Linear Elastic Properties Research Articles

Digital rock physics: Calculation of effective elastic properties of heterogeneous materials using graphical processing units (GPUs)

An application based on graphical processing units (GPUs) applied to 3-D digital images is described for computing the linear anisotropic elastic properties of heterogeneous materials. The application can also retrieve the property contribution tensors of individual inclusions of any shape. The code can be executed on professional GPUs as well as on a basic laptop or personal computer Nvidia GPUs. The application is extremely fast: a calculation of the effective elastic properties of volumes consisting of about 7 million voxel elements (1913) takes less than 4 s of computational time using a single A100 GPU; 3 min for 100 million voxel elements (4793) using a single A100 GPU; 14 min for 350 million voxel elements (7033) using a single A100 GPU. Several comparisons against analytical solutions are provided. In addition, an evaluation of the anisotropic effective elastic properties of a 3-D digital image of a cracked Carrara marble sample is presented. The software can be downloaded from a permanent repository Zenodo, the link with a doi is given in the manuscript.

Three-dimensional finite element analysis of biological signal feedback in the mechanical properties of sound production

In response to the problems of low reliability and long time consumption in traditional research on sound production, this article used electromyography (EMG) signals as input signals to build a high-precision sound production mechanics model. A Proportional-Integral-Derivative (PID) controller was used to dynamically adjust the model and develop a real-time feedback system. This article established a detailed three-dimensional (3D) finite element model including the vocal cords and throat, defined the nonlinear elastic properties and linear elastic properties of different tissues, and used tetrahedral grid partitioning technology to improve the computational accuracy of the model. Through a EMG sensor, an individual EMG was collected and filtered to remove noise. The processed EMGs were used as input parameters for the finite element model to drive the muscle units in the model. By using a PID controller to receive real-time EMG input, the error was calculated and the model was adjusted, enabling accurate simulation of the mechanical properties of vocal cord vibration under different vocal states and achieving real-time feedback. Considering the complexity of vocal cord vibration driven by biological signals, this article simulated and analyzed the modal characteristics of vocal cord vibration, and analyzed the differences in vocal cord vibration characteristics under different vocal states. The sound pressure distribution and resonance frequency were simulated and analyzed to understand the propagation characteristics of sound. Finally, by comparing and analyzing the simulated data with the actual collected data, it was found that the maximum relative error rate of the model under different sound states was 6.14%, and the overall error rate of the model was relatively low, which verified the reliability of the model. The findings demonstrated that the feedback delays of the model in different sound states were all within 100 milliseconds, indicating that the system had high real-time performance and accuracy, which was promising in practical applications.

Fluid-structure interaction simulation of the three-leaflet aortic valve using COMSOL

The simulation of the aortic valve (AV) remains challenging due to its geometric complexity and the multi-physics nature of the problem. In this study, we utilized COMSOL to establish a three-dimensional, three-leaflet AV fluid-structure interaction model and investigated the influence of material properties on the valve's mechanical behavior in a healthy state. The results indicated that variations in the aortic wall material model had a minor impact on AV hemodynamics. Additionally, while the linear elastic properties of the leaflets limit valve opening and closing, this material model allows for rapid assessment of AV performance within the range of material deformation.

Anisotropic swelling due to hydration constrains anisotropic elasticity in biomaterial fibers

Naturally occurring protein fibers often undergo anisotropic swelling when hydrated. Within a tendon, a hydrated collagen fibril’s radius expands by 40% but its length only increases by 5%. The same effect, with a similar relative magnitude, is observed for single hair shafts. Fiber hydration is known to affect elastic properties. Here we show that anisotropic swelling constrains the anisotropic linear elastic properties of fibers. First we show, using data from disparate previously reported studies, that anisotropic swelling can be described as an approximately linear function of water content. Then, under the observation that the elastic energy of swelling can be minimized by the anisotropic shape, we relate swelling anisotropy to elastic anisotropy — assuming radial (transverse) symmetry within a cylindrical geometry. We find an upper bound for the commonly measured axial Poisson ratio νzx<1/2. This is significantly below recently estimated values for collagen fibrils extracted from tissue-level measurements, but is consistent with both single hair shaft and single collagen fibril mechanical and hydration studies. Using νzx, we can then constrain the product γ≡(1−νxy)Ez/Ex — where νxy is the seldom measured transverse Poisson ratio and Ez/Ex is the ratio of axial to radial Young’s moduli.

Influence of Connector Design on Displacement and Micromotion in Tooth-Implant Fixed Partial Dentures Using Different Lengths and Diameters: A Three-Dimensional Finite Element Study.

The literature presents insufficient data evaluating the displacement and micromotion effects resulting from the combined use of tooth-implant connections in fixed partial dentures. Analyzing the biomechanical behavior of tooth-implant fixed partial denture (FPD) prothesis is vital for achieving an optimum design and successful clinical implementation. The objective of this study was to determine the relative significance of connector design on the displacement and micromotion of tooth-implant-supported fixed dental prostheses under occlusal vertical loading. A unilateral Kennedy class I mandibular model was created using a 3D reconstruction from CT scan data. Eight simulated designs of tooth-implant fixed partial dentures (FPDs) were split into two groups: Group A with rigid connectors and Group B with non-rigid connectors. The models were subjected to a uniform vertical load of 100 N. Displacement, strain, and stress were computed using finite element analysis. The materials were defined as isotropic, homogeneous, and exhibiting linear elastic properties. This study focused on assessing the maximum displacement in various components, including the bridge, mandible, dentin, cementum, periodontal ligament (PDL), and implant. Displacement values were predominantly higher in Group B (non-rigid) compared to Group A (rigid) in all measured components of the tooth-implant FPDs. Accordingly, a statistically significant difference was observed between the two groups at the FPD bridge (p value = 0.021 *), mandible (p value = 0.021 *), dentin (p value = 0.043 *), cementum (p value = 0.043 *), and PDL (p value = 0.043 *). Meanwhile, there was an insignificant increase in displacement values recorded in the distal implant (p value = 0.083). This study highlighted the importance of connector design in the overall stability and performance of the prosthesis. Notably, the 4.7 mm × 10 mm implant in Group B showed a displacement nearly 92 times higher than its rigid counterpart in Group A. Overall, the 5.7 mm × 10 mm combination of implant length and diameter showcased the best performance in both groups. The findings demonstrate that wider implants with a proportional length offer greater resistance to displacement forces. In addition, the use of rigid connection design provides superior biomechanical performance in tooth-implant fixed partial dentures and reduces the risk of micromotion with its associated complications such as ligament overstretching and implant overload, achieving predictable prognosis and enhancing the stability of the protheses.

Impact of dilating forcing amplitudes on a peristaltically driven non-Newtonian fluid in an elastic tube: application to swallowing disorders

Abstract We investigate the flow dynamics within an elastic tube transporting a power-law fluid, where the tube is subject to a specified external forcing in the form of a progressive traveling wave. The oesophagus is cylindrical in shape and exhibits linear elastic properties. The flow is creeping, and the long wavelength and low Reynolds number approximations are employed for a solution. The relationship between the pressure distribution within the oesophagus and the radial variation of the tube characterizes the behavior of the tube. Findings reveal that the elasticity and the variations in the applied dilating forcing amplitude substantially impact pressure resulting from sinusoidal wave forcing. Notably, even a nominal increase in the inward radial force amplitude for dilatant fluid results in significant pressure changes compared with Newtonian fluid. We also observe a notable distinction between time-averaged volume flow rate and velocity in pseudo-plastic and dilatant forms. Our study also identifies that the radial velocity experiences either attenuation or enhancement due to the fluid’s shear thickening and thinning characteristics. Moreover, our research uncovers a novel dimension by highlighting that in shifting from pseudo-plasticity to dilatancy, the fluid requires higher pressure to propel the bolus toward the hiatus. This observation has important implications, suggesting that feeding a more dilatant fluid to patients with pre-diagnosed swallowing disorders, such as sliding hiatus hernia, is not advisable, fearing increased pressure.

Mathematical Model of Vibration-Centrifugal Processing of Parts Using Loose Abrasive

The article presents some new theoretical and experimental solution of a scientific and applied problem of technological support for vibratory centrifugal processing of complex-profiled parts in a bulk abrasive environment. This solution aims to increase productivity while ensuring the desired quality of the processed surfaces. The authors have developed a mathematical model that describes the action of abrasive particles on the surface of the parts, taking into account the parameters of the granular abrasive medium based on Voigt’s law. This allows the description of dynamic processes in the processing environment for a wide range of material types. The natural frequencies of oscillations of the processed medium layer have been determined, which depend on the amplitude of its vibrations for different densities of soft and hard materials of the processed medium and the medium with linear-elastic properties. The methodology includes the use of test equipment to conduct experimental research on the process, which involves determining changes in specific metal removal rates and surface roughness using the frequency converter Altivar 71 with the PowerSuite v.2.5.0 software.

Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities

This article explores the nonlinear vibration of beams with different types of nonlinearities. The beam vibration was modeled using Hamilton’s principle, and the equation of motion was solved using method of multiple time scales. Three models were developed assuming (a) geometric nonlinearity, (b) material nonlinearity and (c) combined geometric and material nonlinearity. The material nonlinearity also included both third and fourth nonlinear elasticity terms. The frequency response equation of these models were further evaluated quantitatively and qualitatively. The models capture the hardening effect, i.e., increase in resonant frequency as a function of forcing amplitude for geometric nonlinearity, and the softening effect, i.e., decrease in resonant frequency for material nonlinearity. The model is applied on the first three bending modes of the cantilever beam. The effect of the fourth-order material nonlinearity was smaller compared to the third-order term in the first mode, whereas it is significantly larger in second and third mode. The combined nonlinearity models shows a discontinuous frequency shift, which was resolved by utilizing a set of transition assumptions. This results in a smooth transition between the material and geometric zones in amplitude. These parametric models allow us to fine tune the nonlinear response of the system by changing the physical properties such as geometry, linear and nonlinear elastic properties.

A combined musculoskeletal and finite element model of a foot to predict plantar pressure distribution

In this study, a combined subject-specific numerical and experimental investigation was conducted to explore the plantar pressure of an individual. The research utilized finite element (FE) and musculoskeletal modelling based on computed tomography (CT) images of an ankle-foot complex and three-dimensional gait measurements. Muscle forces were estimated using an individualized multi-body musculoskeletal model in five gait phases. The results of the FE model and gait measurements for the same subject revealed the highest stress concentration of 0.48 MPa in the forefoot, which aligns with previously-reported clinical observations. Additionally, the study found that the encapsulated soft tissue FE model with hyper-elastic properties exhibited higher stresses compared to the model with linear-elastic properties, with maximum ratios of 1.16 and 1.88 MPa in the contact pressure and von-Mises stress, respectively. Furthermore, the numerical simulation demonstrated that the use of an individualized insole caused a reduction of 8.3% in the maximum contact plantar pressure and 14.7% in the maximum von-Mises stress in the encapsulated soft tissue. Overall, the developed model in this investigation holds potential for facilitating further studies on foot pathologies and the improvement of rehabilitation techniques in clinical settings.

Computational homogenization of linear elastic properties in porous non-woven fibrous materials

Porous non-woven fibrous media are widely used in various industrial applications such as filtration, insulation, and medical textiles due to their unique structural and functional properties. However, predicting the mechanical behavior of these materials is challenging due to their complex microstructure and anisotropic nature. In this study, a computational model is developed to simulate the mechanical response of porous non-woven fibrous media under external loading. The model is based on the finite element method and takes into account the geometric and material properties of the fibers and the void spaces between them. The effects of various factors such as fiber size, porosity, and fibers’ intersection ratio on the mechanical behavior of the material are investigated. The results reveal that the material’s porosity and fibers’ intersection ratio are the most significant factors influencing its mechanical properties. Additionally, the increase in fiber diameter has a relatively minor effect on the material’s elastic properties. However, such changes in elastic properties are primarily attributed to the increase in randomness within the fibrous network, which is directly related to the fiber diameter for the investigated structure. The proposed computational model predicts the mechanical properties of porous non-woven fibrous media and can provide invaluable insights into the design and optimization of porous non-woven fibrous media for various scientific and engineering applications.

A novel design of series elastic actuator using tensile springs array

Series elastic actuator (SEA) has already been used in robotics, especially the human-robot interaction field, to acquire compliance and force sensing ability. However, achieving a SEA design with linear and consistent elastic properties while having low friction, minor hysteresis, and good compliance is still challenging. In addition, the inherent conflict between good compliance and high bandwidth must be appropriately handled in the design. This paper proposes a newly designed compliant actuator with a novel elastic component using a tensile springs array. The unique geometry of the spring array enables SEA's consistent rotary stiffness within the whole working range while having trivial friction and hysteresis. We adopt PID and sliding mode control to evaluate the device's performance. It can be verified that the SEA has a constant low rotary stiffness of 1.13 Nm/deg bringing good compliance while having a torque tracking bandwidth of 7 Hz. These desirable properties enable our device to provide compliant, smooth, and predictable output to meet human-robot interaction requirements.

Deep material network via a quilting strategy: visualization for explainability and recursive training for improved accuracy

Recent developments integrating micromechanics and neural networks offer promising paths for rapid predictions of the response of heterogeneous materials with similar accuracy as direct numerical simulations. The deep material network is one such approaches, featuring a multi-layer network and micromechanics building blocks trained on anisotropic linear elastic properties. Once trained, the network acts as a reduced-order model, which can extrapolate the material’s behavior to more general constitutive laws, including nonlinear behaviors, without the need to be retrained. However, current training methods initialize network parameters randomly, incurring inevitable training and calibration errors. Here, we introduce a way to visualize the network parameters as an analogous unit cell and use this visualization to “quilt” patches of shallower networks to initialize deeper networks for a recursive training strategy. The result is an improvement in the accuracy and calibration performance of the network and an intuitive visual representation of the network for better explainability.

Relationship between morphometric and mechanical properties of superficial lumbosacral soft tissue layers in healthy young adults.

Introduction: It is commonly considered that myotonometry is a non-invasive method capable of quantifying linear elastic and viscoelastic properties of the myofascial tissue through the application of a weak mechanical impulse to the surface of the skin. However, before the impulse can reach the myofascial tissue, it must cross more superficial tissues such as the skin and subcutaneous tissue (ST). All these superficial tissues have different distributions and organizations of structural components. Therefore, the study aimed to examine the potential relationships between the mechanical and morphometric properties of various superficial soft tissues surrounding the lumbar multifidus muscle (LM). Methods: Myotonometric measurements of dynamic stiffness, logarithmic decrement, and creep, and ultrasonographic measurements of thickness and echogenicity of cutaneous, subcutaneous, perimuscular tissue, and LM were obtained from 50 healthy individuals in the resting prone position and during contralateral arm lift. Results: The most important findings were that in both the relaxed and contracted LM state, the dynamic stiffness strongly negatively (r = -0.69; p < 0.001 in relaxation, r = -0.83; p < 0.001 in contraction) and creep strongly positively (r = 0.79; p < 0.001 in relaxation, r = 0.85; p < 0.001 in contraction) correlated with the thicknesses of the ST. Similar but weaker correlations were noticed between both these measures and the perimuscular tissue thickness. Elasticity was uncorrelated to the thicknesses of the tissues. With LM contraction (change from the relaxed to contracted state), the relative increase in dynamic stiffness was correlated with the relative decrease in dermis (r = -0.51; p < 0.001) and ST (r = -0.47; p = 0.001) thickness, and with the relative increase in LM (r = 0.36; p = 0.010) thickness. Moreover, the relative decrease (thinning) in the ST thickness was correlated with the relative increase in logarithmic decrement (i.e., decrease in soft tissue elasticity, r = -0.37, p = 0.011). The mechanical properties of the soft tissues were not related to their echogenicity. Discussion: In conclusion, the thicker the subcutaneous and perimuscular layers, the lesser the stiffness and the greater the time-dependent deformation to the external force of the tissues surrounding the LM during its relaxation and isometric contraction. Moreover, the greater the thinning of the ST and the thickening of the LM during its contraction, the higher the increase in lumbosacral tissue stiffness and the decrease in elasticity. Therefore, one should consider the thickness of the ST before planning or analyzing the outcomes of myotonometric or other external biomechanical measurements to avoid drawing the wrong conclusions about the mechanical properties of the myofascial tissue.

Quantification of linear and nonlinear elasticity by compression optical coherence elastography for determining lymph node status in breast cancer

We report the first application of compression optical coherence elastography (C-OCE) to evaluate both linear and nonlinear elastic properties of lymph nodes (LNs) for assessing their status, which is an important factor for detecting metastasis and staging breast cancer. The reported study involved 27 excised sentinel and axillary LNs from 24 patients with breast cancer, including normal LNs (n = 6), reactive LNs with follicular hyperplasia (n = 7) and sinus histiocytosis (n = 8), and metastatic LNs (n = 6). C-OCE data were compared with co-registered gold-standard histopathology and demonstrated a significantly higher contrast in differentiation of LNs as compared to structural optical coherence tomography imaging. Normal LNs are characterized by low stiffness values in the areas of LN cortex (<200 kPa). C-OCE revealed that abnormal reactive LNs with follicular hyperplasia exhibit moderately increased stiffness (200–300 kPa) in the cortex areas and more pronounced stiffness increase (400–600 kPa) in the areas of sinus histiocytosis. LNs with total metastasis exhibit fairly uniformly distributed highest stiffness values (>600 kPa). Since in terms of the tangent Young’s modulus there remained an appreciable overlap among these types of LNs, we also evaluated their elastic nonlinearity parameters. Complementary usage of both linear and nonlinear elastic parameters enabled very clear differentiation of all four main states of LNs. Thus, C-OCE imaging demonstrates high potential for future intraoperative usage to rapidly determine the LN status during breast-conserving surgery and to assess the extent of the cancer cells propagation in regional lymphatic collectors for preserving benign LNs. This is important for reducing the associated risks and complications (such as lymphedema) from excessive surgical removal of lymphoid structures.

Artificial Neural Network-Aided Computational Approach for Mechanophenotyping of Biological Cells Using Atomic Force Microscopy.

The artificial neural network (ANN) based models have shown the potential to provide alternate data-driven solutions in disease diagnostics, cell sorting and overcoming AFM-related limitations. Hertzian model-based prediction of mechanical properties of biological cells, although most widely used, has shown to have limited potential in determining constitutive parameters of cells of uneven shape and nonlinear nature of force-indentation curves in AFM-based cell nano-indentation. We report a new artificial neural network-aided approach, which takes into account, the variation in cell shapes and their effect on the predictions in cell mechanophenotyping. We have developed an artificial neural network (ANN) model which could predict the mechanical properties of biological cells by utilizing the force versus indentation curve of AFM. For cells with 1 μm contact length (platelets), we obtained a recall of 0.97 ± 0.03 and 0.99 ± 0.0 for cells with hyperelastic and linear elastic constitutive properties respectively with a prediction error of less than 10%. Also, for cells with 6-8 μm contact length (red blood cells), we obtained the recall of 0.975 in predicting mechanical properties with less than 15% error. We envisage that the developed technique can be used for better estimation of cells' constitutive parameters by incorporating cell topography into account.

A computational method for determining the linear elastic properties of 2D aperiodic lattice structures

This paper develops a framework for determining the linear elastic properties of non-periodic lattice structures. An element-based material assignment methodology is implemented that facilitates the generation and analyses of arbitrary patterns on a structured mesh. An adapted numerical homogenization strategy features the inclusion of a homogenized region in the neighbourhood of the domain boundary that validates the implementation of periodic boundary conditions for an arbitrary finite patch of a periodic or non-periodic lattice structure. To demonstrate the method, the linear elastic properties of an aperiodic lattice pattern based on the Penrose (P3) pattern is evaluated. Such a structure exhibits order without translational symmetry and consequently lacks a repeating unit cell. The isotropic performance of the aperiodic lattice structure is investigated and compared to that of the well-known square periodic lattice. The framework opens the door to the investigation and analyses of other novel cellular structures which are not based on a repeating unit cell. Additive manufacturing facilitates the physical realization of such lattice structures, presenting them as viable alternatives to conventional periodic structures in the aerospace and bio-engineering industries.

Particle-based numerical simulation of continuous ice-breaking process by an icebreaker

The continuous ice-breaking capacity of an icebreaker is an important indicator of its efficiency. The ice resistance encountered by an icebreaker has a significant influence on its continuous ice-breaking capacity. In this study, we develop a numerical model based on the moving particle semi-implicit (MPS) method, which is a particle method based on continuum mechanics, for predicting the ice resistance encountered by icebreakers during continuous ice-breaking operations. Before fracture, the ice is assumed to be a linear elastic material, and the maximum tensile stress theory is used as the fracture criterion. A scalar function composed of the first principal stress gradient and the first eigenvector of the stress tensor is introduced to express the relative positions of the new crack and corresponding particle pair. As the hull is represented by polygons and the ice fragments are represented by particles, the collision points between the hull and the ice, i.e., between polygons and particles, is determined using a novel search algorithm that expands a cell linked-list algorithm. The collisions between individual ice fragments and between the hull and an ice fragment are considered using a particle-based model that is a modified form of the Hertz contact model. The proposed algorithm was verified using experimental data obtained from three-point bending tests on model and freshwater ice specimens that were performed by the Korea Research Institute of Ships and Ocean Engineering (KRISO) and Korea Maritime and Ocean University (KMOU), respectively. The verification process revealed that the closer the properties of the ice to the linear elastic properties assumed in the numerical model, the higher the accuracy of the proposed algorithm. The verified algorithm was used to predict the ice resistance encountered by a model icebreaker during a continuous ice-breaking process. A series of convergence and parametric tests were performed for the main parameters of the continuous ice-breaking simulation, and the experimental results obtained by KRISO were used for comparison. The maximum relative errors from experiment were approximately 12% and 30% under free (Fr) and semi-fixed (SF) side boundary conditions, respectively. The proposed numerical algorithm can successfully predict the ice resistance encountered by an icebreaker and the occurrence of near- and far-field fractures during a continuous ice-breaking process.

Linear and Nonlinear Elastic Properties of Polystyrene-Based Nanocomposites with Allotropic Carbon Fillers and Binary Mixtures.

We report measurements of linear and nonlinear elastic properties of polystyrene-based nanocomposites with six types of nanofillers, including single and binary mixtures of allotropic carbon nanoparticles. Composite samples were fabricated by the same technology and contained the same filler concentration (5% wt.), which allowed for a direct comparison of their properties. It was shown that the most significant variations of linear and nonlinear elastic properties occur in different nanocomposites. In particular, the most pronounced enhancements of linear elastic moduli (in about 50%) obtained in tensile and flexural tests and in dynamic mechanical analysis were recorded in the sample filled with spherical fullerene nanoparticles. While the most profound rise of absolute values of nonlinear elastic moduli (tens of times) was obtained in the sample filled with the mixture of carbon nanotubes and graphene. The observed tendencies demonstrated the synergistic effect of fillers of different dimensionality on the elastic properties of nanocomposites.

An efficient analytical method to obtain the homogenised frequency-independent elastic material properties of cross-laminated timber elements

Cross-Laminated Timber (CLT) is a renewable, sustainable, and cost-efficient building element that has been growing in popularity in recent years. To improve one of CLT’s weaknesses, its suboptimal noise and vibration isolation performance, computationally efficient, accessible, and extensible CLT vibro-acoustic models are required. An effective approach to achieve such models is the homogenisation of layered materials. This paper presents a validated homogenisation method based on First-order Shear Deformation Theory (FSDT) that obtains the frequency-independent elastic material properties of CLT. This method is applicable to arbitrary linear elastic material properties, orientations, and stacking sequences of the layers. The homogenised material properties are utilised with FSDT Equivalent Single-Layer (ESL) models that are readily implemented with many finite element method codes to calculate the vibro-acoustic behaviour of CLT elements, even including thickness resonance effects when applied with an appropriate model. The presented homogenisation method for CLT is validated in a numerical study by comparing the mechanical mobilities of ESL models against layerwise dynamic models. The numerical study is conducted based on an experimentally validated 5-ply model for 2- to 7-ply CLT plates with proportionally increasing thicknesses and three idealised boundary conditions. The frequency-independent material properties also allow for the graphical exploration of the anisotropic nature of CLT and the calculation of the universal anisotropic index. The flexibility of the homogenisation method, combined with its ready implementation in already widely implemented FSDT models, can have an application and impact beyond the vibro-acoustic considerations of CLT into the general mechanical modelling of CLT as it is implemented in ever more advanced applications.

Mapping Large Strains in Phase-Sensitive OCT: Key Role of Supra-Pixel Displacement Tracking in Incremental Strain Evaluation

Displacement tracking is an important step in realization of compression optical coherence elastography (C-OCE), especially in the context of obtaining nonlinear stress-strain dependences and subsequent evaluation of the tissue Young’s modulus. The rapidly progressing phase-sensitive C-OCE, however, enables direct measurements of only rather small interframe strains (below 1%), for which displacements are also small. Obtaining stress-strain curves for larger strains (~10% and greater) in phase-sensitive C-OCE can be made via cumulation of interframe strains and particle displacements. The resultant values of the so-found cumulative displacements may significantly exceed the pixel size, whereas measurements of the phase variations in C-OCE are usually performed by comparing the signals from the same pixel in a series of compared scans. When displacements of particles in a series of acquired scans reach supra-pixel values, simple pixel-to-pixel estimation of interframe phase variations may lead to significant errors in evaluating linear and nonlinear elastic properties of tissues. Thus, for large strains, adequate accounting for the resultant supra-pixel displacements of order of several pixels and greater is of key importance for undistorted mapping of elastic properties of heterogeneous materials, as well as for correct tracking of boundaries separating tissue regions with different elastic properties. In this paper we discuss the elastographic procedures of correct tracking of supra-pixel displacements in phase-sensitive C-OCE and give real examples demonstrating the importance of such displacement tracking for undistorted reconstruction of two-dimensional maps of linear and nonlinear elastic properties of real biological tissues .