Linear Elastic Modulus Research Articles

(Digital Presentation) A Constant Deformation Modulus for the Simulation of Gas Diffusion Layer

The deformation of gas diffusion layer(GDL) directly affects gas diffusion and electron transfer in the fuel cell. The modulus of stress-strain relationship is the basic parameter in the process of deformation. In this paper, based on beam bending theory and geometric probability analysis, a nonlinear analytic model of stress-strain with physical meaning is established, and a constant deformation modulus of GDL is given. Based on the deformation modulus, we further simulate the inhomogeneous deformation of GDL within a half channel-rib model. The results indicate that the uneven deformation with deformation modulus is more significant than that with linear elastic modulus in the same condition. Finally, a shape-dependent bending radius design for the rib edge is proposed, in which the inhomogeneous deformation of GDL becomes smoother as the radius increases, thereby improving the service condition of GDL and prolonging its service life.

Multifunctional Textile Electronic with Sensing, Energy Storing, and Electrothermal Heating Capabilities.

The development of wearable devices has stimulated significant engineering and technologies of textile electronics (TEs). Improving sensing, energy-storing, and electro-heating capabilities of TEs is still challenging but crucial for their practical applications. Herein, a drip-coating method that constructs a dense β-FeOOH scaffold on a nylon strip for enhancing polypyrrole loading is proposed, which facilitates the fabrication of highly conductive and hydrophobic PFCNS (polypyrrole/β-FeOOH/nylon strip). The space provided by the β-FeOOH scaffold increases the mass of polypyrrole on fibers from 1.1 (polypyrrole/nylon strip) to 3.0 mg cm-2 (polypyrrole/β-FeOOH/nylon strip), which decreases the resistance from 104.96 to 34.29 Ω cm-1. The PFCNS exhibits a linear elastic modulus of 0.758 MPa within 150% strain, performs a unique resistance variation mechanism, and enables great sensing capability with rapid response time (140 ms), long durability (10,000 stretching-recovering), and effective movement monitoring (e.g., breathing, back bending, jumping). The sensing signals for knee bending have been analyzed in detail by combining with both stretching and pressing response mechanisms. The PFCNS electrode attains a diffusion-controlled capacitance of 574 mF cm-2 and discharging-capacitance of 916 mF cm-2. Furthermore, an interdigitally parallel connection is proposed, which assists the PFCNS heater in achieving high temperature (84 °C) at a low voltage (4 V). This work provides a simple route for nylon-based TEs and promises satisfactory application in wearable sensors, power sources, and heaters.

Effective elastic properties of a weakly nonlinear particulate composite

The fundamental problem of finding the effective linear and nonlinear elastic properties of a particulate composite subjected to finite elastic deformations is solved when the matrix and particulate phases are assumed to be weakly nonlinear. Weak nonlinearity is adequate to describe common engineering materials and composites loaded in the elastic regime. A nonlinear analogue of the Eshelby solution for the axisymmetric deformation of spherical particles is derived. Based on this solution, explicit asymptotic expressions for the effective linear and third-order (nonlinear) elastic moduli are derived in the case of a dilute distribution of spherical particles based on a general homogenisation methodology proposed by Hill. It is demonstrated that the current solutions correctly recover well-known relationships for the linear material properties of particulate composites as well as previously derived expressions for the effective nonlinear properties for certain special cases considered previously (e.g. hydrostatic loading, and a neo-Hookean matrix containing voids). The obtained theoretical results also agree with limited experimental data available in the literature.

From Strain Stiffening to Softening-Rheological Characterization of Keratins 8 and 18 Networks Crosslinked via Electron Irradiation.

Networks of crosslinked keratin filaments are abundant in epithelial cells and tissues, providing resilience against mechanical forces and ensuring cellular integrity. Although studies of in vitro models of reconstituted keratin networks have revealed important mechanical aspects, the mechanical properties of crosslinked keratin structures remain poorly understood. Here, we exploited the power of electron beam irradiation (EBI) to crosslink in vitro networks of soft epithelial keratins 8 and 18 (k8–k18) filaments with different irradiation doses (30 kGy, 50 kGy, 80 kGy, 100 kGy, and 150 kGy). We combined bulk shear rheology with confocal microscopy to investigate the impact of crosslinking on the mechanical and structural properties of the resultant keratin gels. We found that irradiated keratin gels display higher linear elastic modulus than the unirradiated, entangled networks at all doses tested. However, at the high doses (80 kGy, 100 kGy, and 150 kGy), we observed a remarkable drop in the elastic modulus compared to 50 kGy. Intriguingly, the irradiation drastically changed the behavior for large, nonlinear deformations. While untreated keratin networks displayed a strong strain stiffening, increasing irradiation doses shifted the system to a strain softening behavior. In agreement with the rheological behavior in the linear regime, the confocal microscopy images revealed fully isotropic networks with high percolation in 30 kGy and 50 kGy-treated keratin samples, while irradiation with 100 kGy induced the formation of thick bundles and clusters. Our results demonstrate the impact of permanent crosslinking on k8–k18 mechanics and provide new insights into the potential contribution of intracellular covalent crosslinking to the loss of mechanical resilience in some human keratin diseases. These insights will also provide inspiration for the synthesis of new keratin-based biomaterials.

Chemomechanical equilibrium at the interface between a simple elastic solid and its liquid phase.

Applying diffusion coupled deformation theory, we investigate how the elastic properties of a solid body are modified when forced to keep its chemical potential aligned with that of its melt. The theory is implemented at the classical level of continuum mechanics, treating materials as simple continua defined by uniform constitutive relations. A phase boundary is a sharp dividing surface separating two continua in mechanical and chemical equilibrium. We closely follow the continuum theory of the swelling of elastomers (gels) but now applied to a simple two phase one-component system. The liquid is modeled by a local free energy density defining a chemical potential and hydrostatic pressure as usual. The model is extended to a solid by adding a non-linear shear elastic energy term with an effective modulus depending on density. Imposing chemomechanical equilibrium with the liquid reservoir reduces the bulk modulus of the solid to zero. The shear modulus remains finite. The stability of the hyper-compressible solid is investigated in a thought experiment. A mechanical load is applied to a rectangular bar under the constraintof fixed lateral dimensions. The linear elastic modulus for axial loading is evaluated and found to be larger than zero, implying that the bar, despite the zero bulk modulus, can support a weight placed on its upper surface. The weight is stabilized by the induced shear stress. The density dependence of the shear modulus is found to be a second order effect reducing the density of the stressed solid (chemostriction).

Hot pressing of Ho2O3 and Dy2O3 based magneto-optical ceramics

The paper presents results of a research on fabrication of magneto-optical ceramics based on Ho2O3 and Dy2O3 sesquioxides. The ceramics were made by hot pressing of powders prepared by self-propagating high-temperature synthesis. The methods and modes of the powder treatment developed made it possible to significantly increase the thickness of the ceramics without deterioration in optical quality in comparison with the samples obtained by vacuum sintering. The characteristics of the ceramics, such as transmission spectrum, thermal conductivity, linear thermal expansion coefficient, microhardness, elastic modulus, and crack resistance have been investigated.

Experimental Bi-axial tensile tests of spinal meningeal tissues and constitutive models comparison

Introduction This study aims at identifying mechanical characteristics under bi-axial loading conditions of extracted swine pia mater (PM) and dura and arachnoid complex (DAC). Methods 59 porcine spinal samples have been tested on a bi-axial experimental device with a pre-load of 0.01 N and a displacement rate of 0.05 mm·s−1. Post-processing analysis included an elastic modulus, as well as constitutive model identification for Ogden model, reduced Gasser Ogden Holzapfel (GOH) model, anisotropic GOH model, transverse isotropic and anisotropic Gasser models as well as a Mooney-Rivlin model including fiber strengthening for PM. Additionally, micro-structure of the tissue was investigated using a bi-photon microscopy. Results Linear elastic moduli of 108 ± 40 MPa were found for DAC longitudinal direction, 53 ± 32 MPa for DAC circumferential direction, with a significant difference between directions (p < 0.001). PM presented significantly higher longitudinal than circumferential elastic moduli (26 ± 13 MPa vs 13 ± 9 MPa, p < 0.001). Transversely isotropic and anisotropic Gasser models were the most suited models for DAC (r2 = 0.99 and RMSE:0.4 and 0.3 MPa) and PM (r2 = 1 and RMSE:0.06 and 0.07 MPa) modelling. Conclusion This work provides reference values for further quasi-static bi-axial studies, and is the first for PM. Collagen structures observed by two photon microscopy confirmed the use of anisotropic Gasser model for PM and the existence of fenestration. The results from anisotropic Gasser model analysis depicted the best fit to experimental data as per this protocol. Further investigations are required to allow the use of meningeal tissue mechanical behaviour in finite element modelling with respect to physiological applications. Statement of significanceThis study is the first to present biaxial tensile test of pia mater as well as constitutive model comparisons for dura and arachnoid complex tissue based on such tests. Collagen structures observed by semi-quantitative analysis of two photon microscopy confirmed the use of anisotropic Gasser model for pia mater and existence of fenestration. While clear identification of fibre population was not possible in DAC, results from anisotropic Gasser model depicted better fitting on experimental data as per this protocol. Bi-axial mechanical testing allows quasi-static characterization under conditions closer to the physiological context and the results presented could be used for further simulations of physiology. Indeed, the inclusion of meningeal tissue in finite element models will allow more accurate and reliable numerical simulations.

Auxetic vibration behaviours of periodic tetrahedral units with a shared edge.

A very low-frequency mode supported within an auxetic structure is presented. We propose a constrained periodic framework with corner-to-corner and edge-to-edge sharing of tetrahedra and develop a kinematic model incorporating two types of linear springs to calculate the momentum term under infinitesimal transformations. The modal analysis shows that the microstructure with its two degrees of freedom has both low- and high-frequency modes under auxetic transformations. The low-frequency mode approaches zero frequency when the corresponding spring constant tends to zero. With regard to coupled eigenmodes, the stress–strain relationship of the uniaxial forced vibration covers a wide range. When excited, a very slow motion is clearly observed along with a structural expansion for almost zero values of the linear elastic modulus.

Adopting traditional image algorithms and deep learning to build the finite model of a 2.5D composite based on X-Ray computed tomography

A novel methodology combining traditional image algorithms with deep learning is proposed to accurately classify each pixel of the XCT image of 2.5D woven fabrics with fewer user involvement. For images with symmetrical microstructures, we first extracted the weft and matrix edges separately and then performed curve fitting to obtain the warp edges. The regions enclosed by the warp and weft edges were weft regions, and the areas between two warps were warp regions. Then, threshold segmentation was adopted to achieve pixel classification. For an image with asymmetrical microstructures, a fully convolutional neural network consisting of one encoder and two decoder networks was trained using the symmetry image. Finally, two finite element models of the 2.5D composite were established to predict the linear elastic modulus, one containing all the geometries and the other containing only the symmetrical geometry. The results show that the former prediction fit the experimental results better.

Effect of linear and Mooney\u2013Rivlin material model on carotid artery hemodynamics

Atherosclerosis is one of the most common cardiovascular diseases leading to high morbidity. The study of arterial dynamics using fluid–structure interaction (FSI) technique by taking into account the physiology of flow, the critical hemodynamic parameters can be determined which plays a crucial role in predictive medicine. Due to advances in the computational facilities, coupled field analysis such as FSI can facilitate understanding of the mechanics of stenosis progression and its early diagnosis. In this study a two-way FSI analysis is carried out using modified Navier–Stokes equations as the governing equations of blood flow for determining hemodynamic parameters. The arterial wall has been described at different linear elastic modulus and compared with hyperelastic Mooney–Rivlin model to evaluate the effect of different arterial stiffness on hemodynamics. The Mooney–Rivlin model predicts flow reduction with the severe backflow at arterial bifurcation resulting in decreased shear stress and oscillatory behavior. Furthermore, these findings may be used in understanding the advantages and disadvantages of using hyperelastic artery model in numerical simulations to better understand and predict the variable that causes cardiovascular diseases and as a diagnostic tool. In the present study, variation due to change in arterial wall properties such as linear elastic and Mooney Rivlin hyperelastic and its influence on hemodynamics are investigated.

Research of cation dependences of structural and elastic properties of metal carbonates series by density functional theory calculations

Using the density functional theory methods with the PBE gradient functional, and taking into account the van der Waals interaction in the basis of localized atomic orbitals, using the CRYSTAL 17 program code, calculations of the structure and elastic constants for MgCO3, ZnCO3, CdCO3 CaCO3 in the calcite structure, CdMg(CO3)2, CaMg(CO3)2, CaZn(CO3)2 in the dolomite structure, BaMg(CO3)2 – norsethite, and CaCO3, SrCO3, PbCO3, BaCO3 in the aragonite structure are calculated. It is shown that the lattice constants, interatomic distances linearly depend on the cation radius RM, and the band gap, atomic charges, overlap populations of electron shells, and crystal density depend on cation electronegativity χM. Elastic compression constants and linear elastic moduli along the c axis are also described by RM. For polycrystalline bulk modulus BH, shear modulus GH, and Young's modulus EH, linear dependences with a good correlation coefficient were obtained: BH (GPa) = 175.95−84.89·RM, GH (GPa) = 87.57−46.05·RM, EH (GPa) = 224.36−103.59·RM. Similar dependences are established for the longitudinal and transverse speeds of sound, the Debye temperature and the coefficient of minimum thermal lattice conductivity. These results can be used to predict the elastic and mechanical characteristics of carbonates with the chemical formula MCO3 and solid solutions based on them.

Numerical computation of effective anisotropic elastic properties of geosynthetics-reinforced pavements

Although several numerical techniques have been recently developed for the prediction of the geosynthetic-reinforced pavements performance, it is often unclear how to quantify such properties, specially when the soil is anisotropic and highly heterogeneous. In this work, following Hashin-Shtrikman bounds, explicit expressions describing anisotropic linear elastic moduli of geosynthetic-reinforced soils are presented. Modelling the geosynthetic material by oblate spheroids with spheroidal distribution inside the matrix of asphalt, the derived expressions provide bounds as a function of laminated material geometry and first principles in the elastic setting. The scheme developed can straightforwardly be extended to multiphase composites. We illustrate the implementation of the model by showing reasonable predictions on the transversely isotropic behaviour of the heterogeneous pavement.

A large displacement model for superelastic material side-notched tube instruments

Side-notched tube structures made of superelastic material are increasingly being studied in surgical robotics as they can easily be integrated into surgical instruments and offer the surgeon enhanced dexterity. Their simple design and ability to achieve large bending angles and small bending radii make them particularly suited for use in constrained workspace surgery. Up to now, however, no model has been able to accurately predict the behavior of such types of structures for large bending angles. This study, therefore, proposes a novel approach to model large displacements of side-notched tubes taking into account the superelasticity of the material, the non-constant curvature of the side-notched structure, as well as the friction induced by the actuating wire. More specifically, an equivalent, strain dependent, linear elastic modulus is used to model the superelastic behavior of the instrument’s material. The deformation of each separate section of the side-notched tube is calculated successively to capture the non-constant curvature of the NiTi backbone. The capstan equation is used to model cable friction. The model was tested on four samples of 2.3 mm diameter and was able to predict the bending angle of the side-notched tubes with a root mean square error (RMSE) of as low as 5.4∘ (3.1%) and the position of each notch with an RMSE of as low as 0.33 mm (2.5%) across its entire bending range (0∘ to 180∘). The model was demonstrated for both tension and relaxation of the actuating wire.

Permeability Evolution of Thermally Cracked Granite with Different Grain Sizes

The permeability of thermally cracked granites is crucial information for understanding and modeling a number of processes in the earth’s crust, such as folding, geothermal activity, magmatic intrusions, and nuclear waste disposal. Factors, including the coefficient of thermal expansion, elastic modulus, grain size, and bonding stress, have a significant impact on thermal cracking and induced permeability. We performed thermal cracking experiments on granite with different grain sizes to determine the effect of grain size on permeability. The results indicated that permeability increased with temperature up to 700 °C for all samples. The ratio of permeability at the target temperature to that at room temperature is an exponential function of temperature. Coarse-grained granite has a higher increase in permeability than fine-grained granite. A mathematical model was presented to explain the effect of grain size on thermal cracking and induced permeability. In addition, the model can also quantitatively describe the influence of the linear thermal expansion coefficient and elastic modulus of minerals on thermal cracking.

Incompressible Transversely Isotropic Hyperelastic Materials and Their Linearized Counterparts

The strain-energy density $W$ for incompressible transversely isotropic hyperelastic materials depends on four independent invariants of the strain tensor. For consistency with the infinitesimal theory, it is well known that there are three necessary conditions on the derivatives of $W$ (evaluated in the undeformed state) that have to be to be satisfied in terms of the three independent elastic moduli of the linear theory for incompressible transversely isotropic materials. We consider three different sets of these linear elastic moduli and express them in terms of the relevant derivatives of $W $ evaluated in the undeformed state. Necessary and sufficient conditions on the linearized strain-energy to ensure positive-definiteness are given and thus we derive such conditions expressed in terms of derivatives of $W$ evaluated in the undeformed state. These conditions are proposed to be fundamental constitutive inequalities which must be satisfied by any physically realistic strain-energy for incompressible transversely isotropic hyperelastic material, in particular those models proposed for fiber-reinforced soft tissues. Some particular strain-energies that have been proposed in the literature are used as illustrations of the results.

Numerical modelling of bilayer tetra periodic metamaterials to predict the elastic response

Metamaterials that exhibit negative Poisson’s ratio are termed as auxetic materials. The chiral and achiral honeycombs comprising of an array of cylinders connected by ligaments are one class of auxetic metamaterials. These structures have been investigated for their in-plane linear elastic behavior in the past. In this paper, novel bilayer tetra periodic structures are proposed by combining chiral and/or achiral honeycombs along the out-of-plane direction. Finite element (FE) models are developed for estimation of in-plane linear Elastic modulus and Poisson’s ratio. In the first step, the present FE model is verified with the help of experimental data for single layer tetra-chiral and tetra-achiral structures available in the literature. Subsequently, following identical methodology, the linear elastic constants of bilayer structures are computed. A comparison of bilayer tetra periodic structures with the single-layer tetra chiral/achiral metamaterials is presented. Further, a parametric analysis (for varied geometries) was performed to find a correlation between the geometry and mechanical behavior.

Development of hydroxyapatite reinforced alginate–chitosan based printable biomaterial-ink

This study reports synthesis of sodium alginate/ chitosan/ hydroxyapatite (HAp) based biomaterial-ink. An ionic interaction between polyanionic alginate and polycationic chitosan has been observed that forms a physical gel. The dispersion of HAp has been achieved through ultra-sonication, and stability of HAp in the hydrogel system has been achieved through hydrogen bonding with chitosan. Post printing crosslinking has been carried out with a 10 w/v % aqueous calcium chloride (CaCl2) solution. The combinations of biomaterial-ink have been characterized through Attenuated Total Reflectance-Fourier transform infrared spectroscopy (ATR-FTIR), Scanning Electron Microscope (SEM), contact angle measurements. Further, the inks were characterized to estimate the printability and rheological responses. ATR-FTIR study confirms the ionic interaction between alginate and chitosan and identifies the presence of HAp in the biomaterial-ink. SEM morphology depicted the post-printing shape retention ability of the bioprinted constructs and revealed the structure’s rough morphology. All the biomaterial-ink combinations depicted hydrophilic nature as confirmed by the contact angle measurements. Rheological studies of the printable ink with hydroxyapatite revealed shear thinning properties and acceptable viscosity, essential for extrusion during bioprinting. The biomaterial-ink comprised only sodium alginate, and chitosan also displayed shear thinning abilities and showed lower working viscosity resulting in poor printability. The addition of hydroxyapatite to the hydrogel revealed acceptable post-printing structural stability. However, beyond 0.2% by weight of HAp imparts brittleness in the final structure. The linear viscoelastic regime, elastic modulus, and viscous modulus of the inks have been determined through the oscillatory strain sweep test. Creep recovery study, essential for predicting material behaviour immediately after ejection from the nozzle, indicated the material’s viscoelastic behaviour. The power law model has been used to estimate the flow index that predicted shear thinning abilities of the biomaterial-ink, and a correlation between the experimental and theoretical model was established. Herschel–Bulkley empirical model was used to determine yield stress (minimum stress required for extrusion from the nozzle) of the biomaterial-ink. Rheological studies and printability studies indicated Ink 5% 2% 0.1% as a promising combination for tissue engineering applications.

Mechanistic pathway of water adsorption to impact on the nonlinear elasticity of single-crystalline ZnO NWs

Surface modification via adsorbates is significant for property prediction in nanostructures where surface effect is dominant. This is especially vital for zinc oxide (ZnO) nanowires (NWs) which has no native passivation layer. As water is an ubiquitous environmental factor and its aggregation on ZnO surface is favoured, molecular statics (MS) simulations are used to study the deformation of ZnO with surface water adsorption in the finite strain regime (up to 0.1). Three types of water covered surface structures are considered to examine their effects on the size-dependence of linear (Y0) and nonlinear (Y1) elastic moduli. The pathway of adsorption to impact NWs is identified by revealing the radial distribution of Y0, Y1 and residual stress for the NWs. The physical origins of the water adsorption effects are further discussed in terms of the layer-wise equilibrium structure and potential energy variation.

Repeatability of Linear and Nonlinear Elastic Modulus Maps From Repeat Scans in the Breast.

Compression elastography allows the precise measurement of large deformations of soft tissue in vivo. From an image sequence showing tissue undergoing large deformation, an inverse problem for both the linear and nonlinear elastic moduli distributions can be solved. As part of a larger clinical study to evaluate nonlinear elastic modulus maps (NEMs) in breast cancer, we evaluate the repeatability of linear and nonlinear modulus maps from repeat measurements. Within the cohort of subjects scanned to date, 20 had repeat scans. These repeated scans were processed to evaluate NEM repeatability. In vivo data were acquired by a custom-built, digitally controlled, uniaxial compression device with force feedback from the pressure-plate. RF-data were acquired using plane-wave imaging, at a frame-rate of 200 Hz, with a ramp-and-hold compressive force of 8N, applied at 8N/sec. A 2D block-matching algorithm was used to obtain sample-level displacement fields which were then tracked at subsample resolution using 2D cross correlation. Linear and nonlinear elasticity parameters in a modified Veronda-Westmann model of tissue elasticity were estimated using an iterative optimization method. For the repeated scans, B-mode images, strain images, and linear and nonlinear elastic modulus maps are measured and compared. Results indicate that when images are acquired in the same region of tissue and sufficiently high strain is used to recover nonlinearity parameters, then the reconstructed modulus maps are consistent.

Polystyrene-Based Nanocomposites with Different Fillers: Fabrication and Mechanical Properties.

The paper presents a comprehensive analysis of the elastic properties of polystyrene-based nanocomposites filled with different types of inclusions: small spherical particles (SiO2 and Al2O3), alumosilicates (montmorillonite, halloysite natural tubules and mica), and carbon nanofillers (carbon black and multi-walled carbon nanotubes). Block samples of composites with different filler concentrations were fabricated by melt technology, and their linear and non-linear elastic properties were studied. The introduction of more rigid particles led to a more profound increase in the elastic modulus of a composite, with the highest rise of about 80% obtained with carbon fillers. Non-linear elastic moduli of composites were shown to be more sensitive to addition of filler particles to the polymer matrix than linear ones. A non-linearity modulus βs comprising the combination of linear and non-linear elastic moduli of a material demonstrated considerable changes correlating with those of the Young’s modulus. The changes in non-linear elasticity of fabricated composites were compared with parameters of bulk non-linear strain waves propagating in them. Variations of wave velocity and decay decrement correlated with the observed enhancement of materials’ non-linearity.