Distribution Of Material Properties Research Articles

Free vibration Analysis of Beams with Functional Gradient Materials with Cracks

The article presents the development of a dynamic model for a functionally graded material (FGM) beam incorporating cracks. Initially, it assumes an exponential distribution of material properties along the thickness direction of the beam and simulates the opening crack using a zero-mass rotational spring model. This approach enables the calculation of bending stiffness and local flexibility at the cracked section. Subsequently, drawing upon Timoshenko beam theory and von Kármán geometric nonlinear theory, the study formulates the energy equation of the beam and establishes the partial differential control equations for the cracked FGM using Hamilton's principle. The method of separation of variables is employed to discretize the partial differential motion equations into ordinary differential motion equations. Beam functions serve as mode functions, whose unknown coefficients are determined according to the boundary and continuity conditions, thereby yielding the natural frequencies and mode shapes of the cracked FGM beam. Numerical analysis is conducted to evaluate the impact of boundary conditions, the relative position of cracks, and the length-to-thickness ratio on the natural frequencies of the cracked FGM beam.

Mechanical and elemental characterization of ant mandibles: consequences for bite mechanics.

Mandible morphology has an essential role in biting performance, but the mandible cuticle can have regional differences in its mechanical properties. The effects of such a heterogeneous distribution of cuticle material properties in the mandible responses to biting loading are still poorly explored in chewing insects. Here, we tested the mechanical properties of mandibles of the ant species Formica cunicularia by nanoindentation and investigated the effects of the cuticular variation in Young's modulus (E) under bite loading with finite-element analysis (FEA). The masticatory margin of the mandible, which interacts with the food, was the hardest and stiffest region. To unravel the origins of the mechanical property gradients, we characterized the elemental composition by energy-dispersive X-ray spectroscopy. The masticatory margin possessed high proportions of Cu and Zn. When incorporated into the FEA, variation in E effectively changed mandible stress patterns, leading to a relatively higher concentration of stresses in the stiffer mandibular regions and leaving the softer mandible blade with relatively lower stress. Our results demonstrated the relevance of cuticle E heterogeneity in mandibles under bite loading, suggesting that the accumulation of transition metals such as Cu and Zn has a relevant correlation with the mechanical characteristics in F. cunicularia mandibles.

Analytical modeling of acoustic exponential materials and physical mechanism of broadband anti-reflection

Spatially exponential distributions of material properties are ubiquitous in many natural and engineered systems, from the vertical distribution of the atmosphere to acoustic horns and anti-reflective coatings. These media seamlessly interface different impedances, enhancing wave transmission and reducing internal reflections. This work advances traditional transfer matrix theory by integrating analytical solutions for acoustic exponential materials, which possess exponential density and/or bulk modulus, offering a more accurate predictive tool and revealing the physical mechanism of broadband anti-reflection for sound propagation in such non-uniform materials. Leveraging this method, we designed an acoustic dipole array that effectively mimics exponential mass distribution. Through experiments with precisely engineered micro-perforated plates, we demonstrate an ultra-low reflection rate of about 0.86% across a wide frequency range from 420 Hz to 10,000 Hz. Our modified transfer matrix approach underpins the design of exponential materials, and our layering strategy for stacking acoustic dipoles suggests a pathway to more functional gradient acoustic metamaterials.

Development of a piezo stack – Laser doppler vibrometer sensing approach for characterizing shear wave dispersion and local viscoelastic property distributions

Laser Doppler vibrometry and wavefield analysis have recently shown great potential for nondestructive evaluation, structural health monitoring, and studying wave physics. However, there are limited studies on these approaches for viscoelastic soft materials, especially, very few studies on the laser Doppler vibrometer (LDV)-based acquisition of time–space wavefields of dispersive shear waves in viscoelastic materials and the analysis of these wavefields for characterizing shear wave dispersion and evaluating local viscoelastic property distributions. Therefore, this research focuses on developing a piezo stack-LDV system and shear wave time–space wavefield analysis methods for enabling the functions of characterizing the shear wave dispersion and the distributions of local viscoelastic material properties. Our system leverages a piezo stack to generate shear waves in viscoelastic materials and an LDV to acquire time–space wavefields. We introduced space-frequency-wavenumber analysis and least square regression-based dispersion comparison to analyze shear wave time–space wavefields and offer functions including extracting shear wave dispersion relations from wavefields and characterizing the spatial distributions of local wavenumbers and viscoelastic properties (e.g., shear elasticity and viscosity). Proof-of-concept experiments were performed using a synthetic gelatin phantom. The results show that our system can successfully generate shear waves and acquire time–space wavefields. They also prove that our wavefield analysis methods can reveal the shear wave dispersion relation and show the spatial distributions of local wavenumbers and viscoelastic properties. We expect this research to benefit engineering and biomedical research communities and inspire researchers interested in developing shear wave-based technologies for characterizing viscoelastic materials.

Properties of biomolecular condensates defined by Activator of G-protein Signaling 3.

Activator of G-protein signaling 3 (AGS3; also known as GPSM1), a receptor-independent activator of G-protein signaling, oscillates among defined subcellular compartments and biomolecular condensates (BMCs) in a regulated manner that is likely related to the functional diversity of the protein. We determined the influence of cell stress on the cellular distribution of AGS3 and core material properties of AGS3 BMCs. Cellular stress (oxidative, pHi and thermal) induced the formation of AGS3 BMCs in HeLa and COS-7 cells, as determined by fluorescent microscopy. Oxidative stress-induced AGS3 BMCs were distinct from G3BP1 stress granules and from RNA processing BMCs defined by the P-body protein Dcp1a. Immunoblots indicated that cellular stress shifted AGS3, but not the stress granule protein G3BP1 to a membrane pellet fraction following cell lysis. The stress-induced generation of AGS3 BMCs was reduced by co-expression of the signaling protein Gαi3, but not the AGS3-binding partner DVL2. Fluorescent recovery following photobleaching of individual AGS3 BMCs indicated that there are distinct diffusion kinetics and restricted fluidity for AGS3 BMCs. These data suggest that AGS3 BMCs represent a distinct class of stress granules that serve as a previously unrecognized signal processing node.

General analysis of the dissipation of strain energy in circular columns

This theoretical paper is concerned with general analysis of the strain energy dissipation in columns of circular cross-section. The columns are under longitudinal displacements that vary continuously with time. The columns exhibit non-linear viscoelastic behavior that is studied by mechanical models constructed by using non-linear springs and dashpots. Besides, the columns are functionally graded along the radius of the cross-sections. A simple expression for the dissipated strain energy in the columns under consideration is derived. The expression holds for columns having portions with different radius of the cross-section. Also, the expression derived is applicable for columns built-up by concentric layers. Results indicating how the dissipated strain energy is influenced by various factors (distribution of material properties, geometry of the columns and loading) are presented. These results are found by using a non-linear viscoelastic model with one spring and one dashpot. A check-up is performed by determining the dissipated strain energy through subtracting the strain energy in the spring of viscoelastic model from the whole strain energy in the column.

Physics-informed neural network reconciles Australian displacements and tectonic stresses

Stress orientation information is invaluable to evaluate active tectonic forces within the Earth’s crust. The global dataset provided by the World Stress Map offers a rich resource of stress indicators, facilitating the calibration of mechanical models to extract complete stress and displacement fields. However, traditional inversion processes are hampered by the manual tuning of geomechanical properties and boundary conditions to reconcile simulations with observations. In this study, we introduce ML-SEISMIC (machine learning for stress estimation integrating satellite image and computational modelling), a physics-informed deep neural network approach to autonomously align stress orientation data with an elastic model. It nearly completely bypasses the need for explicit boundary condition inputs and yields comprehensive distributions of material properties, displacements, and stress tensors. Application of this methodology to Australia, coupled with precise global navigation satellite systems observations, unveils a robust and scale-independent interpolation framework. Additionally, it pinpoints regions where stress orientation reinterpretation is warranted. Our results present a streamlined yet powerful process, offering a substantial leap forward in geodynamic investigations. This approach promises to unify velocity and stress orientation observations with physical models, ushering in a new era of insights into Earth’s dynamic processes.

Design of equi-strength annular disks made of functionally graded materials

This research proposes a robust method for designing functionally graded disks subject to internal and external pressures. The design objective is to find the profile of equi-strength disks. The von Mises yield criterion controls the initiation of plastic yielding. The yield stress and Young’s modulus are entirely arbitrary functions of the polar radius. Poisson’s ratio is constant. The solution is facilitated using the dimensionless yield stress as an independent variable instead of the polar radius. In particular, a numerical technique is only required to solve two ordinary differential equations. Moreover, one of these equations is independent of the other. Therefore, the equations can be solved individually, simplifying the solution method. The limitation imposed by the thickness gradient on the acceptability of plane stress conditions is considered. Particular designs are proposed assuming that the power function describes the radial distribution of material properties. A critical condition that allows for deriving relatively simple design solutions is emphasized. It is shown that this condition is satisfied for many specific material property distributions used in the literature.

DEVELOPMENT OF AN OPEN-SOURCE FINITE ELEMENT ANKLE MODEL FOR IN-SILICO INVESTIGATION OF THE ANKLE JOINT

AbstractObjectivesThis abstract provides an update on the Open Ankle Models being developed at the University of Bath. The goal of this project is to create three fully open-source finite element (FE) ankle models, including bones, ligaments, and cartilages, appropriate musculoskeletal loading and boundary conditions, and heterogeneous material property distribution for a standardised representation of ankle biomechanics and pre-clinical ankle joint analysis.MethodsA computed tomography (CT) scan data (pixel size of 0.815 mm, and slice thickness of 1 mm) was used to develop the 3D geometry of the bones (tibia, talus, calcaneus, fibula, and navicular). Each bone was given the properties of a heterogeneous elastic material based on the CT greyscale. The density values for each bone element were calculated using a linear empirical relation, ρ= 0.0405 + (0.000918) HU and then power law equations were utilised to get the Young's Modulus value for each bone element [1]. At the bone junction, a thickness of cartilage ranging from 0.5–1 mm, and was modelled as a linear material (E=10 MPa, ν=0.4 [2]). All ligament insertions and positions were represented by four parallel spring elements, and the ligament stiffness and material attributes were applied in accordance with the published literature [2]. The ankle model was subjected to static loading (balance standing position). Four noded tetrahedral elements were used for the discretization of bones and cartilages. All degrees of freedom were restricted at the proximal ends of the tibia and fibula. The ground reaction forces were applied at the underneath of the calcaneus bone. The interaction between the cartilages and bones was modelled using an augmented contact algorithm with a sliding elastic contact between each cartilage. A tied elastic contact was used between the cartilages and the bone. FEbio 2.1.0 (University of Utah, USA) was used to construct the open-source ankle model.ResultsWhen the double-legged stance phase loading condition was taken into consideration, stress at the antero-medial tibial wall (ranged from 1 to 7 MPa) was found to be similar to the prior work [2], indicating bulk of the load transfer was through this region. The maximum principal strain was predicted at the different regions on bones around the ankle joint. The proximal surface of the talus, and tibial distal surface were shown to have the highest maximum principal strains followed by antero-medial walls of the tibia bone, at the proximal location.ConclusionsThe present open 3D FE model of the ankle will assist researchers in better understanding ankle biomechanics, precisely predicting load transfer, and examining the ankle to address unmet clinical needs for this joint. The results of the current investigation are realistic in terms of load transfer and stress-strain distribution across the ankle joint and well comparable to those reported in the literature [2]. However, sensitivity and ankle instability simulations will be performed in future work to investigate the model's reliability and robustness.Declaration of Interest(b) declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported:I declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research project.

A black-box optimization strategy for customizable global elastic deformation behavior of unit cell-based tri-anti-chiral metamaterials

Metamaterials are a class of materials with a distinctive unit cell-based periodic architecture, often resulting in unique mechanical properties. The potential of metamaterials can be further improved by using gradients of unit cell parameters and thereby creating a specific distribution of material properties in a part. This design freedom comes with the challenge of finding new suitable design and optimization strategies. In this study, a Finite Element simulation-based optimization framework to create a predefined deformation behavior of unit cell-based metamaterials is presented. The framework consists of a numerical homogenization method to create an efficient linear elastic material representation, an interpolation scheme for a fast correlation of unit cell parameters with homogenized material properties and a black-box based optimization part. The framework is tested on a tri-anti-chiral metamaterial with additional geometric parameters and a newly developed transition unit cell. Several specified lateral deformations of simple 2D rectangular test specimens under tensile load are used as primary optimization targets and the homogenized results are validated against Finite Element simulations of fully modeled tri-anti-chiral structures. In addition, the effect of the design space and the number of design variables is studied and several combinations of optimization objectives and constraints are tested.

Hydrodynamic response to bathymetric changes in Tampa Bay, Florida

Bathymetric changes within estuarine and coastal waters can alter the hydrodynamic evolution of sea level and currents, which in turn can influence the ecosystem by altering material property distributions. Here we apply the Tampa Bay Coastal Ocean Model (TBCOM), with an unstructured, high-resolution grid to investigate the hydrodynamic response to bathymetric changes at the periphery of the Tampa Bay mouth over a relatively small area when compared to the whole model domain. Two separate numerical experiments are conducted with the same forcing, one using the original bathymetry and the other employing a revised synthetic bathymetry. The simulated sea level, amplitude and phase of the M2 tide, and associated currents are compared for the two experiments. Significant changes in water level (up to+/-10 cm) and current velocities (up to 20 cm/s) are found in the shallow peripheral area with the two different bathymetric data sets. These bathymetric influences are not limited to the locations where the bathymetric changes occur; they also extend to remote areas of the bay. Since Tampa Bay bathymetry varies with storm-induced sediment redistributions and human actives such as shipping channel dredging and beach nourishment, these findings emphasize the need for accurate and updated bathymetry for coastal ocean modeling and applications.

Topology optimization approach for functionally graded metamaterial components based on homogenization of mechanical variables

The micron resolutions that 3D printers are reaching allow for a change of paradigm in the design of components, optimizing not only the topology of the component, but also the microstructure of the material, which can adopt different objectives at different locations in the component, reaching different mechanical properties and different optimal microstructures at those locations. This constitutes a flip in the design objectives to focus on tailored material work, aimed either at local objectives or at component-wide ones, instead of pursuing homogeneous material properties for global objectives. For this new concurrent structure-material design leading to optimized components made of functionally graded (FG) metamaterials, new topology optimization (TO) procedures are needed in which the objective is to obtain component-wise mechanical variables or distributions of these variables, rather than global component objectives as compliance, which is a typical objective of classical TO approaches.In this work we present a new TO approach aimed at FG metamaterial design pursuing homogeneous mechanical variables. We focus on homogenization of deformation level along the component by minimizing its standard deviation across the domain. The proposed formulation can be naturally generalized to anisotropy, nonlinear behavior, and other optimization objectives. Convergence to a suitable optimized solution, with a distribution of material properties resulting in a homogeneously deformed component, is obtained. These FG material properties may be obtained from local metamaterial design. Classical material/void configurations may also be obtained following our procedure, and results for such cases can be compared qualitatively to the Solid Isotropic Material with Penalization (SIMP) approach.

Dynamic analysis of 2DFGM porous nanobeams under moving load with surface stress and microstructure effects using Ritz method

This paper investigates the dynamic behavior of micro/nanobeams made of two-dimensional functionally graded porous material (2DFGPM) under accelerated, decelerated, and uniform moving harmonic load, using surface elasticity and modified couple stress theories. The key feature of this formulation is that it deals with a higher order shear deformation beam theory. The non-classical equilibrium equations are developed using Lagrange's equation and the concept of physical neutral surface. The equations of motion are derived using the same approach, accounting for the porosity effect and the modified power-law distribution of material properties. The trigonometric Ritz method is used with sinusoidal trial functions for the displacement field, and the Newmark method is applied to obtain the dynamical response of 2DFGPM nanobeams. The results are compared with previous studies, and the impact of critical parameters such as gradation indices, volume fraction ratio, pattern of porosity, velocity, frequency, and motion type of the applied force are explored. This study highlights the importance of considering the porosity effect, as neglecting it can lead to significant errors in the predicted results. Additionally, the study found that the accelerated and decelerated motions of the applied load have a greater impact on the dynamical deflection of 2DFGPM nanobeams than the uniform motion. The findings of this study can provide guidance for the optimal design of micro/nanobeams subjected to a moving force with multifunctional properties.

Simulation and Optimization of Hemispherical Resonator's Equivalent Bottom Angle for Frequency-Splitting Suppression.

As an inertial sensor with excellent performance, the hemispherical resonator gyro is widely used in aerospace, weapon navigation and other fields due to its advantages of high precision, high reliability, and long life. Due to the uneven distributions of material properties and mass of the resonator in the circumferential direction, the frequencies of the two 4-antinodes vibration modes (operational mode) of resonator in different directions are different, which is called frequency splitting. Frequency splitting is the main error source affecting the accuracy of the hemispherical resonator gyro and must be suppressed. The frequency splitting is related to the structure of the resonator. For the planar-electrode-type hemispherical resonator gyro, in order to suppress the frequency splitting from the structure, improve the accuracy of the hemispherical resonator gyro, and determine and optimize the equivalent bottom angle parameters of the hemispherical resonator, this paper starts from the thin shell theory, and the 4-antinodes vibration mode and waveform precession model of the hemispherical resonator are researched. The effect of the equivalent bottom angle on the 4-antinodes vibration mode frequency value under different boundary conditions is theoretically analyzed and simulated. The simulation results show that the equivalent bottom angle affects the 4-antinodes vibration mode of the hemispherical resonator through radial constraints. The hemispherical resonator with mid-surface radius R=15 mm and shell thickness h=1 mm is the optimization object, and the stem diameter D and fillet radius R1 are experimental factors, with the 4-antinodes vibration mode frequency value and mass sensitivity factor as the response indexes. The central composite design is carried out to optimize the equivalent bottom angle parameters. The optimized structural parameters are: stem diameter D=7 mm, fillet radii R1=1 mm, R2=0.8 mm. The simulation results show that the 4-antinodes vibration mode frequency value is 5441.761 Hz, and the mass sensitivity factor is 3.91 Hz/mg, which meets the working and excitation requirements wonderfully. This research will provide guidance and reference for improving the accuracy of the hemispherical resonator gyro.

Limit elastic speed analysis for functionally graded rotating beam

This study aims to determine the limit elastic angular speed of the rotating beam made up of functionally graded material. The speed at which the material yielding is instigated is termed as limit elastic speed. Assuming material distribution as function of power law, modified rule of mixture was used to determine the distribution of material properties and later was used to calculate the effective yield stress for different volume fraction index. A metal matrix of aluminium has been considered with a reinforcement of silicon carbide. The B-spline collocation method has been used to solve the governing equation obtained using the principle of virtual work. This paper outlines the effect of volume fraction on the deformation and stress at limit elastic speed; influence of slenderness ratio on the limit speed was also reported.

Derivation of heterogeneous material distributions and their sensitivity to HM-coupled two-phase flow models exemplified with the LASGIT experiment

Advective gas transport in bentonite, a possible buffer material in repositories for radioactive materials, is difficult to simulate in numerical continuum models, partly due to the complicated microstructure of bentonite. To generate reliable models of repositories nevertheless, spatially distributed heterogeneous material properties can be used to allow localization of gas flow. In this study, a pore-size-dependent stochastic approach of the gas entry pressure is derived from Mercury Intrusion Porosimetry, which is used to replicate measurements from the LASGIT experiment. In addition, three benchmark tests are simulated to investigate the dependence of heterogeneous distributions of material properties on the mesh discretization, the temporal dependence, and the coupling between the processes influenced by the heterogeneous parameters. The numerical modeling results of the LASGIT experiment show that the onset of gas flow into the system and the subsequent increase in pressure and stress can be well reproduced using heterogeneous distributions. Compared to a model with homogeneous material properties, heterogeneous distributions may allow the generation of dilatancy-controlled microfractures—an important feature with regard to the advective gas flow in bentonites. However, it can be observed that the heterogeneous distributions in LASGIT are less significant, as technical gaps or differences in material types could have a greater impact.

Compressible cementitious composite materials: Multiscale modeling and experimental investigation

Tunnel linings installed in difficult geological conditions characterized by a high expansion potential, such as Opalinus Clay and rocks containing anhydrite, may exhibit a loss of integrity due to excessive ground deformations in case water penetrates the rocks. One of the potential remedies against lining deterioration and failure of the tunnel structure is the incorporation of a compressible cementitious layer around the tunnel. This compressible layer serves as a cushion that protects the tunnel structure by tolerating a certain amount of deformations prior to collapse. The deformation capacity of the compressible layer can be enhanced by introduction of various soft inclusions or air bubbles in the cementitious mix. However, such soft inclusions reduce the overall elasticity modulus and strength of the composite. Hence, it is crucial to determine the optimal mix that provides the required compaction potential without compromising on stiffness and strength. For this design purpose computational modeling can be adopted. The model should be able to account for the material properties of the individual components and their volume fraction, which strongly influence the overall behavior of the cementitious composite, and to capture the main features characterizing compressible composites, such as a yielding plateau after a certain threshold loading has been reached. The compaction process of such a composite is described by a voxel model with a discrete distribution of material properties, where the voxels are compacted by applying an Eigenforce when the local stress state reaches a threshold value. This threshold is determined within the framework of continuum micromechanics on the scale of individual inclusions. The model predictions are compared with data from experimental investigations on the compression behavior of different cementitious mixes.

Closed Form Expressions for Nonlinear Analysis of FG-GPLRC Beam Under Thermal Loading: Thermal Postbuckling and Nonlinear Bending

Considering that the exact solution for thermal buckling and post-buckling of the graphene platelets (GPLs)-reinforced composite beam in exposure to temperature changes has not been so far addressed, this problem is investigated in this research. The governing equations of the beam under thermal buckling load were acquired using the principle of virtual work, first-order shear deformation theory, and von Kármán strain field. The effective properties of the materials were then determined using the Halpin–Tsai model and rule of mixtures. Three coupled nonlinear equations are established and solved directly. Results are obtained for beams with clamped and simply supported edges. After validating the results, the effects of changing the GPLs distribution pattern and weight fraction changes on the critical thermal buckling load were evaluated. It is highlighted that for beams with simply supported edges and asymmetric distribution of material properties, the response is not of the bifurcation type.

Flutter of carbon-based nanohybrid composite panels

Recently, carbon-based composite aerospace and mechanical structures have considerable attention due to their great material and mechanical properties. Carbon nanotubes (CNTs) or graphene platelets (GPLs) reinforcements for different matrices are common for the design of modern multilayer structures. In the present paper, the supersonic flutter of nanohybrid composite multilayer panels is examined and discussed. The nanohybrid multilayer panel is made of different technologically justified configurations of polymer layers reinforced by CNTs and GPLs The effective material properties of each CNTs and GPLs layer are determined according to two well-established homogenization techniques: the Mori–Tanaka scheme and the modified Halpin–Tsai model, respectively. Reddy’s third-order shear deformation theory is applied to avoid determining shear correction factors for different distributions of material properties. Hamilton’s principle and the first-order piston theory are applied to formulate aeroelastic coupled equations of motion of the panel. The numerical meshless method is employed to discretize dynamic equations and find generalized multi-parametric characteristic equations functionally dependent on the parameters of the structure with different boundary conditions. The accuracy of the obtained solution and results is examined by comparing the determined natural frequency and critical aerodynamic pressure with those obtained in previous studies. Then, a comprehensive parametric study is carried out to show the effects of hybridization of different distribution patterns of CNTs and GPLs, weight fractions, total layer number, and aspect ratio of hybrid composite panels on the flutter bounds. Results show that the present method provides a highly effective general numerical model for flutter analysis of hybrid nanocomposite panels with different boundary conditions for all thickness categories including thick plates. Moreover, an optimization nanoparticles distribution for the flutter of the nanohybrid composite panel has been obtained.

MatNLI: An open-source MATLAB-based solver for the non-linear inversion in elastography

Elastography has emerged as one of the most promising non-invasive clinical tools. In elastography, a stiffness map or elastogram is generated by solving an inverse problem of elasticity utilizing the tissue motion data acquired using magnetic resonance imaging or ultrasound. Among various inverse algorithms devoted to elastography, non-linear inversion coupled with the finite element method has demonstrated excellent applicability in extracting complex physics of the tissue. The development and implementation of such an inverse algorithm are challenging and often unavailable to clinicians. In the present work, we offer an open-source parallel MATLAB implementation of an efficient non-linear inversion algorithm based on the finite element method for different isotropic material models, viz., linear elastic and viscoelastic materials in the regime of compressible and nearly incompressible materials. Additionally, the framework has been extended to account for anisotropy by assuming transversely isotropic material. For the optimization module, the gradient of the objective function to the model parameters has been computed using the Adjoint method. Different case studies involving smooth variations and piece-wise discontinuities in the material property distribution are explored, and the efficacy of the inversion algorithm in reconstructing the stiffness map is discussed. In addition, noise is added to the synthetic data to depict a realistic setup, i.e., to prevent inverse crimes, and enhance the numerical stability and robustness of the current implementation. The present framework with general-purpose computer implementation could be beneficial for academic and clinical uses and may aid researchers in strengthening their existing frameworks and developing new algorithmic ideas.