Micromechanical Strain Research Articles

The Micromechanical Environment of the Impinged Achilles Tendon.

Although tendon predominantly experiences longitudinal tensile forces, transverse forces due to impingement from bone are implicated in both physiological and pathophysiological processes. However, prior studies have not characterized the micromechanical strain environment in the context of tendon impingement. To address this knowledge gap, mouse hindlimb explants are imaged on a multiphoton microscope, and image stacks of the same population of tendon cells are obtained in the Achilles tendon before and after dorsiflexion-induced impingement by the heel bone. Based on the acquired images, multiaxial strains are measured at the extracellular matrix (ECM), pericellular matrix (PCM), and cell scales. Impingement generated substantial transverse compression at the matrix-scale, which led to longitudinal stretching of cells, increased cell aspect ratio, and enormous volumetric compression of the PCM. These experimental results are corroborated by a finite elementmodel, which further demonstrated that impingement produces high cell surface stresses and strains that greatly exceed those brought about by longitudinal tension. Moreover, in both experiments and simulations, impingement-generated microscale stresses and strains are highly dependent on initial cell-cell gap spacing. Identifying factors that influence the microscale strain environment generated by impingement could contribute to a more mechanistic understanding of impingement-induced tendinopathies.

A phase-field fracture model in thermo-poro-elastic media with micromechanical strain energy degradation

This work extends the hydro-mechanical phase-field fracture model to non-isothermal conditions with micromechanics based poroelasticity, which degrades Biot’s coefficient not only with the phase-field variable (damage) but also with the energy decomposition scheme. Furthermore, we propose a new approach to update porosity solely determined by the strain change rather than damage evolution as in the existing models. As such, these poroelastic behaviors of Biot’s coefficient and the porosity dictate Biot’s modulus and the thermal expansion coefficient. For numerical implementation, we employ an isotropic diffusion method to stabilize the advection-dominated heat flux and adapt the fixed stress split method to account for the thermal stress. We verify our model against a series of analytical solutions such as Terzaghi’s consolidation, thermal consolidation, and the plane strain hydraulic fracture propagation, known as the KGD fracture. Finally, numerical experiments demonstrate the effectiveness of the stabilization method and intricate thermo-hydro-mechanical interactions during hydraulic fracturing with and without a pre-existing weak interface.

Machine learning-enabled identification of micromechanical stress and strain hotspots predicted via dislocation density-based crystal plasticity simulations

The present work uses a full-field crystal plasticity model with a first principles-informed dislocation density (DD) hardening law to identify the key microstructural features correlated with micromechanical fields localization, or hotspots, in polycrystalline Ni. An ensemble learning approach to machine learning interpreted with Shapley additive explanation was implemented to predict nonlinear correlations between microstructural features and micromechanical stress and strain hotspots. Results reveal that regions within the microstructure in the vicinity of grain boundaries, higher Schmid factors, low slip transmissions and high intergranular misorientations, are more prone to being micromechanical hotspots. Additionally, under combined loading and large plastic deformations, slip transmissions take precedence over intergranular misorientations in formation of both strain and stress hotspots. The present work demonstrates a successful integration of physics-based crystal plasticity with DD-based hardening into machine learning models to reveal the microscale features responsible for the formation of local stress and strain hotspots within the grains and near the grain boundaries, as function of applied deformation states, grain morphology/size distribution, and microstructural texture, providing insights into micromechanical damage initiation zones in polycrystalline metals.

Deformation mechanism in nanolaminate FeCrAl alloys by in situ micromechanical strain rate jump tests at elevated temperatures

FeCrAl alloys have attracted extensive attention as one of the potential cladding materials for the commercial light water reactors. Although the creep behaviors of coarse-grain FeCrAl alloys have been investigated at elevated temperatures, little is known on the deformation mechanism of fine-grain FeCrAl alloys. Here, we performed surface mechanical grinding treatment to fabricate nanolaminated ferritic FeCrAl alloys. In situ micropillar compression tests were applied to determine the underlying deformation mechanism of nanolaminated FeCrAl alloys at elevated temperatures. The strain rate sensitivity and activation energy for the dominant deformation mechanism were estimated considering the presence of a threshold stress.

Predicting the micromechanics of embedded nerve fibers using a novel three-layered model of mouse distal colon and rectum

Mechanotransduction plays a central role in evoking pain from the distal colon and rectum (colorectum) where embedded sensory nerve endings convert micromechanical stresses and strains into neural action potentials. The colorectum displays strong through-thickness and longitudinal heterogeneity with collagen concentrated in the submucosa thus indicating the significant load-bearing role of this layer. The density of sensory nerve endings is also significantly the greatest in the submucosa, suggesting a nociceptive function. Thus biomechanical heterogeneity in the colorectum influences the micromechanical stresses and strains surrounding afferent endings embedded within different layers of the colorectum which is critical for the mechanotransduction of various mechanical stimuli. In this study we aimed to: (1) calibrate and validate a three-layered computational model of the colorectum; (2) predict intra-tissue distributions of stresses and strains during mechanical stimulation of the colorectum ex vivo (i.e. circumferential stretching, punctuate probing, and mucosal shearing); and (3) establish a methodology to calculate local micromechanical stresses and strains surrounding afferent nerve endings embedded in the colorectum. We established three-layered FE models that include mucosa, submucosa, and muscular layers, and incorporated residual stretches, to calculate intra-tissue stresses and strains when the colorectum undergoes the mechanical stimuli used to characterize afferent neural encoding ex vivo. Finally, we established a methodology for detailed calculations of the local micromechanical stresses and strains surrounding afferent endings embedded in the colorectum and demonstrated this with a representative example. Our novel methodologies will bridge the existing neurophysiological and biomechanical evidence from experiments to advance our mechanistic understanding of colorectal mechanotransduction.

Glancing-incidence focussed ion beam milling: A coherent X-ray diffraction study of 3D nano-scale lattice strains and crystal defects

This study presents a detailed examination of the lattice distortions introduced by glancing incidence Focussed Ion Beam (FIB) milling. Using non-destructive multi-reflection Bragg coherent X-ray diffraction we probe damage formation in an initially pristine gold micro-crystal following several stages of FIB milling. These experiments allow access to the full lattice strain tensor in the micro-crystal with ∼25 nm 3D spatial resolution, enabling a nano-scale analysis of residual lattice strains and defects formed. Our results show that 30 keV glancing incidence milling produces fewer large defects than normal incidence milling at the same energy. However the resulting residual lattice strains have similar magnitude and extend up to ∼50 nm into the sample. At the edges of the milled surface, where the ion-beam tails impact the sample at near-normal incidence, large dislocation loops with a range of Burgers vectors are formed. Further glancing incidence FIB polishing with 5 keV ion energy removes these dislocation loops and reduces the lattice strains caused by higher energy FIB milling. However, even at the lower ion energy, damage-induced lattice strains are present within a ∼20 nm thick surface layer. These results highlight the need for careful consideration and management of FIB damage. They also show that low-energy FIB-milling is an effective tool for removing FIB-milling induced lattice strains. This is important for the preparation of micro-mechanical test specimens and strain microscopy samples.

Calculation of strain amplification matrix for strain invariant failure theory based on representative volume element models with periodical boundary condition

Strain invariant failure theory (SIFT) is a micro-mechanics-based failure theory for multi-scale failure analysis of composite materials originally proposed by Gosse and Christensen. In this paper, the approach for obtaining strain amplification matrix which is a key step for the execution of SIFT is improved by adopting representative volume element (RVE) finite element models considering periodical boundary condition, based on which more actual deformation mode is reflected. The deformation modes and strain data at the characteristic points of the centroid cell of multi-cell RVE model are analyzed and taken as a reference. It can be concluded that more reasonable deformation mode and relationship between the micro-mechanical and macro-mechanical strain states are obtained by employing the new model. Finally, numerical examples are provided to illustrate the determination of strain amplification factors within the RVEs considering periodical boundary condition at the characteristic points.

Bovine and degenerated human annulus fibrosus: a microstructural and micromechanical comparison

The complex structure of the annulus fibrosus is strongly related to its mechanical properties. Recent work showed that it is possible to observe the relative movement of fibre bundles in loaded cow tail annulus; the aim of this work was to describe and quantify annulus fibrosus micromechanics in degenerated human disc, and compare it with cow tail annulus, an animal model often used in the literature. Second harmonic generation was used to image the collagen matrix in twenty strips of annulus fibrosus harvested from intervertebral disc of seven patients undergoing surgery. Samples were loaded to 6% tensile strain in 1% steps. Elastic modulus was calculated from loading curves, and micromechanical strains were calculated from the images using custom software. The same protocol was applied to twenty strips of annulus harvested from cow tail discs. Significant morphological differences were found between human and cow tail samples, the most striking being the lack of collagen fibre crimp in the former. Fibres were also observed bending and running from one lamella to the other, forming a strong flexible interface. Interdigitation of fibre bundles was also present at this interface. Quantitative results show complex patterns of inter-bundle and inter-lamellar behaviour, with inter-bundle sliding being the main strain mechanism. Elastic modulus was similar between species, and it was not affected by the degree of degeneration. This work gives an insight into the complex structure and mechanical function of the annulus fibrosus, which should be accounted for in disc numerical modelling.

Top-down method to introduce ultra-high elastic strain

Abstract

Dynamic contact strain measurement by time‐resolved stroboscopic energy dispersive synchrotron X‐ray diffraction

AbstractRecent developments of synchrotron X‐ray sources and dedicated high‐energy beamlines are now enabling strain measurements from large volumes of industrially relevant metallic materials. Such capability is allowing the validation of novel and alternative nondestructive experimental methods of strain measurement or computational models of complex deformation processes. This study describes the first dynamic contact strain measurement of a ball bearing using stroboscopic energy dispersive X‐ray diffraction. The experiment probed the dynamic contact strain in the outer raceway of a test bearing. The inner raceway of the bearing was attached to a shaft rotating at 150 revolutions per minute, and the outer raceway, where the measurements were made, was fixed in a stationary bearing housing. A triggering system was used to synchronise the data acquisition of the energy dispersive X‐ray diffraction detector with the bearing rotation. Specifically, diffraction data were acquired, stroboscopically, from the material volume within the raceway, in a known location, when the ball was positioned directly below it. A total of 20 s of accumulated diffraction signal was recorded, acquiring 2 ms of data per revolution, providing diffraction patterns of sufficient quality for the dynamic contact strain to be measured. Macromechanical stress field was calculated from the micromechanical strains measured from five lattice planes. This allowed a comparison of the experimentally measured stress field and that of finite element simulations. Good agreement was observed between the finite element results and experimental measurements indicating the applicability of this novel dynamic strain measurement technique for tribological systems.

Magnetically actuated cell-laden microscale hydrogels for probing strain-induced cell responses in three dimensions

Living cells respond to their mechanical microenvironments during development, healing, tissue remodeling and homeostasis attainment. However, this mechanosensitivity has not yet been established definitively for cells in three-dimensional (3D) culture environments, in part because of challenges associated with providing uniform and consistent 3D environments that can deliver a large range of physiological and pathophysiological strains to cells. Here, we report microscale magnetically actuated, cell-laden hydrogels (μMACs) for investigating the strain-induced cell response in 3D cultures. μMACs provide high-throughput arrays of defined 3D cellular microenvironments that undergo reversible, relatively homogeneous deformation following non-contact actuation under external magnetic fields. We present a technique that not only enables the application of these high strains (60%) to cells but also enables simplified microscopy of these specimens under tension. We apply the technique to reveal cellular strain-threshold and saturation behaviors that are substantially different from their 2D analogs, including spreading, proliferation, and differentiation. μMACs offer insights for mechanotransduction and may also provide a view of how cells respond to the extracellular matrix in a 3D manner. Micromechanical strain is shown to play a key role in the growth and development of tissue and muscle cells in three-dimensional environments. Feng Xu and co-workers have developed an innovative medium for visualizing and influencing cell growth with biocompatible, water-based hydrogels. Using photolithography, the team fabricated a micrometre-thick, multilayer device in which cell-laden hydrogels sat above a separate hydrogel film infused with magnetic iron nanoparticles. Applying a magnetic field caused the lower hydrogel film to deform homogenously, altering the strain of the three-dimensional cell-growth region by up to 60 per cent. This method has the advantage that it does not use damaging mechanical contacts. The transparent hydrogels enable real-time microscopy imaging of fibroblast and myoblast viability and proliferation under realistic strain conditions — valuable data for artificial muscle applications and pathophysiological studies of injury healing. We report microscale magnetically actuated, cell-laden hydrogels (μMACs) for investigating the strain-induced cell response in three-dimensional (3D) microenvironments. These μMACs provide high-throughput arrays of defined 3D cellular microenvironments that undergo reversible, relatively homogeneous deformation following non-contact actuation under external magnetic fields. Such technique not only enables the application of high strains (up to 60%) to cells but also enables simplified microscopic visualization of these specimens under tension. The μMACs offer insights for mechanotransduction and may also provide a view of how cells respond to extracellular matrix in 3D.

Temperature Dependence of the Anisotropy and Creep in a Single-Crystal Nickel Superalloy

The thermomechanical response of the second-generation single-crystal nickel superalloy (SC180) was obtained for wide range of temperatures (25–1000°C). Uniaxial tension and stress relaxation experiments were performed to study the influence of [100] and [110] crystallographic orientation on stress anisotropy and creep responses. Experiments were conducted using micromechanical testing systems and strains were measured using two-dimensional digital image correlation technique. Results were reported on coefficient of thermal expansion, Young’s modulus (E), yield strength, work hardening (n), and activation energies (Q). The stress relaxation experiments were used to calculate activation energy in [100] and [110] crystallographic directions and found to be 300 kJ/mol and 350 kJ/mol, respectively.

Grain-level statistical plasticity analysis on strain cycle fatigue of a FCC metal

The micromechanical strain cycle fatigue-life is systematically investigated by the micro-level numerical simulation, compared with symmetrical strain cycle experiments of copper, focusing on the characteristics of polycrystalline aggregation and the mechanism of microscale plastic deformation. A methodology to predict the low-cycle fatigue life by micro-level simulation along with statistical analysis is proposed through the following steps: (1) A crystal plasticity model is developed based on the nonlinear kinematic hardening mechanism of crystal slipping system. This model is applied to the calculations of crystal grain interior stresses and plastic strains. (2) A statistical representative volume element (SRVE) is constructed for a pure copper as a material model which features a polycrystalline Voronoi aggregation consisting of a number of crystal grains. This SRVE can be used for statistical analysis of the material inhomogeneous stresses and strains during cycle loading. (3) The simulations are performed to model the experimental cycle evolution of strain fatigue by using the SRVE under the symmetrical tensile–compressive loading. (4) Statistical and micromechanical analyses are carried out for the inhomogeneous interior stresses and strains of the SRVE of the polycrystalline copper in the low cycle regime. The resulting analysis can render the microscale interpretation and numerical simulation for the low-cycle fatigue evolution accordingly.

Tuning the Electro-optical Properties of Germanium Nanowires by Tensile Strain

In this Letter we present the electrical and electro-optical characterization of single crystalline germanium nanowires (NWs) under tensile strain conditions. The measurements were performed on vapor–liquid–solid (VLS) grown germanium (Ge) NWs, monolithically integrated into a micromechanical 3-point strain module. Uniaxial stress is applied along the ⟨111⟩ growth direction of individual, 100 nm thick Ge NWs while at the same time performing electrical and optical characterization at room temperature. Compared to bulk germanium, an anomalously high and negative-signed piezoresistive coefficient has been found. Spectrally resolved photocurrent characterization on strained NWs gives experimental evidence on the strain-induced modifications of the band structure. Particularly we are revealing a rapid decrease in resistivity and a red-shift in photocurrent spectra under high strain conditions. For a tensile strain of 1.8%, resistivity decreased by a factor of 30, and the photocurrent spectra shifted by 88 meV. Individual stressed NWs are recognized as an ideal platform for the exploration of strain-related electronic and optical effects and may contribute significantly to the realization of novel optoelectronic devices, strain-enhanced field-effect transistors (FETs), or highly sensitive strain gauges.

Microelectromechanical strain and pressure sensors based on electric field aligned carbon cone and carbon black particles in a silicone elastomer matrix

Methods for developing microelectromechanical strain and pressure sensors based on aligned carbon particle strings within dielectric elastomer matrices are presented. Two different types of carbon particles were used: a mixture of carbon cone and carbon disk particles and spherical carbon black particles. The particles were assembled and aligned into strings by an alternating electric field with a strength of 4 kV/cm and a frequency of 1 kHz, utilizing the dielectrophoretic effect. The particle fraction was about 0.1 vol. %, which is an order of magnitude lower than their percolation threshold (∼2 vol. %). The aligned strings were produced in a couple of minutes. The matrices were subsequently cured thus stabilizing the strings. Micromechanical strain sensors with a capacitive readout were produced by aligning the particles into a single string-like formation in the in-plane direction, the string dimensions being 3 μm width and 30 μm length. The pressure sensors with piezoresistive readout were made by aligning the particles into multiple unidirectional strings in the out-of-plane direction, the thickness of the sensors being of the order of 100 μm and the lateral area of 1.5 cm2. The strain and the pressure sensors show reversible piezocapacitive and piezoresistance effects when stretched and compressed, respectively.

3-Dimensional Cell Culture Scaffold For Everyone: Drug Screening, Tissue Engineering and Cancer Biology

Although cells live in three-dimensional environments which consist of neighboring cells and cells’ own extra-cellular matrices (ECMs), so far Cell Biology restricted itself to only two dimensions of Petri dishes. However, micromechanical strains on cell surfaces significantly differ on Petri dishes from that in ECMs. It is now possible to culture most cells in three-dimensional environments using a chemically defined synthetic matrix peptide, PuraMatrix™, and this will change the face of basic research and in study areas where animal models have been traditionally used. An example of hepatocyte culture is described.

Individual strings of conducting carbon cones and discs in a polymer matrix: Electric field‐induced alignment and their use as a strain sensor

AbstractWe demonstrate micromechanical strain sensors with integrated readout based on carbon nanocones and discs (CNCs) which are aligned into a string‐like formation using an alternating electric field and studied by AC impedance spectroscopy and electromechanical methods. The CNC particles are first dispersed into a polymer matrix with a particle fraction of 0.1 vol %. This value is well below the percolation threshold (∼ 2 vol %), which suppresses particle aggregation and facilitates transparency allowing the use of an UV‐curable polymer. Alignment was carried out with a 1 kHz, 4 kV/cm electric field and is a consequence of dielectrophoretic effect. It develops in minutes and makes the initially insulating, nonaligned material conductive. This is followed by UV curing of the polymer matrix, which renders a solid state device. The stretching of the aligned strings in the cured polymer leads to a reversible piezoresistive effect, and a gauge factor of about 50 is observed. This is in a sharp contrast to CNC films with particle fraction above percolation threshold (13 vol %), which are conductive but not sensitive to stretching. The strings are Ohmic in nature and moreover show higher DC conductivity (22–500 S/m) compared to identically prepared carbon black strings (1–22 S/m). © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011

A strain sensor based on an aligned carbon particle string in a UV-cured polymer matrix

We demonstrate micro-mechanical strain sensors by aligning carbon black particles into single wirelike strings in a polymer matrix using an alternating electric field (dielectrophoresis) when the particle fraction is 0.1 vol. %. The strings are stabilized by UV-curing the polymer matrix and characterized electrically and electromechanically. Particle alignment makes the material conductive, and the stretching of such strings in polymer matrices gives a reversible change in resistivity. A gauge factor of about 150 is demonstrated. Nonaligned films containing 12 vol. % of carbon particles in the same polymer are conductive but not sensitive to similar stretching.

Micromechanical analysis of the behavior of stiff clay

Cementations formed in geological timescale are observed in various stiff clays. A micromechanical stress strain model is developed for modeling the effect of cementation on the deformation behavior of stiff clay. The proposed approach considers explicitly cementations at intercluster contacts, which is different from conventional model. The concept of inter-cluster bonding is introduced to account for an additional cohesion in shear sliding and a higher yield stress in normal compression. A damage law for inter-cluster bonding is proposed at cluster contacts for the debonding process during mechanical loading. The model is used to simulate numerous stress-path tests on Vallericca stiff clay. The applicability of the present model is evaluated through comparisons between the predicted and the measured results. In order to explain the stress-induced anisotropy arising from externally applied load, the evolution of local stresses and local strains at inter-cluster planes are discussed.

Application of High Magnification Digital Image Correlation Technique to Micromechanical Strain Analysis

Abstract: This paper describes an experimental apparatus and its application for the full‐field measurement of heterogeneous strains at high magnifications. The apparatus consists of an image acquisition and analysis system, an optical microscope and a stable tensile stage. Magnified images of the specimen surface are acquired and analysed using the digital image correlation (DIC) method. The response of the heterogeneous microstructure of a nodular cast iron is investigated during a tensile test. Strains obtained by using the DIC method and averaged over the observation window correlate with strain measurements simultaneously obtained by using an extensometer. The strain maps of DIC reveal the heterogeneous development of plasticity in the nodular cast iron microstructure. The apparatus has the potential to investigate material behaviour at the microscopic scale.