Strain Amplification Mechanisms Research Articles

Modeling and simulation of osteocyte process–fluid interaction in a canaliculus

An osteocyte is a bone cell situated inside a hard bone matrix in an interstice (lacuna). It has many dendritic structures called cellular processes that radiate outward from the cell through the bone matrix via cylindrical openings (canaliculi). Osteocytes can sense stress and strain applied by the interstitial fluid flow and respond by releasing biochemical signals that regulate bone remodeling. In vitro experiments have suggested that the stress and strain typically experienced at the macroscale tissue level have to be amplified 10× in order for osteocytes to have a significant response in vivo. This stress and strain amplification mechanism is not yet well understood. Previous studies suggest that the processes are the primary sites for mechanosensation thanks to the tethering elements that attach the process membrane to the canalicular wall. However, there are other potential factors which may also contribute to stress and strain amplification, such as canalicular wall geometry and osteocyte-associated proteins in the interstitial space called pericellular matrix. In this work, we perform computational studies to study how canalicular wall roughness affects stress and strain amplification. Our major finding is that the wall roughness induces significantly greater wall shear stress (WSS) on the process when the wall roughness increases flow resistance; and the roughness has relatively smaller influence on the WSS when the resistance remains the same.

Microchannel‐Confined Chinese Ink‐Based Highly Stretchable Liquid‐State Strain Sensor for Early Warning of Road Collapse

AbstractStretchable strain sensors are widely used in the fields of wearable devices, soft robotics, healthcare monitoring, and more. Despite tremendous efforts, strain sensors capable of detecting large‐scale soil deformation for urban geological hazard prevention have not yet been demonstrated. In this paper, a soft strain sensor of a highly stretchable Ecoflex‐0030 elastomeric matrix with microchannel‐confined environmentally benign conductive Chinese ink as the liquid‐state strain‐sensitive material that can reliably detect a wide range of working strain up to 300% is demonstrated. The sensor exhibits a negligible hysteresis error of 2.1%, with a considerably good gauge factor of 1.95. The sensor performance is evaluated under both creep and cyclic loading tests, indicating superior stability (0.65% fluctuation), and repeatability (0.28% variation in 1000 cycles), even under a lower underground environment temperature of 18°C. As a proof‐of‐concept demonstration, a liquid‐state strain sensor array with a strain amplification mechanism capable of accurately monitoring the formation of various underground cavities and providing timely demanded information for early warning of catastrophic road collapse is demonstrated and verified by the computer vision‐based particle image velocimetry (PIV) method.

The Influence of Colloidal Properties of Carbon Black on Static and Dynamic Mechanical Properties of Natural Rubber.

The influence of carbon black (CB) structure and surface area on key rubber properties such as monotonic stress-strain, cyclic stress–strain, and dynamic mechanical behaviors are investigated in this paper. Natural rubber compounds containing eight different CBs were examined at equivalent particulate volume fractions. The CBs varied in their surface area and structure properties according to a wide experimental design space, allowing robust correlations to the experimental data sets to be extracted. Carbon black structure plays a dominant role in defining the monotonic stress–strain properties (e.g., secant moduli) of the compounds. In line with the previous literature, this is primarily due to strain amplification and occluded rubber mechanisms. For cyclic stress–strain properties, which include the Mullins effect and cyclic softening, the observed mechanical hysteresis is strongly correlated with carbon black structure, which implies that hysteretic energy dissipation at medium to large strain values is isolated in the rubber matrix and arises due to matrix overstrain effects. Under small to medium dynamic strain conditions, classical strain dependence of viscoelastic moduli is observed (the Payne effect), the magnitude of which varies dramatically and systematically depending on the colloidal properties of the CB. At low strain amplitudes, both CB structure and surface area are positively correlated to the complex moduli. Beyond ~2% strain amplitude the effect of surface area vanishes, while structure plays an increasing and eventually dominant role in defining the complex modulus. This transition in colloidal correlations reflects the transition in stiffening mechanisms from flexing of rigid percolated particle networks at low strains to strain amplification at medium to high strains. By rescaling the dynamic mechanical data sets to peak dynamic stress and peak strain energy density, the influence of CB colloidal properties on compound hysteresis under strain, stress, and strain energy density control can be estimated. This has considerable significance for materials selection in rubber product development.

High-Stiffness Torque Sensor With a Strain Amplification Mechanism for Cooperative Industrial Manipulators

This study presents a high-stiffness torque sensor with a strain amplification mechanism for cooperative industrial manipulators. A novel strain amplification mechanism for a torque sensor has been designed to increase the stiffness of the sensor. The mechanism has a single structure composed of trapezoidal beams, flexure structures, and inner and outer frames. In this configuration, the displacement that occurs in the beam is amplified by the flexure structure. The amplified displacement is measured using capacitance sensing technology. As a result, the developed torque sensor has a high stiffness (198.7 kN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\cdot$</tex-math></inline-formula> m/rad) and compactness (diameter of 110 mm and a thickness of 9.8 mm) that integrates with all the electronics. Additionally, it has a low cost and it is easy to manufacture. Through several experimental setups, we evaluated the sensing performances of the sensor with regard to accuracy, high stiffness, and repeatability.

Impact-Induced Cortical Strain Concentrations at the Sulcal Base and Its Implications for Mild Traumatic Brain Injury.

This study investigated impact-induced strain fields within brain tissue surrogates having different cortical gyrification. Two elastomeric surrogates, one representative of a lissencephalic brain and the other of a gyrencephalic brain, were drop impacted in unison at four different heights and in two different orientations. Each surrogate contained a radiopaque speckle pattern that was used to calculate strain fields. Two different approaches, digital image correlation (DIC) and a particle tracking method, enabled comparisons of full-field and localized strain responses. The DIC results demonstrated increased localized deviations from the mean strain field in the surrogate with a gyrified cortex. Particle tracking algorithms, defining four-node quadrilateral elements, were used to investigate the differences in the strain response of three regions: the base of a sulcus, the adjacent gyrus, and the internal capsule of the surrogates. The results demonstrated that the strains in the cortex were concentrated at the sulcal base. This mechanical mechanism of increased strain is consistent with neurodegenerative markers observed in postmortem analyses, suggesting a potential mechanism of local damage due to strain amplification at the sulcal bases in gyrencephalic brains. This strain amplification mechanism may be responsible for cumulative neurodegeneration from repeated subconcussive impacts. The observed results suggest that lissencephalic animal models, such as rodents, would not have the same modes of injury present in a gyrencephalic brain, such as that of a human. As such, a shift toward representative mild traumatic brain injury animal models having gyrencephalic cortical structures should be strongly considered.

Mechanical Stimuli in the Local In Vivo Environment in Bone: Computational Approaches Linking Organ-Scale Loads to Cellular Signals.

Connecting organ-scale loads to cellular signals in their local in vivo environment is a current challenge in the field of bone (re)modelling. Understanding this critical missing link would greatly improve our ability to anticipate mechanotransduction during different modes of stimuli and the resultant cellular responses. This review characterises computational approaches that could enable coupling links across the multiple scales of bone. Current approaches using strain and fluid shear stress concepts have begun to link organ-scale loads to cellular signals; however, these approaches fail to capture localised micro-structural heterogeneities. Furthermore, models that incorporate downstream communication from osteocytes to osteoclasts, bone-lining cells and osteoblasts, will help improve the understanding of (re)modelling activities. Incorporating this potentially key information in the local in vivo environment will aid in developing multiscale models of mechanotransduction that can predict or help describe resultant biological events related to bone (re)modelling. Progress towards multiscale determination of the cell mechanical environment from organ-scale loads remains elusive. Construction of organ-, tissue- and cell-scale computational models that include localised environmental variation, strain amplification and intercellular communication mechanisms will ultimately help couple the hierarchal levels of bone.

An embeddable optical strain gauge based on a buckled beam.

We report, for the first time, a low cost, compact, and novel mechanically designed extrinsic Fabry-Perot interferometer (EFPI)-based optical fiber sensor with a strain amplification mechanism for strain measurement. The fundamental design principle includes a buckled beam with a coated gold layer, mounted on two grips. A Fabry-Perot cavity is produced between the buckled beam and the endface of a single mode fiber (SMF). A ceramic ferrule is applied for supporting and orienting the SMF. The principal sensor elements are packaged and protected by two designed metal shells. The midpoint of the buckled beam will experience a deflection vertically when the beam is subjected to a horizontally/axially compressive displacement. It has been found that the vertical deflection of the beam at midpoint can be 6-17 times larger than the horizontal/axial displacement, which forms the basis of a strain amplification mechanism. The user-configurable buckling beam geometry-based strain amplification mechanism enables the strain sensor to achieve a wide range of strain measurement sensitivities. The designed EFPI was used to monitor shrinkage of a square brick of mortar. The strain was measured during the drying/curing stage. We envision that it could be a good strain sensor to be embedded in civil materials/structures under a harsh environment for a prolonged period of time.

A Force and Displacement Self-Sensing Piezoelectric MRI-Compatible Tweezer End Effector With an On-Site Calibration Procedure

This paper describes a self-sensing technique for a piezoelectrically driven magnetic resonance imaging (MRI)-compatible tweezer style end effector, suitable for robot assisted MRI guided surgery. Nested strain amplification mechanisms are used to amplify the displacement of the piezo actuators to practical levels for robotics. By using a hysteretic piezoelectric model and a two port network model for the compliant nested strain amplifiers, it is shown that force and displacement at the tweezer tip can be estimated if the input voltage and charge are measured. One piezo unit is used simultaneously as a sensor and an actuator, preserving the full actuation capability of the device. An on-site calibration procedure is proposed that calibrates the combined electromechanical model without requiring specific loading conditions on the inner piezoelectric actuators. Experimental validation shows an average of 12% error between the self-sensed and true values.

Nested Piezoelectric Cellular Actuators for a Biologically Inspired Camera Positioning Mechanism

Using successive stages, or nesting compliant amplification mechanisms, soft actuators with performance suitable for robotic applications can be constructed with piezoelectric ceramic as the active material. This paper presents a mathematical framework that describes the interactions among the various amplification mechanisms in a hierarchical nested structure. A formal treatment of nested amplification mechanisms results in two theorems that describe the stiffness properties of the whole actuator in terms of the properties of each mechanism in the hierarchy. These theorems show that the stiffness properties of the actuator can be computed by considering only the outermost few layers in the nested configuration. By virtue of this hierarchical structure, the actuator also assumes a cellular structure; it functions by summing the effects of on-off inputs coupled by a flexible connective medium. This requires a paradigm shift when selecting control strategies. A multilayer strain amplification mechanism is designed to meet the required range of travel for a biologically inspired camera positioning mechanism, and a switching control method for the actuator's 16 on-off inputs is discussed.

Piezoelectric Tweezer-Type End Effector With Force- and Displacement-Sensing Capability

This paper presents the design and development of robotic tweezers with a force- and displacement-sensing capability driven by piezoelectric stack actuators. In order to satisfy sufficient stroke and tip force for future medical operations, a rhombus strain amplification mechanism is adopted. One of the serially connected piezoelectric stack actuators nested in the end effector is used as a force sensor. The force-displacement characteristics at the outermost layer with respect to the forces of the innermost PZT actuators (i.e., forward model) is obtained from a lumped parameter model of the rhombus strain amplification mechanism and a Bernoulli-Euler beam model of the tweezer-style end effector. The end-effector tip force and displacement are measured using an inverse model of the nested multilayer structure relating these quantities to an induced voltage across the innermost PZT actuator. The prototype end effector has the size of 69 mm (length) × 14 mm (height) × 13 mm (width). The performance test shows that the prototype has 1.0-N force and 8.8-mm displacement at the tip. The sensing accuracy was also evaluated through experiments. The experimental results show that the prototype has mean error of 0.086 N for force and 0.39 mm for displacement, which are equivalent to 11% of their maximum measurable values.

Practical insight through perturbation analysis

Though industrial processes are perceived to be dauntingly complex from a mathematical modelling perspective, simple mathematical models often provide remarkable insight. One of the reasons behind this apparent contradiction is that the mathematical models often involve small and/or large non-dimensional parameters and therefore are amenable to simplification through the use of perturbation analysis. In many cases, the leading order perturbation approximation provides the bulk of the information about the structure and behaviour of the solution and is often sufficient to obtain profound insight into the phenomenon under examination. This article illustrates such utility of the perturbation analysis by using examples in which leading order perturbation approximations provide substantial insight into the mode transition phenomena in the vibrational behaviour of curved beams and helices. The methodology described in this article can be used in a wide range of applications to reveal the simplest possible structure of the mathematical model that answers the question under examination. References R. S. Anderssen. Acceptance speech on the award of the George Szekeres Medal. October, 2004. C. M. Bender, and S. A. Orszag. Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, 1978. F. R. de Hoog. Why are simple models often appropriate in industrial mathematics? In R.S. Anderssen et al., (editors), {18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation}, pages 23--36, 2009, http://www.mssanz.org.au/modsim09/Plenary/deHoog.pdf T. Tarnopolskaya, F. R. de Hoog, N. H. Fletcher, and S. Thwaites. Asymptotic analysis of the free in-plane vibrations of beams with arbitrarily varying curvature and cross-section. Journal of Sound and Vibration, 196: 659--680, 1996, doi:10.1006/jsvi.1996.0507 T. Tarnopolskaya, F. R. de Hoog, A. Tarnopolsky, and N. H. Fletcher. Vibration of beam and helices with arbitrarily large uniform curvature. Journal of Sound and Vibration, 228(2): 305--332, 1999, doi:10.1006/jsvi.1999.2413 T. Tarnopolskaya, F. R. de Hoog, and N. H. Fletcher. Low-frequency mode transition in the free in-plane vibration of curved beams. Journal of Sound and Vibration, 228(1): 69--90, 1999, doi:10.1006/jsvi.1999.2400 N. H. Fletcher, T. Tarnopolskaya, and F. R. de Hoog. Wave propagation on helices and hyperhelices: a fractal regression. Proc. R. Soc. Lond. A, 457(1): 33-43, 2001, doi:10.1098/rspa.2000.0654 N. H. Fletcher. Hyperhelices: a classical analog for strings and hidden dimensions. Am. J. Phys., 72(5): 701--703, 2004, doi:10.1119/1.1652038 K. A. Seffen and E.Toews. Hyperhelical actuators: coils and coiled-coils. AIAA Structures, Structural Dynamics and Materials Conference, 2004, California. J. Ueda, T. W. Secord, and H. H. Asada. Large effective-strain piezoelectric actuators using nested cellular architecture with exponential strain amplification mechanisms. IEEE/ASME Transactions on Mechatronics, 15(5): 770--782, 2010, doi:10.1109/TMECH.2009.2034973

Large Effective-Strain Piezoelectric Actuators Using Nested Cellular Architecture With Exponential Strain Amplification Mechanisms

Design and analysis of piezoelectric actuators having over 20% effective strain using an exponential strain amplification mechanism are presented in this paper. Piezoelectric ceramic material, such as lead zirconate titanate (PZT), has large stress and bandwidth, but its extremely small strain, i.e., only 0.1%, has been a major bottleneck for broad applications. This paper presents a new strain amplification design, called a “nested rhombus” multilayer mechanism, that increases strain exponentially through its hierarchical cellular structure. This allows for over 20% effective strain. In order to design the whole actuator structure, not only the compliance of piezoelectric material but also the compliance of the amplification structures needs to be taken into account. This paper addresses how the output force and displacement are attenuated by the compliance involved in the strain amplification mechanism through kinematic and static analysis. An insightful lumped parameter model is proposed to quantify the performance degradation and facilitate design tradeoffs. A prototype-nested PZT cellular actuator that weighs only 15 g has produced 21% effective strain (2.5 mm displacement from 12-mm actuator length and 30 mm width) and 1.7 N blocking force.

ピエゾアクチュエータを用いたMRI対応グリッパの開発(機械力学,計測,自動制御)

This paper proposes an MRI compatible robotic gripper using piezoelectric actuators with strain amplification mechanisms. The structure of the gripper is designed based on reverse action tweezers. This gripper utilizes the piezoelectric effect for sensing the force and the displacement. The physical properties of the gripper are calculated from elasticity of both actuator and gripper. The dimensions of the gripper are determined by taking the elastic properties of both the actuators and gripping mechanism into account. The performance of the assembled gripper was confirmed by CAE simulation and experiments. The sensing accuracy of the gripping force and the displacement of the tip of the developed gripper were evaluated through the experiments.

Design, Fabrication, and Performance of a Piezoelectric Uniflex Microactuator

Microactuators provide controlled motion and force for applications ranging from radio frequency switches to microfluidic valves. Large amplitude response in piezoelectric actuators requires amplification of the small strain, exhibited by the piezoelectric material, used in the construction of such actuators. This paper studies a uniflex microactuator that combines the strain amplification mechanisms of a unimorph and flexural motion to produce large displacement and blocking force. The design and fabrication of the proposed uniflex microactuator are described in detail. An analytical model is developed with three connected beams and a reflective symmetric boundary condition that predicts actuator displacement and blocking force as a function of the applied voltage. The model shows that the uniflex design requires appropriate parameter ranges, particularly the clearance between the unimorph and aluminum cap, to ensure that both the unimorph and flexural amplification effects are realized. With a weakened joint at the unimorph/cap interface, the model is found to predict the displacement and blocking force for the actuators fabricated in this work.

Human osteoblasts response to different magnitudes of mechanical stimulation in vitro

To investigate the effect of different magnitudes of tensile strain on human osteoblasts differentiation. According to the strain amplification mechanism at cellular level and a data calculated by finite element analysis, the cellular level strain of 0.8%, 1.6%, 2.4% and 3.2% was respectively applied to human osteoblasts for 48 h at a frequency of 1 Hz. Alkaline phosphatase activity and the expression of osteoblast-related genes were detected by Semi-Quantitative RT-PCR and densitometric analysis. Alkaline phosphatase activity significantly increased at 0.8% and 1.6%. The level of osteocalcin mRNA increased at 2.4% and 3.2%. Cbfa1/Runx2 gene expression only increased at 3.2%. Comparing to static control, mRNA level of type I collagen increased at every magnitude. The mRNA level decreased at 0.8% and increased at 3.2% when compared to the group with 1.6% elongation. Higher magnitudes of strain enhance expression of osteocalcin, type I collagen gene and Cbfa1/Runx2 in human osteoblasts, but lost the ability to increase ALP activity which is remained by lower magnitudes of strain. Type I collagen gene expression increases in a strain magnitude dependent manner.

1A1-C14 ピエゾアクチュエータを用いたMRI対応グリッパの開発(手術支援ロボティクス・メカトロニクス)

A MRI compatible robotic gripper that has an ability to grasp an object in MRI environment has been designed. This gripper uses piezoelectric actuators with strain amplification mechanisms that provide lightweight, highly efficient, and large strain actuators. A method for designing the gripper considering the elasticity of the actuators and the structure is presented. The structure is designed based on reverse action tweezers. Using CAE software, the performance of the assembled gripper is examined in terms of displacement and force, then the size of the structure is determined. This paper introduces a prototype design for the robotic gripper with 7mm of the tip displacement.

In-situ measurements of chondrocyte deformation under transient loading

Chondrocytes are responsible for the elaboration and maintenance of the extracellular (EC) matrix in articular cartilage, and previous studies have demonstrated that mechanical loading modulates the biosynthetic response of chondrocytes in cartilage explants. The goal of this study is to investigate the deformation behaviour of the chondrocyte and its microenvironment under transient loading, in order to address the relationship between the applied dynamic deformation and cellular strain. In-situ strain measurements were performed on cells in the middle (MZ) zone at early time points during ramp loading and at equilibrium. In this study, we characterized the behaviour of cartilage at the zonal and cellular levels under compressive loading using digital image analysis on miniature samples tested in a custom microscopy-based loading device. The experimental results indicate that significant strain amplification occurs in the microenvironment of the cell, with the minimum (compressive) principal strain found to be nearly 7X higher in the intracellular region (IC), and ~5X higher in the pericellular (PC) matrix than in the EC matrix at peak ramp. A similar strain amplification mechanism was observed in the maximum (tensile) principal strain, and this behaviour persisted even after equilibrium was reached. The experimental results of this study were interpreted in the context of a finite element model of chondrocyte deformation, which modelled the cell as a homogeneous gel, possessing either a spherical or ellipsoidal geometry, surrounded by a semi permeable membrane, and accounted for the presence of a PC matrix. The results of the FEA demonstrate significant strain amplification mechanism in the IC region, greater than had previously been suggested in earlier computational studies of cell-EC matrix interactions. Based on the FEA, this outcome is understood to result from the large disparity between EC matrix and intracellular properties. The results of this study suggest that mechanotransduction of chondrocytes may be significantly mediated by this strain amplification mechanism during loading.

Processing of Miniature Hollow Sphere Transducers

During the past two decades, we have designed and fabricated a large family of composite ferroelectrics for use as sensors, actuators, and transducers. These devices employ stress and strain amplification mechanisms and provide superior acoustic matching to seawater and the human body. Recently we have concentrated on flat-panel arrays thinner than 3 mm constructed from miniature flextensional transducers (Cymbals) or small hollow sphere transducers (BBs) embedded in polymers. This paper focuses on fabrication of BB hollow spheres. Millimeter size hollow spheres are produced using a coaxial nozzle slurry process or sacrificial core coating from 1-10 mm diameter with 10-200 w m wall-thickness. The principal resonance modes are the breathing mode (ranging from 100 kHz at 15 mm diameter to 1.5 MHz at 1 mm diameter) and the wall thickness vibration (10-100 MHz). We also discuss a method for providing the BBs with internal electrodes, a process which allows for even smaller diameters in the sub-millimeter range.

Processing of Miniature Hollow Sphere Transducers

During the past two decades, we have designed and fabricated a large family of composite ferroelectrics for use as sensors, actuators, and transducers. These devices employ stress and strain amplification mechanisms and provide superior acoustic matching to seawater and the human body. Recently we have concentrated on flat-panel arrays thinner than 3 mm constructed from miniature flextensional transducers (Cymbals) or small hollow sphere transducers (BBs) embedded in polymers. This paper focuses on fabrication of BB hollow spheres. Millimeter size hollow spheres are produced using a coaxial nozzle slurry process or sacrificial core coating from 1-10 mm diameter with 10-200 w m wall-thickness. The principal resonance modes are the breathing mode (ranging from 100 kHz at 15 mm diameter to 1.5 MHz at 1 mm diameter) and the wall thickness vibration (10-100 MHz). We also discuss a method for providing the BBs with internal electrodes, a process which allows for even smaller diameters in the sub-millimeter range.