analyze GaN-based light-emitting diodes (LEDs) with an ex situ sputtered AlN nucleation layer on patterned sapphire substrates (PSSs). The strain on PSSs is measured by Raman spectral mapping, and the results demonstrate that the strain distribution within the LED structures strongly correlates to the pattern array of the PSS. Cone regions with less dislocations have lower strain than plane regions. The array pattern of the PSS’s surface can directly affect strain existing in the later crystal growth even at the position of the layer before the p-GaN growth. Moreover, the two-dimensional micro-PL mapping of the GaN-based LED samples on a PSS reveals a close relationship with the strain distribution on the sample surface. It is found that the strain as well as the PL intensity difference can be mitigated by proper pre-strained layers in order to realize high efficiency LEDs.

Measuring Three-dimensional Strain Distribution of Knee Joint Cartilage under Compressive Load

Measuring Three-dimensional Strain Distribution of Knee Joint Cartilage under Compressive Load

Elastic strain field due to an inclusion of a polyhedral shape with a non-uniform lattice misfit

An analytical solution in a closed form is obtained for the three-dimensional elastic strain distribution in an unlimited medium containing an inclusion with a coordinate-dependent lattice mismatch (an eigenstrain). Quantum dots consisting of a solid solution with a spatially varying composition are examples of such inclusions. It is assumed that both the inclusion and the surrounding medium (the matrix) are elastically isotropic and have the same Young's modulus and Poisson ratio. The inclusion shape is supposed to be an arbitrary polyhedron, and the coordinate dependence of the lattice misfit, with respect to the matrix, is assumed to be a polynomial of any degree. It is shown that, both inside and outside the inclusion, the strain tensor is expressed as a sum of contributions of all faces, edges, and vertices of the inclusion. Each of these contributions, as a function of the observation point's coordinates, is a product of some polynomial and a simple analytical function, which is the solid angle subtended by the face from the observation point (for a contribution of a face), or the potential of the uniformly charged edge (for a contribution of an edge), or the distance from the vertex to the observation point (for a contribution of a vertex). The method of constructing the relevant polynomial functions is suggested. We also found out that similar expressions describe an electrostatic or gravitational potential, as well as its first and second derivatives, of a polyhedral body with a charge/mass density that depends on coordinates polynomially.

Subchondral bone microarchitecture and failure mechanism under compression: A finite element study

Subchondral bone (SCB) microdamage is commonly observed in traumatic joint injuries and has been strongly associated with post-traumatic osteoarthritis (PTOA). Knowledge of the three-dimensional stress and strain distribution within the SCB tissue helps to understand the mechanism of SCB failure, and may lead to an improved understanding of mechanisms of PTOA initiation, prevention and treatment. In this study, we used high-resolution micro-computed tomography (µCT)-based finite element (FE) modelling of cartilage-bone to evaluate the failure mechanism and the locations of SCB tissue at high-risk of initial failure under compression. The µCT images of five cartilage-bone specimens with an average SCB thickness of 1.23±0.20mm were used to develop five µCT-based FE models. The FE models were analysed under axial compressions of approximately 30MPa applied to the cartilage surface while the bone edges were constrained. Strain and stress-based failure criteria were then applied to evaluate the failure mechanism of the SCB tissue under excessive compression through articular cartilage. µCT-based FE models predicted two locations in the SCB at high-risk of initial failure: (1) the interface of the calcified-uncalcified cartilage due to excessive tension, and (2) the trabecular bone beneath the subchondral plate due to excessive compression. µCT-based FE models of cartilage-bone enabled us to quantify the distribution of the applied compression which was transferred through the articular cartilage to its underlying SCB, and to investigate the mechanism and the mode of SCB tissue failure. Ultimately, the results will help to understand the mechanism of injury formation in relation to PTOA.

Three-dimensional surface topography of graphene by divergent beam electron diffraction

There are only a handful of scanning techniques that can provide surface topography at nanometre resolution. At the same time, there are no methods that are capable of non-invasive imaging of the three-dimensional surface topography of a thin free-standing crystalline material. Here we propose a new technique—the divergent beam electron diffraction (DBED) and show that it can directly image the inhomogeneity in the atomic positions in a crystal. Such inhomogeneities are directly transformed into the intensity contrast in the first-order diffraction spots of DBED patterns and the intensity contrast linearly depends on the wavelength of the employed probing electrons. Three-dimensional displacement of atoms as small as 1 angstrom can be detected when imaged with low-energy electrons (50–250 eV). The main advantage of DBED is that it allows visualization of the three-dimensional surface topography and strain distribution at the nanometre scale in non-scanning mode, from a single shot diffraction experiment.

Application of digital volume correlation to study the efficacy of prophylactic vertebral augmentation

BackgroundProphylactic augmentation is meant to reinforce the vertebral body, but in some cases it is suspected to actually weaken it. Past studies only investigated structural failure and the surface strain distribution. To elucidate the failure mechanism of the augmented vertebra, more information is needed about the internal strain distribution. This study aims to measure, for the first time, the full-field three-dimensional strain distribution inside augmented vertebrae in the elastic regime and to failure. MethodsEight porcine vertebrae were prophylactically-augmented using two augmentation materials. They were scanned with a micro-computed tomography scanner (38.8μm voxel resolution) while undeformed, and loaded at 5%, 10%, and 15% compressions. Internal strains (axial, antero-posterior and lateral-lateral components) were computed using digital volume correlation. FindingsFor both augmentation materials, the highest strains were measured in the regions adjacent to the injected cement mass, whereas the cement-interdigitated-bone was less strained. While this was already visible in the elastic regime (5%), it was a predictor of the localization of failure, which became visible at higher degrees of compression (10% and 15%), when failure propagated across the trabecular bone. Localization of high strains and failure was consistent between specimens, but different between the cement types. InterpretationThis study indicated the potential of digital volume correlation in measuring the internal strain (elastic regime) and failure in augmented vertebrae. While the cement-interdigitated region becomes stiffer (less strained), the adjacent non-augmented trabecular bone is affected by the stress concentration induced by the cement mass. This approach can help establish better criteria to improve vertebroplasty.

Bragg-edge neutron transmission strain tomography for in situ loadings

An approach for tomographic reconstruction of three-dimensional strain distributions from Bragg-edge neutron transmission strain images is outlined and investigated. This algorithm is based on the link between Bragg-edge strain measurements and the Longitudinal Ray Transform, which has been shown to be sensitive only to boundary displacement. By exploiting this observation we provide a method for reconstructing boundary displacement from sets of Bragg-edge strain images. In the case where these displacements are strictly the result of externally applied tractions, corresponding internal strain fields can then be found through traditional linear-static finite element methods. This approach is tested on synthetic data in two-dimensions, where the rate of convergence in the presence of measurement noise and beam attenuation is examined.

Novel silica stabilization method for the analysis of fine nanocrystals using coherent X-ray diffraction imaging.

High-energy X-ray Bragg coherent diffraction imaging (BCDI) is a well established synchrotron-based technique used to quantitatively reconstruct the three-dimensional morphology and strain distribution in nanocrystals. The BCDI technique has become a powerful analytical tool for quantitative investigations of nanocrystals, nanotubes, nanorods and more recently biological systems. BCDI has however typically failed for fine nanocrystals in sub-100 nm size regimes - a size routinely achievable by chemical synthesis - despite the spatial resolution of the BCDI technique being 20-30 nm. The limitations of this technique arise from the movement of nanocrystals under illumination by the highly coherent beam, which prevents full diffraction data sets from being acquired. A solution is provided here to overcome this problem and extend the size limit of the BCDI technique, through the design of a novel stabilization method by embedding the fine nanocrystals into a silica matrix. Chemically synthesized FePt nanocrystals of maximum dimension 20 nm and AuPd nanocrystals in the size range 60-65 nm were investigated with BCDI measurement at beamline 34-ID-C of the APS, Argonne National Laboratory. Novel experimental methodologies to elucidate the presence of strain in fine nanocrystals are a necessary pre-requisite in order to better understand strain profiles in engineered nanocrystals for novel device development.

Novel microstructural findings in M. plantaris and their impact during active and passive loading at the macro level

There are several studies dealing with experimental and structural analyses of skeletal muscles that are aimed at gaining a better understanding of three-dimensional muscle deformation and force generation. A variety of these contributions have performed structural or mechanical analyses, but very few have combined these approaches at different levels. To fill this gap, the present study aims to bring together three-dimensional micro-structural and mechanical findings in rabbit M. plantaris to study load transfer mechanisms inside the muscle during passive loading and active muscle contraction. During these two deformation states, the three-dimensional surface of the aponeurosis–tendon complex was recorded using optical measurement systems. In this way, the strain distribution on the muscle can be calculated to interpret the load transfer mechanisms inside the muscle. The results show that the three-dimensional strain distribution during muscle activation is completely different from the distribution during passive loading. Under both loading conditions, the strain distribution is irregular. To interpret these findings, the gross try and the fascicle architecture of the M. plantaris were determined. In doing so, a highly complex microstructure featuring tube- and sail-like structure was identified. Moreover, a compartmentalisation of the muscle into two compartments was detected. The smaller, bipennated muscle compartment was embedded into the larger, unipennated compartment. To the authors׳ knowledge, this type of inner structure has never been previously documented in single-headed muscles.