Stretch Strain Research Articles

Achilles tendon compliance: Implications for gait, injury and rehabilitation

Tendons are inherently elastic materials: they strain in response to the stress that is applied to them. When muscles contract and produce force, this force is transferred to the skeleton via the tendon and hence causes the tendon to stretch and store elastic strain energy which can be used later for propulsion. The Achilles tendon is the best example of this, because its tendon is very long compared to the muscle fibres it attaches to. We have used B-mode ultrasound imaging in combination with motion analysis to examine the strain on the Achilles tendon during walking, running and hopping.

Transverse magnetoresistance of uniaxially deformed thin polycrystallinen- Bi films

Large inuence of uniaxial stretch (strain) S and compression P on transverse and perpendicular resistivity ‰ and magnetoresistance (MR) of polycrystalline n-Bi lms was investigated. The calculations were performed on the basis of polycrystalline Bi thin lm model and electron intervalley repopulation in deformed lm crystallites. The calculations show that in n-Bi lms the inuence of P on ‰ can be many times larger because T -holes in Bi lms signicantly reduce the effect of deformation. It was found that S and P cause considerably different dependences of ‰ and MR on magnetic eld strength. The effect of P on the ‰ and MR is of opposite sign as compared to S and can be larger than that of S. In strong non-quantizing magnetic eld region the transverse ‰ appears to be independent of deformation. The investigated high-quality 1.5 „m thick Bi lms consisting of up to 200 „m length crystallites were deposited on non-crystalline substrate and annealed at critical temperature close to the lm melting temperature. The experimental results conrm the theoretical predictions.

Strain measurement in the left ventricle during systole with deformable image registration

The objective of this study was to validate a deformable image registration technique, termed Hyperelastic Warping, for left ventricular strain measurement during systole using cine-gated, non-tagged MR images with strains measured from tagged MRI. The technique combines deformation from high resolution, non-tagged MR image data with a detailed computational model, including estimated myocardial material properties, fiber direction, and active fiber contraction, to provide a comprehensive description of myocardial contractile function. A normal volunteer (male, age 30) with no history of cardiac pathology was imaged with a 1.5 T Siemens Avanto clinical scanner using a TrueFISP imaging sequence and a 32-channel cardiac coil. Both tagged and non-tagged cine MR images were obtained. The Hyperelastic Warping solution was evolved using a series of non-tagged images in ten intermediate phases from end-diastole to end-systole. The solution may be considered as ten separate warping problems with multiple templates and targets. At each stage, an active contraction was initially applied to a finite element model, and then image-based warping penalty forces were utilized to generate the final registration. Warping results for circumferential strain (R(2)=0.75) and radial strain (R(2)=0.78) were strongly correlated with results obtained from tagged MR images analyzed with a Harmonic Phase (HARP) algorithm. Results for fiber stretch, LV twist, and transmural strain distributions were in good agreement with experimental values in the literature. In conclusion, Hyperelastic Warping provides a unique alternative for quantifying regional LV deformation during systole without the need for tags.

Analysis and Interpretation of Stress Fiber Organization in Cells Subject to Cyclic Stretch

Numerical simulations that incorporate a biochemomechanical model for the contractility of the cytoskeleton have been used to rationalize the following observations. Uniaxial cyclic stretching of cells causes stress fibers to align perpendicular to the stretch direction, with degree of alignment dependent on the stretch strain magnitude, as well as the frequency and the transverse contraction of the substrate. Conversely, equibiaxial cyclic stretching induces a uniform distribution of stress fiber orientations. Demonstrations that the model successfully predicts the alignments experimentally found are followed by a parameter study to investigate the influence of a range of key variables including the stretch magnitude, the intrinsic rate sensitivity of the stress fibers, the straining frequency, and the transverse contraction of the substrate. The primary predictions are as follows. The rate sensitivity has a strong influence on alignment, equivalent to that attained by a few percent of additional stretch. The fiber alignment increases with increasing cycling frequency. Transverse contraction of the substrate causes the stress fibers to organize into two symmetrical orientations with respect to the primary stretch direction.

Investigations on the Flamelet Inner Structure of Turbulent Premixed Flames

Planar Rayleigh scattering measurements were used to investigate the inner structure of flamelets in premixed turbulent Bunsen flames. Measurements were performed in a high pressure chamber, where pressure is varied from 0.3 to 0.9 MPa. Two lean equivalence ratios (0.6 and 0.7) of methane/air mixtures were studied. Local information regarding the thickness and the local curvature of the flamelets were obtained. It is observed that an increase of the equivalence ratio induces a decrease of the mean local flamelet thickness. When pressure is increased from 0.3 to 0.9 MPa, the mean flamelet thickness does not decrease as for laminar case. The different external phenomena (turbulence and stretch (curvature and strain rate)) which could explain this trend are investigated.

Structural strain energy function applied to the ageing of the human aorta

Stiffening of the aorta with progressing age leads to decrease of aortic compliance and thus to an increase of pulse pressure amplitude. Using a strain energy function (SEF) which takes into account the composition of the arterial wall, we have studied the evolution of key structural components of the human thoracic aorta using data obtained from the literature. The SEF takes into account the wavy nature of collagen, which upon gradual inflation of the blood vessel is assumed to straighten out and become engaged in bearing load. The engagement of the individual fibers is assumed to be distributed log-logistically. The use of a SEF enables the consideration of axial stretch ( λ z ) and residual strain (opening angle) in the biomechanical analysis. Both λ z and opening angle are known to change with age. Results obtained from applying the SEF to the measurements of aortic pressure–diameter curves indicate that the changes in aortic biomechanics with progressing age are not to be sought in the elastic constants of elastin and collagen or their volume fractions of the aortic wall but moreover in alterations of the collagen mesh arrangement and the waviness of the collagen fibers. In old subjects, the collagen fiber ensemble engages in load bearing much more abruptly than in young subjects. Reasons for this change in collagen fiber dynamics may include fiber waviness remodeling or cross-linkage by advanced glycation end-products (AGE). The abruptness of collagen fiber engagement is also the model parameter that is most responsible for the decreased compliance at progressed ages.

Enhanced Allman quadrilateral for finite drilling rotations

The paper concerns a four-node quadrilateral element based on Allman shape functions undergoing finite (unrestricted) drilling rotations, and aims at improving its accuracy and facilitating its implementation. Firstly, the classical Allman shape functions are valid only for small in-plane rotations, and must be used with a co-rotational frame, which embeds finite rotations. We derive a new form of Allman shape functions, which is valid for finite drilling rotations, and allows to avoid the use of such a frame. Secondly, the classical Allman quadrilateral shows locking in the in-plane shear test. We study this problem, identify its source, and remove it by enhancing the element with two additional modes, via the Enhanced Assumed Displacement Gradient (EADG) method. To accomplish this, we extend the original version of the method to mixed functionals including rotations. Two variational formulations including the drilling rotation via the rotation constraint (RC) equation are considered; one based on the Green strain, and the other on the relaxed non-symmetric right stretch strain. Numerical tests of the corresponding finite elements show that the improved Allman elements are as exact in linear tests as the EADG4 element, and perform very well in a severe in-plane shear test for one layer of elements undergoing large rotations.

RVE-based studies on the coupled effects of void size and void shape on yield behavior and void growth at micron scales

The present paper extends the Gurson and GLD models [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth, Part I—yield criteria and flow rules for porous ductile media. J. Mech. Phys. Solids 99, 2–15; Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Technol. 116, 290–297] to involve the coupled effects of void size and void shape on the macroscopic yield behavior of non-linear porous materials and on the void growth. A spheroidal representative volume element (RVE) under a remote axisymmetric homogenous strain boundary condition is carefully analyzed. A wide range of void aspect ratios covering the oblate spheroidal, spherical and prolate spheroidal void are taken into account to reflect the shape effect. The size effect is captured by the Fleck–Hutchinson phenomenological strain gradient plasticity theory [Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advance in Applied Mechanics, vol. 33, Academic Press, New York, pp. 295–361]. A new size-dependent damage model like the Gurson and GLD models is developed based on the traditional minimum plasticity potential principle. Consequently, the coupled effects of void size and void shape on yield behavior of porous materials and void growth are discussed in detail. The results indicate that the void shape effect on the yield behavior of porous materials and on the void growth can be modified dramatically by the void size effect and vice versa. The applied stress triaxiality plays an important role in these coupled effects. Moreover, there exists a cut-off void radius r c, which depends only on the intrinsic length l 1 associated with the stretch strain gradient. Voids of effective radius smaller than the critical radius r c are less susceptible to grow. These findings are helpful to our further understanding to some impenetrable micrographs of the ductile fracture surfaces.

A three‐dimensional in vitro model system to study the adaptation of craniofacial skeletal muscle following mechanostimulation

The aim of this study was to investigate the in vitro response of human craniofacial muscle-derived myotubes (primitive/nascent muscle fibres), in three-dimensional constructs, to strain in vitro to mimic clinical scenarios, using expression of the mechanoresponsive gene gelatinase-A/matrix metalloproteinase-2 (MMP-2) as a marker of remodelling of muscle extracellular matrix. Three-dimensional (3D) constructs of cells derived from explants of human masseter muscle (human craniofacial muscle-derived cells; hCMDC) in collagen sponges were subjected to mechanical, uniaxial strain using the Bio-Stretch system. 3D myotube constructs were exposed to the strain regimes of rapid ramp stretch (RRS) or cyclical ramp strain (CRS) with 7.5% and 15% strain. The activity of MMP-2 was assessed by zymography of construct-conditioned medium, whilst lysates of the constructs were used to measure creatine phosphokinase (CPK) activity to confirm the presence of myotubes in the strained constructs. Scanning electron microscopy of the collagen sponges and the CPK assays confirmed the presence of myotubes. MMP-2 was expressed by all the samples and controls, but expression was found to be significantly higher in those cultures strained continuously (RRS), compared to cyclical strain (CRS), and in those strained at 15% compared to 7.5%. Thus, MMP-2 expression, and hence extracellular matrix remodelling, is up-regulated in response to strain and is dependent upon the amount and type of strain to which the muscle is subjected.

Stereographic projections of Poisson's ratio in auxetic crystals

AbstractAuxetic behavior (negative values of Poisson's ratio) in some cubic metals for a stretch along a cube‐face diagonal was investigated in detail by R. H. Baughman et al., F. Milstein, K. Huang, M. Jain, M. P. Verma. Directions with extreme values of Poisson's ratio in crystals for a stretch along a cube‐face diagonal and corresponding lateral strain along the orthogonal cube‐face diagonal and cube‐axis were considered by the authors. In this paper the stereographic projections of Poisson's ratio for a set of natural crystals with cubic, hexagonal and monoclinic symmetry were computed. From these stereographic projections the Poisson's ratio for any possible directions of stretch and lateral strain in the crystal were calculated and orientations of stretch and lateral strain with extreme values of Poisson's ratio were obtained. Crystals with auxetic behavior were revealed. Orientations of stretch directions and lateral strain directions with negative values of Poisson's ratio were determined. By analysis of the above results cuts with optimal negative values of Poisson's ratio were revealed in zinc, molybdenum sulfide, carbon, graphite, polypropylene, monoclinic natural minerals labradorite and augite, a complex silicate and in a set of cubic alloys. The exotic behavior of change of cross‐section of a cylindrical rod during stretching along the rod axis was revealed in the naturally‐occurring mineral SiO2 cristobalite – an example of a molecular auxetic. The elastic constants of crystals from the manual of Landolt–Börnstein were used in the calculations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A fractal flame-wrinkling large eddy simulation model for premixed turbulent combustion

Combustion plays an important role in a wide variety of industrial applications, such as gas-turbines, furnaces, spark-ignition engines, and various air-breathing engines. The ability to predict and understand the behavior of reacting flows in practical devices is fundamental to improved combustors with higher efficiency and reduced levels of emissions. At present, large eddy simulation is considered the most promising approach for premixed combustion modeling since the large-scale energy containing flow structures are resolved on the grid. However, the typically thin reaction zone cannot be resolved. To overcome this difficulty flamelet models, in which the reaction is assumed to take place in thin layers, wrinkled by the turbulence can sometimes be used. In these models, the turbulent flame speed can be represented as the product of the laminar flame speed, S u, corrected for the effects of stretch (strain and curvature) and the flame-wrinkling, Ξ. In this study, we propose to model Ξ using fractal theory. This model requires sub-models for the fractal dimension, and the inner and outer cut-offs—the latter being set by the grid. A model is proposed for the inner cut-off, whereas an empirical parameterization is used to provide the fractal dimension. The proposed model is applied to flame kernel growth in homogeneous isotropic turbulence in a fan-stirred bomb and to a lean premixed flame in a plane symmetric dump combustor. Good qualitative and quantitative agreement with experimental data were obtained for the proposed model in both cases. Comparison with other well-known turbulent flame speed closure models shows that the proposed model behaves at least as good, or even better, than the reference models.

The scorching breath of angiotensin

Oxidative damage is emerging as a common theme in many common conditions that shorten life-span. One of these conditions is hypertension [1]. Vascular reactive oxygen species (ROS) are produced in endothelial, adventitial and vascular smooth muscle cells. Most prominent amongst ROS is superoxide (•O). The primary enzyme activity involved in •O generation is NAD(P)H oxidase, which in blood vessels is expressed in endothelial cells, vascular smooth muscle cells, adventitial fibroblasts, monocytes and macrophages. Overall NAD(P)H oxidase activity in cells is achieved by several components. These include cell-membraneassociated p22 and gp91 [or gp91 (nox2) homologues, nox1 and nox4], as well as cytosolic p47 and p67 [2]. Vascular NAD(P)H oxidase is upregulated by vasoactive factors, cytokines, growth factors, stretch, shear stress and pulsatile strain [2]. At low concentrations, ROS serve a physiological role as signalling molecules involved in endothelial function and vascular contractility [1]. However, pathological increases in ROS results in a plethora of effects that damage the vessel wall [3]. Moreover, •O anions generated by NAD(P)H oxidase may contribute to the initiation and maintenance of hypertension [4].

Dilute Polyacrylamide Solutions under Uniaxial Extensional Flow

The shear and extensional viscosities, dynamic viscosities, and normal forces of a series of polyacrylamide solutions of varying molar mass have been determined in a Boger fluid at varying concentrations. The critical strain rate under extensional flow that can be defined from the departure from Newtonian behavior, ec, was found to be independent of the concentration and varied in the same way as the critical coil−stretch strain rate with the molar mass. A quantitative comparison indicated that ec is a decade lower than the strain rate predicted to characterize the coil−stretch transition. This difference indicates that ec reflects the average deformation of the chains over the range of strain rates.

P1-D-44 Ultrasonic Measuring Method of Accumulated Tensile Elasticity Strain Energy on the Stretch Strain Metal Beam using Sing-around method

P1-D-44 Ultrasonic Measuring Method of Accumulated Tensile Elasticity Strain Energy on the Stretch Strain Metal Beam using Sing-around method

Cuts with negative Poisson’s ratio in alloys and rocks

Stretching of material with negative Poisson’s ratio leads to an unexpected transverse expansion. Stretching of anisotropic material can cause expansion in one direction and contraction in another direction. For example it is possible for Poisson’s ratio in crystals to be negative in one direction and highly positive in another direction. In the paper a set of hexagonal, monoclinic and cubic crystals of rocks, minerals and alloys were investigated. The stereographic projections of Poisson’s ratio were computed for each crystal. From these stereographic projections the Poisson’s ratio for any directions of stretch and lateral strain in crystal were calculated and orientations of stretch and lateral strain with extremes values of Poisson’s ratio were obtained. By analysis of the above results cuts with negative values of Poisson’s ratio were revealed in zinc, molybdenum sulfide, polypropylene, graphite, carbon, natural precious minerals labradorite and augite, complex silicate and in copper, zinc, iron, nickel, indium, silver and gold alloys. For these crystals the angular dependence of stretched orientations corresponding to negative Poisson’s ratio were determined. Elastic modules of crystals from the manual of Landolt–Bornstein were applied in calculations. Some simple models with negative Poisson’s ratio are considered and some possible applications of materials with negative Poisson’s ratio basing on their unusual acoustic properties are discussed.

Warping and in-plane twist parameters in kinematics of finite rotation shells

The finite rotation shell equations are derived from a 3D mixed formulation with explicit rotations. Constitutive equations are written in terms of the relaxed Biot stress and right stretch strain. The shell kinematics is based on a generalised Reissner hypothesis and rotations depending on the thickness coordinate. The generalized Reissner hypothesis includes a bubble-like term for the warping of a cross-section. The rotations linearly vary over the thickness and are parametrised by a canonical rotation vector. The components of the rotation vector can be identified as the in-plane twist parameter and two warping parameters. Consequences of this new rotation vector for shell equations, especially for rotation constraints and strain measures, are examined, and a comparison with the formulation which includes the in-plane twist parameter is made. The new rotation vector is treated as an implicit kinematical parameter and recovered from the rotation constraint. Hence, a 6-parameter shell formulation, admitting C 0 approximations, is retained.

Kinematics of finite rotation shells with in-plane twist parameter

The paper concerns shell equations derived from a 3D mixed formulation with explicit rotations. The constitutive equation is postulated in terms of the relaxed Biot stress and right stretch strain. The shell kinematics is based on the Reissner hypothesis and on a constant/linear approximation of the rotation tensor with respect to the thickness coordinate. The rotation around the shell director is parametrized by the drill and in-plane twist parameters, with the latter one associated with the linear approximation. The in-plane twist parameter is new, and hence consequences of its presence for the shell rotation constrains and strain measures are examined, and compared to the formulation with the drill rotation only. In the presented formulation, the drill rotation is retained explicitly, and can be recovered from the drill rotation constraint, while the in-plane twist parameter is an internal parameter of the theory. In this way the enhanced shell kinematics does not increase the number of degrees of freedom of a discrete model.

Three-dimensional finite element analysis of subdural hematoma.

Head motion, an important factor in acute subdural hematoma (ASDH), can be broken down into translational and rotational elements. We used three-dimensional finite element analysis to examine the thresholds of angular and tangential acceleration required to tear bridging veins in humans during head impact. The lengths of midsagittal and parasagittal bridging veins were calculated first. To assess the effect of translational and rotational acceleration, the strain of each vein was then computed under three different motions. The threshold of ASDH was expressed in terms of tangential and rotational acceleration. Deformation-angle histories of the midsagittal and parasagittal bridging veins showed that veins that drain forward into the superior sinus at a 130-degree angle incurred the greatest stretch strain during occipital impact. In the midsagittal plane, pure rotation induced greater stretch strain on these veins (14.4%) than pure translation (2.5%) or combined translation and rotation motion (10.4%). A tangential acceleration of 3,912.9 G or an angular acceleration of 71.2 krad/s2 seemed to approximate the threshold for ASDH in the human midsagittal plane, whereas 5,010.9 G and 97.4 krad/s2 approximated the threshold in the parasagittal plane. Impact direction and orientation of bridging veins are both important factors in ASDH. Threshold criteria for ASDH can be expressed in terms of tangential and rotational acceleration.

Finite rotation quadrilateral element for multi-layer beams

The paper presents the finite rotations beam equations derived on use of the generalized Reissner hypothesis with a scalar parameter for the transverse extension. The beam strain and change of curvature measures are obtained from the right stretch strain, and the virtual work is given for Biot-type stress and couple resultants. The strain energy for the first-order isotropic elastic material is assumed in terms of the right stretch strain, and constitutive equations for the beam stress and couple resultants are derived. Two finite rotation elements are developed from the derived beam equations: a beam element with the transverse stretch and a quadrilateral element. First, the beam element with the uniformly under-integrated tangent operator is developed. Next, the formula linking the middle-line variables and the interface variables of the beam is introduced consistently with the generalized Reissner kinematics. Linearization of this formula is performed, and the derived tangent operator is used to convert the two-node beam element to a four-node quadrilateral. Both the finite elements have been tested on several numerical examples, some of highly non-linear characteristics, and their accuracy is very good. It has been established that the quadrilateral element, which is intended for applications to multi-layer beams, performs very well for high elemental aspect ratios, and can therefore be applied to modelling of very thin layers. Copyright © 1999 John Wiley & Sons, Ltd.

A shell theory with independent rotations for relaxed Biot stress and right stretch strain

A shell theory incorporating rotations as the independent variable, among them the drilling rotation, is derived systematically from three-dimensional equations of a classical (non-polar) continuum.