Micromechanical Strain Research Articles

Concentration Independent Modulation of Local Micromechanics in a Fibrin Gel

Methods for tuning extracellular matrix (ECM) mechanics in 3D cell culture that rely on increasing the concentration of either protein or cross-linking molecules fail to control important parameters such as pore size, ligand density, and molecular diffusivity. Alternatively, ECM stiffness can be modulated independently from protein concentration by mechanically loading the ECM. We have developed a novel device for generating stiffness gradients in naturally derived ECMs, where stiffness is tuned by inducing strain, while local mechanical properties are directly determined by laser tweezers based active microrheology (AMR). Hydrogel substrates polymerized within 35 mm diameter Petri dishes are strained non-uniformly by the precise rotation of an embedded cylindrical post, and exhibit a position-dependent stiffness with little to no modulation of local mesh geometry. Here we present the device in the context of fibrin hydrogels. First AMR is used to directly measure local micromechanics in unstrained hydrogels of increasing fibrin concentration. Changes in stiffness are then mapped within our device, where fibrin concentration is held constant. Fluorescence confocal imaging and orbital particle tracking are used to quantify structural changes in fibrin on the micro and nano levels respectively. The micromechanical strain stiffening measured by microrheology is not accompanied by ECM microstructural changes under our applied loads, as measured by confocal microscopy. However, super-resolution orbital tracking reveals nanostructural straightening, lengthening, and reduced movement of fibrin fibers. Furthermore, we show that aortic smooth muscle cells cultured within our device are morphologically sensitive to the induced mechanical gradient. Our results demonstrate a powerful cell culture tool that can be used in the study of mechanical effects on cellular physiology in naturally derived 3D ECM tissues.

Semi-confined compression of microfabricated polymerized biomaterial constructs

Mechanical forces are critical parameters in engineering functional tissue because of their established influence on cellular behaviour. However, identifying ideal combinations of mechanical, biomaterial and chemical stimuli to obtain a desired cellular response requires high-throughput screening technologies, which may be realized through microfabricated systems. This paper reports on the development and characterization of a MEMS device for semi-confined biomaterial compression. An array of these devices would enable studies involving mechanical deformation of three-dimensional biomaterials, an important parameter in creating physiologically relevant microenvironments in vitro. The described device has the ability to simultaneously apply a range of compressive mechanical stimuli to multiple polymerized hydrogel microconstructs. Local micromechanical strains generated within the semi-confined hydrogel cylinders are characterized and compared with those produced in current micro- and macroscale technologies. In contrast to previous work generating unconfined compression in microfabricated devices, the semi-confined compression model used in this work generates uniform regions of strain within the central portion of each hydrogel, demonstrated here to range from 20% to 45% across the array. The uniform strains achieved simplify experimental analysis and improve the utility of the compression platform. Furthermore, the system is compatible with a wide variety of polymerizable biomaterials, enhancing device versatility and usability in tissue engineering and fundamental cell biology studies.

Experimental and finite element analysis of the mouse caudal vertebrae loading model: prediction of cortical and trabecular bone adaptation

In this study, we attempt to predict cortical and trabecular bone adaptation in the mouse caudal vertebrae loading model using knowledge of bone's local mechanical environment at the onset of loading. In a previous study, we demonstrated appreciable 25.9 and 11% increases in both trabecular and cortical bone volume density, respectively, when subjecting the fifth caudal vertebrae (C5) of C57BL/6 (B6) mice to an acute loading regime (amplitude of 8N, 3000 cycles, 10 Hz, 3 times a week for 4 weeks). We have also established a validated finite element (FE) model of the C5 vertebra using micro-computed tomography (micro-CT), which characterizes, in 3D, the micro-mechanical strains present in both cortical and trabecular compartments due to the applied loads. To investigate the relationship between load-induced bone adaptation and mechanical strains in-vivo and in-silico data sets were compared. Using data from the previous cross-sectional study, we divided cortical and trabecular compartments into 15 subregions and determined, for each region, a bone formation parameter ΔBV/BS (a cross-sectional measure of the bone volume added to cortical and trabecular surfaces following the described loading regime). Linear regression was then used to correlate mean regional values of ΔBV/BS with mean values of mechanical strains derived from the FE models which were similarly regionalized. The mechanical parameters investigated were strain energy density (SED), the orthogonal strains (e (x), e (y), e (z)) and the three shear strains (e (xy), e (yz), e (zx)). For cortical regions, regression analysis showed SED to correlate extremely well with ΔBV/BS (R (2) = 0.82) and e (z) (R (2) = 0.89). Furthermore, SED was found to predict expansion of the cortical shell correlating significantly with the regional percentage increases in cortical tissue volume (R (2) = 0.92), cortical marrow volume (R (2) = 0.91) and cortical thickness (R (2) = 0.56). For trabecular regions, FE parameters were found not to correlate with load-induced trabecular bone morphology. These results indicate that load-induced cortical morphology can be predicted from population data, whereas the prediction of trabecular morphology requires subject-specific micro- architecture.

Analysis of three-dimensional micro-mechanical strain formulations for granular materials: Evaluation of accuracy

An important objective of recent research on micro-mechanics of granular materials is to develop macroscopic constitutive relations in terms of micro-mechanical quantities at inter-particle contacts. Although the micro-mechanical formulation of the stress tensor is well established, the corresponding formulation for the strain tensor has proven to be much more evasive, still being the subject of much discussion. In this paper, we study various micro-mechanical strain formulations for three-dimensional granular assemblies, following the work of Bagi in two dimensions ( Bagi, 2006). All of these formulations are either based on an equivalent continuum approach, or follow the best-fit approach. Their accuracy is evaluated by comparing their results, using data from Discrete Element Method simulations on periodic assemblies, to the macroscopic deformation. It is found that Bagi’s formulation ( Bagi, 1996), which is based on the Delaunay tessellation of space, is the most accurate. Furthermore, the best-fit formulation based on particle displacements only did unexpectedly well, in contrast to previously reported results for two-dimensional assemblies.

Enhanced direct bandgap emission in germanium by micromechanical strain engineering

We propose a new class of optoelectronic devices in which the optical properties of the active material is enhanced by strain generated from micromechanical structures. As a concrete example, we modeled the emission efficiency of strained germanium supported by a cantilever-like platform. Our simulations indicate that net optical gain is obtainable even in indirect germanium under a substrate biaxial tensile strain of about 1.75% with an electron-hole injection concentration of 9 x 10(18) cm(-3) while direct bandgap germanium becomes available at a strain of 2%. A large wavelength tuning span of 300 nm in the mid-IR range also opens up the possibility of a tunable on-chip germanium biomedical light source.

A novel in vivo mouse model for mechanically stimulated bone adaptation – a combined experimental and computational validation study

To facilitate the investigation of bone formation, in vivo, in response to mechanical loading a caudal vertebra axial compression device (CVAD) has been developed to deliver precise mechanical loads to the fifth caudal vertebra (C5) of the C57BL/6 female mouse. A combined experimental and computational approach was used to quantify the micro-mechanical strain induced in trabecular and cortical components following static and dynamic loading using the CVAD. Cortical bone strains were recorded using micro-strain gages. Finite element (FE) models based on micro-computed tomography were constructed for all C5 vertebrae. Both theoretical and experimental cortical strains correlated extremely well (R 2>0.96) for a Young's modulus of 14.8 GPa, thus validating the FE model. In this study, we have successfully applied mechanical loads to the C5 murine vertebrae, demonstrating the potential of this model to be used for in vivo loading studies aimed at stimulating both trabecular and cortical bone adaptation.

Displacement encoding for the measurement of cartilage deformation

Articular cartilage is a load bearing and lubricating tissue in animal joints. Heterogeneous deformations arise in the structured and zonal tissue under the application of mechanical load. The character of these deformations is altered by degenerative joint disease. Here, we document an MRI-based technique for determining deformations throughout the volume of the tissue based on displacement encoding with stimulated echoes (DENSE) and a fast spin echo (FSE) readout. A DENSE-FSE technique was designed to image cartilage at 9.4 Tesla in a deformed state during the application of cyclic mechanical loading. Artifact elimination arising from stimulated echoes and FSE was accomplished by radio frequency pulse phase cycling. The error of the technique was random and was quantified in terms of precision as better than 0.17% strain. Heterogeneous deformation field patterns in axial, transverse, and shear directions were quantified in a single tissue explant loaded in simple uniaxial compression. The technique is appropriate for documenting tissue deformations during applied physiologically relevant stress levels and loading rates. It may also be applied to characterize the micromechanical strain environment in normal, diseased, or regenerated cartilage in response to applied mechanical loading.

In vitro bone regeneration and micro-mechanical strain in mechanoactive scaffolds

In vitro bone regeneration and micro-mechanical strain in mechanoactive scaffolds

The effects of low-intensity ultrasound on growing bone after sciatic neurectomy

The purpose of this study was to investigate the therapeutic effects of low-intensity ultrasound (US) on the sciatic-neurectomy-induced bone mass decrement in growing rats. A total of 20 male Sprague-Dawley rats (166.7 ± 11.3 g) underwent right leg sciatic neurectomy. They were randomly assigned into two groups, US treatment group (UST) and control group (CON). The rats receiving US treatment were treated with a 125 mW/cm 2 continuous low-intensity US stimulation for 15 min/day on the lateral site of the right leg. The control rats did not receive any US treatment. All the animals were euthanized after 4-week US treatment. Both the original data and bilateral difference ratio of femur or tibia weight, histomorphometry data and bone densitometry data showed that the sciatic neurectomy obviously reduced bone mass in the operated limbs of both groups. However, the continuous low-intensity US treatment did not ameliorate the neurectomy-induced loss of bone mass. Thus, the low-intensity US generated micromechanical strains might not induce enough bone formation activity to reverse the bone loss in this model of intact bones. (E-mail: winli@ntu.edu.tw)

Effects of thermal residual stresses on effective elastoplastic behavior of metal matrix composites

During the fabrication processes of particle-reinforced metal-matrix composites, thermal residual stresses are normally developed due to the difference of the coefficients of thermal expansion between the matrix and the reinforcement. The effect of thermal residual stresses is analytically investigated on the elastoplastic behavior of the composites. Micromechanical stress and strain fields are calculated due to the combination of applied external loads and prescribed thermal mismatch eigenstrains. Ensemble-volume averaging procedures are then employed to derive the effective yield function of the composites. It is shown that the residual stresses result in a combined kinematic hardening and isotropic hardening effect. Comparisons between the analytical predictions and experimental data are performed to illustrate the capability of the proposed model.

Micromechanical analysis of the finite elastic–viscoplastic response of multiphase composites

Nonlinear thermoelastic–viscoplastic constitutive equations for large deformations with isotropic and directional hardening, are incorporated into a micromechanical finite strain analysis. As a result of this analysis, which is based on the homogenization technique for periodic microstructures, a global thermoinelastic constitutive law is established that governs the overall response of multiphase materials under finite deformations. This constitutive law is expressed in terms of the instantaneous effective mechanical and thermal stress tangent tensors together with the instantaneous global inelastic stress tensor that represents the viscoplastic effects. Results for a thermoinelastic matrix reinforced by a hyperelastic compressible material are given that illustrate the response of fibrous and particulate composites to various types of loading.

Suture growth modulated by the oscillatory component of micromechanical strain.

Sutures are fibrous connective tissue articulations between intramembranous craniofacial bones. Sutures are composed of fibroblastic cells with their matrices in the center and osteogenic cells in the periphery producing a matrix that is mineralized during skeletal growth. Whether oscillatory forces stimulate sutural growth is unknown. In the present work, we applied static and cyclic forces with the same peak magnitude of 5N to the maxilla in growing rabbits and quantified (1) acute in vivo sutural bone strain responses and (2) chronic growth responses in the premaxillomaxillary suture (PMS) and nasofrontal suture (NFS). Bone strain recordings showed that the waveforms of static force and 1-Hz cyclic force were expressed as corresponding static and cyclic sutural strain patterns in both the PMS and NFS, with the mean peak PMS strain (-1451 +/- 137 microepsilon for the cyclic and -1572 +/- 138 microepsilon for the static) approximately 10-fold higher than the mean peak NFS strain (124 +/- 9 microepsilon for the cyclic and 134 +/- 9 microepsilon for the static). Strain polarity was the opposite: compressive for the PMS but tensile for the NFS. However, on application of repetitive 5N cyclic and static forces in vivo for 10 minutes/day over 12 days, cyclic loading induced significantly greater sutural widths for the compressed PMS (95.1 +/- 8.3 microm) than sham control (69.8 +/- 8.2 microm) and static loading (58.9 +/- 2.8 microm; p < 0.01). Interestingly, the same trend was true for the NFS under tensile strain: significantly greater sutural width for cyclic loading (267.4 +/- 64.2 microm) than sham control (196.0 +/- 10.1 microm) and static loading (169.9 +/- 11.4 microm). Cell counting in 110 x 110 microm grids laid over sutures disclosed significantly more sutural cells on repetitive cyclic loading than sham control and static loading (p < 0.05) for both the PMS and NFS. Fluorescent labeling of newly formed sutural bone demonstrated more osteogenesis on cyclic loading in comparison with sham control and static loading. Thus, the oscillatory component of cyclic force or more precisely the resulting cyclic strain experienced in sutures is a potent stimulus for sutural growth. The increased sutural growth by cyclic mechanical strain in the tensed NFS and compressed PMS suggests that both microscale tension and compression induce anabolic sutural growth response.

粒状体のひずみについて

This paper intends to propose a new micro-mechanical definition of strain tensor for granular materials, using the Dirichlet (or modified Voronoi) tessellation defined for granular assemblies. Although another definition of strain tensor has been proposed up to the present, it is shown that the new definition has a lot of advantageous points, such as the good correspondence to the compatibility condition. Regarding the most general case, the micro-mechanical definition is also given for couple stress and rotational strain. For the inner work in granular materials, it is shown that the proposed strain satisfies the Hill's condition in a modified and radical form. To clarify the necessity of the micro-mechanical strain, three kinds of simple shear deformation, which are same macroscopically but different micro-mechanically, are analyzed using the proposed strain definition.

Experimental evaluation of MEMS strain sensors embedded in composites

Micromechanical in-plane strain sensors were fabricated and embedded in fiber-reinforced laminated composite plates. Three different strain sensor designs were evaluated: a piezoresistive filament fabricated directly on the wafer; a rectangular cantilever beam; and a curved cantilever beam. The cantilever beam designs were off surface structures, attached to the wafer at the root of the beam. The composite plate with embedded sensor was loaded in uniaxial tension and bending. Sensor designs were compared for repeatability, sensitivity and reliability. The effects of wafer geometry and composite plate stiffness were also studied. Typical sensor sensitivity to a uniaxial tensile strain of 0.001 (1000 /spl mu//spl epsi/) ranged from 1.2 to 1.5% of the nominal resistance (dR/R). All sensors responded repeatably to uniaxial tension loading. However, for compressive bending loads imposed on a 2-3-mm-thick composite plate, sensor response varied significantly for all sensor designs. This additional sensitivity can be attributed to local buckling and subsequent out of plane motion in compressive loading. The curved cantilever design, constructed with a hoop geometry, showed the least variation in response to compressive bending loads. All devices survived and yielded repeatable responses to uniaxial tension loads applied over 10 000 cycles.

Thermo-Viscoelastic Constitutive Modeling of Polymer Composites Subjected to Space Irradiation

In this paper, a general linear constitutive theory of thermo-viscoelasticity for irradiated polymer composites is presented. The model is based upon thermodynamic considerations involving Helmholtz and Gibbs free energies, Clausius and Duhem inequality and micro-mechanical strain, and stress fields associated with the fiber and matrix materials. The results show that the transverse and shear creep compliances for a T300/934 graphite-epoxy composite increase as the volume fraction of matrix increases and/or the fiber-matrix interfacial debonding increases. The results, when compared with the available limited experimental data, exhibit good correlation.

Strain analysis of silicon-on-insulator films produced by zone melting recrystallization

Silicon-on-Insulator (SOI) wafers produced by the Zone-Melting-Recrystallization (ZMR) method were evaluated to determine the level of built-in strain. Micromechanical strain measurement structures were produced by surface micromachining the thin film silicon epitaxial layer. A variety of test structures and a new tensile strain measurement device were used to determine the level of strain in the material. Results indicated that the maximum strain in the ZMR material is less than 2/spl times/10/sup -4/ and that there is a significant orientation dependence. >

The effect of interfacial imperfections on the micromechanical stress and strain distribution in fibre reinforced composites

A mathematical model for the determination of micromechanical stress and strain distribution in a unidirectional fibre reinforced composite is developed. The model consists of three phases represented as concentric cylinders, including the existence of an interphase. Both fibre and matrix have well defined elastic properties, while the interphase properties follow an exponential law of variation. The effect of an abrupt variation of elastic properties at the fibre—interphase boundary on the micromechanical state of stress is also presented. The degree of adhesion between fibre and matrix is described by means of adhesion parameters introduced, and a parametric study is performed wherein the stress and strain distribution around the fibre are determined as a function of adhesion efficiency and fibre volume fraction. Analytical results were confirmed by means of a finite element technique introduced and applied to the model.

Thermoelastic constitutive modeling of irradiated polymer composites with matrix property change and fiber/matrix debonding

In this paper, thermoelastic models are presented for the evaluation of the constitutive response of irradiated fiber-reinforced polymer composites with change in the fiber and matrix properties and fiber/matrix interfacial debonding. These models are based upon thermodynamic considerations involving Helmholtz and Gibbs free energies and micromechanical stress and strain fields associated with the fiber and matrix materials. The proposed union between the energy functions and micromechanics provides a unifying framework that can deal with the potential property changes in the fibers and matrix and at the fibre/matrix interface. The results for a typical graphite/epoxy polymer composite system show reasonable trends when compared with the available experimental data for primary elastic constants. The parametric study for all the principal elastic constants involving matrix stiffening, softening and fiber/matrix interfacial debonding exhibit a number of interesting results. A significant influence of interfacial fiber/matrix debonding on the matrix-dominated material properties, such as (E 2) c r and (G 66) c r, has also been noted.

Prediction of fiber-matrix interphase effects on damping of composites using a micromechanical strain energy/finite element approach

Few previous micromechanical models of damping in a unidirectional composite lamina have dealt with the fiber-matrix interphase, and none of these models have considered loading conditions other than the uniaxial longitudinal case. This paper describes the use of a general purpose strain energy/finite element method for micromechanical modeling of both damping and stiffness in composites including the fiber-matrix interphase region. Composite damping and moduli for longitudinal and transverse normal loading and inplane and out-of-plane shear loading are obtained. Particular interest is paid to the effects of the size of the fiber-matrix interphase on composite damping, and to the contribution of the interphase to the total energy dissipation in the composite. The determination of the four inplane loss factors should be of use for macromechanical analysis of damping of laminated composite structures, which requires lamina damping data as input.

Overall Instantaneous Viscoplastic Properties of Composites

A computer procedure was developed to analyze viscoplasticity and strain rate effects of continuous fiber reinforced composite materials. The procedure provides the overall instantaneous moduli, coefficients of thermal expansion and micromechanical stresses and strains. It was implemented with the help of a displacement formulation of the finite element method and a periodic hexagonal array microstructural model. It also can be adapted to evaluate instantaneous overall viscoplastic properties at integration points in finite element analyses of composite structures. This procedure was primarily developed to simulate the viscoplastic response of an aramid/epoxy laminate, used in the production of ARALL® laminates, in an off-axis tension test.