Surface Stress Loading Research Articles

Ex-vivo quantification of ovine pia arachnoid complex biomechanical properties under uniaxial tension

BackgroundThe pia arachnoid complex (PAC) is a cerebrospinal fluid-filled tissue conglomerate that surrounds the brain and spinal cord. Pia mater adheres directly to the surface of the brain while the arachnoid mater adheres to the deep surface of the dura mater. Collagen fibers, known as subarachnoid trabeculae (SAT) fibers, and microvascular structure lie intermediately to the pia and arachnoid meninges. Due to its structural role, alterations to the biomechanical properties of the PAC may change surface stress loading in traumatic brain injury (TBI) caused by sub-concussive hits. The aim of this study was to quantify the mechanical and morphological properties of ovine PAC.MethodsOvine brain samples (n = 10) were removed from the skull and tissue was harvested within 30 min post-mortem. To access the PAC, ovine skulls were split medially from the occipital region down the nasal bone on the superior and inferior aspects of the skull. A template was used to remove arachnoid samples from the left and right sides of the frontal and occipital regions of the brain. 10 ex-vivo samples were tested with uniaxial tension at 2 mm s−1, average strain rate of 0.59 s−1, until failure at < 5 h post extraction. The force and displacement data were acquired at 100 Hz. PAC tissue collagen fiber microstructure was characterized using second-harmonic generation (SHG) imaging on a subset of n = 4 stained tissue samples. To differentiate transverse blood vessels from SAT by visualization of cell nuclei and endothelial cells, samples were stained with DAPI and anti-von Willebrand Factor, respectively. The Mooney-Rivlin model for average stress–strain curve fit was used to model PAC material properties.ResultsThe elastic modulus, ultimate stress, and ultimate strain were found to be 7.7 ± 3.0, 2.7 ± 0.76 MPa, and 0.60 ± 0.13, respectively. No statistical significance was found across brain dissection locations in terms of biomechanical properties. SHG images were post-processed to obtain average SAT fiber intersection density, concentration, porosity, tortuosity, segment length, orientation, radial counts, and diameter as 0.23, 26.14, 73.86%, 1.07 ± 0.28, 17.33 ± 15.25 µm, 84.66 ± 49.18°, 8.15%, 3.46 ± 1.62 µm, respectively.ConclusionFor the sizes, strain, and strain rates tested, our results suggest that ovine PAC mechanical behavior is isotropic, and that the Mooney-Rivlin model is an appropriate curve-fitting constitutive equation for obtaining material parameters of PAC tissues.

Nonlinear coupled thermoelastic analysis of thermal wave propagation in a functionally graded finite solid undergoing finite strain

In this research, a study of nonlinear thermoelastic, transient responses and thermal wave propagation of functionally graded (FG) finite length solid under a thermal shock and surface stress loading is carried out. The coupled equations are derived from the concept of large displacement as well as finite strains. Therefore, the nonlinear Lagrangian strain–displacement expression and second Piola–Kirchhoff stress are employed in that the components of displacement and stresses are obtained in the original coordinate. Besides, the assumption of very small temperature changes compared to the reference temperature is released in the present research. The thermal wave propagation is discussed for surface stress traction and thermal shock. The thermal stress, displacement and temperature distributions are illustrated graphically for some grading patterns of FG solid, and the effects of grading patterns of the material properties on wave propagation are investigated. The obtained results indicate significant effects of volume fraction on stress and thermal wave propagation of a medium under mechanical and thermal loading. Moreover, the results show that the increase in volume fraction leads to increase in the wave speed in both different conditions.

Impact of Isolation and Immobilization Layers on the Electro-Mechanical Response of Piezoresistive Nano Cantilever Sensors.

In the last decade, piezoresistive nano cantilever sensors have been extensively explored, especially for chemical and biological sensing applications. Piezoresistive cantilever sensors are multi-layer structures with different constituent materials. Performance of such sensors is a function of their geometry and constituent materials. For a fixed material set, the pre-requisite for optimizing the performance of a composite piezoresistive cantilever sensor is careful geometrical design of its constituent layers. Even though, treatise encompasses various designs of such sensors, typically for computational simplicity the functional layers i.e., the isolation and immobilization layers are neglected in the modeling stages. In this paper, we elucidate the impact of the functional layers on the electro-mechanical response of composite piezoresistive nano cantilever sensors. Systematic and detailed computations are performed using theoretical models and numerical simulations. Results show that both the isolation and immobilization layers play a critical role in governing the sensor performance. Simulation results depict that compared to a sensor with an isolation layer of thickness 100 nm, a sensor without isolation layer has 36.29% and 42.51% better deflection sensitivity and electrical sensitivity respectively. Furthermore, it is found that when an immobilization layer of thickness 40 nm is added atop the isolation layer, the deflection sensitivity and electrical sensitivity reduces by 12.98% and 15.83% respectively. Through our investigation it is shown that the isolation and immobilization layers not only play a vital role in determining the stability and electro-mechanical response of the sensor but their negligence in the design stages can be detrimental. Apart from investigating the impact of the immobilization layer thickness, to model the sensor closer to real time operational conditions, we have performed analysis to understand the impact of non-uniformity in the immobilization layer thickness and non-uniform surface stress loading on the electro-mechanical response of the sensor. Results and inferences obtained from this study will help NEMS engineers to optimize the performance of piezoresistive nano cantilever sensors and to design multi-layer cantilever platform structures for other transducers.

Size-dependent effects of surface stress on resonance behavior of microcantilever-based sensors

The mass and surface stress loadings in microcantilever-based sensors, caused by surface adsorption of target analytes/biomolecules, change their resonance behavior. Despite numerous efforts, the mechanisms of surface stress impact on the resonance behavior of microcantilevers are not fully understood. This results in substantial discrepancies between theoretically predicted and experimentally measured resonance frequency shifts in wide microcantilevers with aspect ratios (width-to-thickness) larger than 10, commonly found in chemical and biological sensing applications. This also impedes the proper decoupling of the effects of mass and surface stress loading and hinders the development of accurate microcantilever-based sensors. In this work, we attempt to decrease the discrepancy found between theoretical models and experiments by introducing a new mechanism that correlates the nonlinear geometric effects associated with surface stress-induced variation of microcantilever biaxial curvature to its frequency and modal responses, with a correlation intensity that strongly depends on the microcantilever aspect ratio. A new comprehensive analytical model combining the new mechanism with currently available theoretical models is proposed and used to study the resonance behavior of microcantilevers with different deformations and sizes. Using the new model, it is shown that in wide microcantilevers, the theoretically predicted resonance frequency shifts agree with experimental and finite element simulations results within 30% whereas the predictions by other currently available theoretical models are off by more than one order of magnitude. The new model is also used to investigate the modal response of microcantilevers where it anticipates the bending-extensional mode coupling associated with the flexural vibration modes of microcantilevers with a coupling strength that depends on the microcantilever curvature. The presented model is expected to provide a new tool to decouple the effects of mass and surface stress loadings on the resonance behavior of microcantilevers used in chemical and biological sensors.

Modeling and Deformation Analysis of Piezoresistive Cantilever for Bio-sensing Applications

Objectives: To design a simple piezoresistive cantilever punched with different shaped objects in the concept of Stress Concentrated Region (SCR) and study the effects of geometrical changes, addition of materials and applied loads to find out optimum conditions resulting high displacement sensitivity. Methods/Analysis: Design and simulation of piezoresistive cantilever with different punched objects (Circle, Triangle, Rectangle and T-Shape) to explore the maximum deformation. These design attempts indicate the bending of a cantilever under an applied load and solves the deformation of the beam under an applied force. The study also extended to analyze the sensitivity with the change of piezoresistive materials for same applied input force and given geometry. Findings: From the analyses of both the efforts, it is observed that the SiO2 based MEMS piezoresistive cantilever found to exhibit high deformation in turn sensitivity. The reasons for improvement in the sensitivity were discussed in detail by means of dimensional modifications, applied loads and materialistic properties. The design and simulations of a piezoresistive cantilever were carried out using commercial MEMS software tool COMSOL v 5.2a. Novelty/Improvement: This type of study would be useful to detect very minute biological mass changes that enable to overcome low resolution of the read out system for piezoresistive approach. The study of deformation of piezoresistive cantilever under surface stress loading may be treated as loading condition that take place in biochemical sensors.

Frequency response of curved bilayer microcantilevers with applications to surface stress measurement

Bilayer microcantilevers are normally curved because of fabrication-induced stresses. When used in biological/chemical sensing applications, the absorption of target agents onto the functionalized surface of the microcantilever creates a surface stress that shifts its resonance frequency. Despite numerous efforts, the mechanisms of surface stress-induced shift in the resonance frequency of microcantilevers remain elusive. To address this problem, this work presents a detailed analysis of the frequency response of microcantilevers, with different width-to-thickness ratios and curvature levels, using classical lamination theory and the Rayleigh–Ritz method. Based on the results of this analysis, a new relationship between resonance frequency shift and curvature variation due to differential surface stress loading is established. By comparing the strain energies associated with the in-plane and out-of-plane displacements of the microcantilever at different curvature levels, a new implicit model for surface stress-induced resonance frequency shift in microcantilevers is presented. Verified against the results of experiments carried out on gold/polysilicon microcantilevers, the new model is expected to provide a better understanding of surface stress-microcantilever resonator interaction, which is critical to systematic optimization of resonance-based micro sensors.

Modeling Piezoresistive Microcantilever Sensor Response to Surface Stress for Biochemical Sensors

This paper considers mechanical stress and strain in a piezoresistive cantilever sensor under surface stress loading, which is the loading condition that occurs in biochemical sensing applications. Finite element simulations examine the piezoresistor sensitivity due to changes in cantilever length, width, and thickness, and piezoresistor size, location, and depth. A few unexpected results are found. Unlike cantilevers designed for atomic force microscopy, cantilevers for biochemical sensing should be short and wide. While shallow piezoresistors offer good sensitivity, the piezoresistor may extend far into the thickness of the cantilever and still be quite effective. The paper concludes with comments on design guidelines for piezoresistive cantilever sensors.

The effect of piezoresistive microcantilever geometry on cantilever sensitivity during surface stress chemical sensing

We have designed, fabricated, and tested five piezoresistive cantilever configurations to investigate the effect of shape and piezoresistor placement on the sensitivity of microcantilevers under both point loading and surface stress loading. The experimental study reveals that: (1) high aspect ratio cantilevers that are much longer than they are wide are optimal for point-loading applications such as microscopy and force measurements; (2) low aspect ratio cantilevers that are short and wide are optimal for surface stress-loading scenarios such as those that occur in biological and chemical sensor applications. The sensitivity data for both point loads and surface stress are consistent with previously developed finite-element models.

Surface Stress, Thickness, and Mass of the First Few Layers of Polyelectrolyte

The effects of surface stress and mass loading upon the adsorption of polyelectrolytes onto flexible silicon micromechanical cantilever sensors (MCSs) were studied in situ. A self-assembled monolayer of 2-mercaptoethylamine chloride (2-MEA) on gold was used to achieve single-side adsorption on the MCS. Such a preparation gave a positive surface potential, whereas a bare SiOx surface gave a negative surface potential. Wide scan X-ray photoelectron spectroscopy confirmed that the adsorption of polystyrenesulfonate (PSS) and polyallylamine hydrochloride (PAH) followed the general rule expected from the electrostatic interaction between the substrate and the polyelectrolyte, whereas the adsorption polyethyleneimine (PEI) did not. The adsorption of PAH on SiO(x) from a 3 mM water solution containing 1 M NaCl was associated with a deflection of the MCS toward the polyelectrolyte monolayer (tensile surface stress) owing to the hydrogen bonding between neighboring amino groups. Here, a surface stress change of 1.4 +/- 0.1 N/m was estimated. The adsorption of PSS from a 3 mM water solution containing 1 M NaCl on a 2-MEA surface induced a deflection of the MCS away from the polyelectrolyte layer (compressive stress), toward the SiO(x) side. Here, a surface stress change of 3.1 +/- 0.3 N/m was determined. The formation of a PAH layer on top of the PSS layer resulted in a deflection of the MCS toward the PAH layer. This indicated that the adjacent PSS layer was deswelling, corresponding to a surface stress change of 0.5 +/- 0.1 N/m.

Numerically evaluated displacement and stress solutions for a 3D viscoelastic half space subjected to a vertical distributed surface stress loading using the Radon and Fourier transforms

AbstractIn this article a numerical solution for a 3D isotropic, viscoelastic half‐space subjected to vertical rectangular surface stress loading of constant amplitude is evaluated with the aid of the Radon and Fourier integral transforms. Dynamic displacement and stress fields are computed for the half‐space surface as well as for points inside the domain. The analysis is performed in the frequency domain. Viscoelastic effects are incorporated by means of the elastic–viscoelastic correspondence principle. The equations of motion are solved in the Radon–Fourier transformed domain. Inverse transformations to the physical domain are accomplished numerically. The scheme used to perform the numerical inverse transformations is addressed. The solution is validated by comparison with results available in the literature. A sample of original dynamic results for displacement and stress fields for the 3D half‐space is furnished. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Development of a double-microcantilever for surface stress measurement in microsensors

Microsensors based on piezoresistive microcantilevers have been proposed to measure the surface stress change from biochemical reaction. However, the sensor performance is adversely influenced by the thermal stress induced during operation. A mechanics model is employed to analyze the piezoresistive microcantilever subject to surface stress and thermal stress loading, and a double-microcantilever design is also developed to improve the measurement sensitivity. The double-microcantilever is composed of a top immobilized cantilever and another bottom sensing cantilever such that the biaxial surface stress in the former can be converted into uniaxial strain in the latter. Analyses show that the sensitivity can be further increased by a higher length ratio and a lower thickness ratio of the two cantilevers. More than two orders of sensitivity increase can be achieved and the induced thermal effect can also be minimized.

The Linear Stability of Boundary-Layer Flow over Compliant Walls—The Effects of the Wall Mean State, Induced by Flow Loading

This paper is concerned with the linear hydrodynamic stability of boundary-layer flow over a compliant wall subjected to steady-state stresses on its surface. Surface stress loading induces an equilibrium state of stress and strain in the compliant wall, termed the wall mean (basic) state. Flow stability is affected by the surface loading, as a result of an interaction between the propagating wall perturbation and the induced wall mean state. This perturbation-mean state interaction in the wall is accounted for in this paper by the application of a nonlinear elasticity theory, suitably linearized about the mean state, in which the compliant material is assumed to obey a linear isotropic (stress-strain) law between the second Piola-Kirchoff stress tensor and the Green strain tensor. Surface loading due to combine hydrostatic pressure and boundary-layer viscous shear is considered. It is found that hydrostatic pressure can strongly affect the stability of flow over compliant walls; with a stabilizing influence on the Tollmen-Schlichting instabilities and a destabilizing influence on the compliance-related instabilities. The underlying mechanics for both incompressible compliant layers are explained. The present study shows that the pressure of the operational environment should be taken into account when evaluating the performance of compliant coatings as transition-delaying or noise-reducing devices in underwater applications.

Surface Wave Reflection from Metal-Strips and Transducers

Various contributions to the surface wave reflection, viz., piezo-shorting, mass and stress loading and electrical regeneration, are treated appropriately for the estimation of overall reflection from metallic strips and transducers. The effect of mass loading is studied for metal strips deposited on YZ LiNbO3 and ST-X quartz substrates. A simple theory is developed which predicts zero reflection for an open aluminium strip and short gold strip on YZ LiNbO3 for specific values of metallisation ratio. The theory also describes the reflection process in ordinary bi-directional and group type unidirectional transducers. Experimental results obtained on YZ LiNbO3 substrate are in close agreement with the theoretical predictions. The theory may prove to be useful in the design of SAW transversal and resonator filters.