Effect of Particle Size on Compaction of Materials with Different Deformation Mechanisms with and without Lubricants

This work investigates the effect of excipient particle size on compaction properties of brittle, plastic and viscoelastic materials with and without added lubricants. Sieve cuts of Microcrystalline cellulose (MCC), Starch and Dibasic calcium phosphate dihydrate were obtained by sieving, then samples were tested without lubrication or with added lubricant (0.5% Mg stearate mixed for either 5 or 30-min). Compacts were left overnight before testing. It was found that in the absence of lubricant, compact tensile strength (TS) was dependent on particle size only for starch. With Mg stearate, lubricant sensitivity shows a strong dependence on excipient particle size for both starch and MCC, where smaller particles are less affected by lubricant. Dibasic calcium phosphate dihydrate was not sensitive to lubricant even after 30 min mixing. This study highlights that in the absence of lubricant, initial particle size of excipients has no impact on compact strength not only for Dibasic calcium phosphate dihydrate (brittle), but also for MCC (plastic). On the other hand, TS is dependent on particle size both with or without added lubricant for starch (viscoelastic).     

Localized dynamic light scattering: a new approach to dynamic measurements in optical microscopy.

We present a new approach to probing single-particle dynamics that uses dynamic light scattering from a localized region. By scattering a focused laser beam from a micron-size particle, we measure its spatial fluctuations via the temporal autocorrelation of the scattered intensity. We demonstrate the applicability of this approach by measuring the three-dimensional force constants of a single bead and a pair of beads trapped by laser tweezers. The scattering equations that relate the scattered intensity autocorrelation to the particle position correlation function are derived. This technique has potential applications for measurement of biomolecular force constants and probing viscoelastic properties of complex media.     

The mechanics of F-actin microenvironments depend on the chemistry of probing surfaces

To understand the microscopic mechanical properties of actin networks, we monitor the motion of embedded particles with controlled surface properties. The highly resolved Brownian motions of these particles reveal the viscoelastic character of the microenvironments around them. In both non-cross-linked and highly cross-linked actin networks, particles that bind F-actin report viscoelastic moduli comparable to those determined by macroscopic rheology experiments. By contrast, particles modified to prevent actin binding have weak microenvironments that are surprisingly insensitive to the introduction of filament cross-links. Even when adjacent in the same cross-linked gel, actin-binding and nonbinding particles report viscoelastic moduli that differ by two orders of magnitude at low frequencies (0.5-1.5 rad/s) but converge at high frequencies (> 10(4) rad/s). For all particle chemistries, electron and light microscopies show no F-actin recruitment or depletion, so F-actin microheterogeneities cannot explain the deep penetration (approximately 100 nm) of nonbinding particles. Instead, we hypothesize that a local depletion of cross-linking around nonbinding particles explains the phenomena. With implications for organelle mobility in cells, our results show that actin binding is required for microenvironments to reflect macroscopic properties, and conversely, releasing actin enhances particle mobility beyond the effects of mere biochemical untethering.     

Mechanics of living cells measured by laser tracking microrheology

To establish laser-tracking microrheology (LTM) as a new technique for quantifying cytoskeletal mechanics, we measure viscoelastic moduli with wide bandwidth (5 decades) within living cells. With the first subcellular measurements of viscoelastic phase angles, LTM provides estimates of solid versus liquid behavior at different frequencies. In LTM, the viscoelastic shear moduli are inferred from the Brownian motion of particles embedded in the cytoskeletal network. Custom laser optoelectronics provide sub-nanometer and near-microsecond resolution of particle trajectories. The kidney epithelial cell line, COS7, has numerous spherical lipid-storage granules that are ideal probes for noninvasive LTM. Although most granules are percolating through perinuclear spaces, a subset of perinuclear granules is embedded in dense viscoelastic cytoplasm. Over all time scales embedded particles exhibit subdiffusive behavior and are not merely tethered by molecular motors. At low frequencies, lamellar regions (820 +/- 520 dyne/cm(2)) are more rigid than viscoelastic perinuclear regions (330 +/- 250 dyne/cm(2), p < 0.0001), but spectra converge at high frequencies. Although the actin-disrupting agent, latrunculin A, softens and liquefies lamellae, physiological levels of F-actin, alone (11 +/- 1.2 dyne/cm(2)) are approximately 70-fold softer than lamellae. Therefore, F-actin is necessary for lamellae mechanics, but not sufficient. Furthermore, in time-lapse of apparently quiescent cells, individual lamellar granules can show approximately 4-fold changes in moduli that last >10 s. Over a broad range of frequencies (0.1-30, 000 rad/s), LTM provides a unique ability to noninvasively quantify dynamic, local changes in cell viscoelasticity.     

Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer.

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G'(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G'(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.     

The role of mucus gel viscosity, spinnability, and adhesive properties in clearance by simulated cough

We investigated the role of the viscoelastic and adhesive properties of mucus gel simulants on the clearance of mucus by simulated cough. Mucus-like gels with widely varying viscoelastic properties were prepared from polysaccharides crosslinked with sodium borate. Cough was simulated by opening a solenoid valve connecting a model trachea to a pressurized tank. The clearance of gels lining the model trachea was quantified by observing marker particle transport. Viscosity elastic modulus, relaxation time and yield stress were measured with a steady-shear viscoelastometer. Spinnability (thread formation) was determined with a filancemeter. Adhesivity (surface tension) was measured by the platinum ring technique. The viscoelastic and adhesive properties of the mucus gel simulants spanned the ranges observed for bronchial secretions from patients with COPD. The relationship between simulated cough clearance and the viscoelastic and adhesive properties of the gels was analyzed by stepwise linear regression of the non-zero data matrix. The major independent variable relating to clearance was viscosity. Secondary, but highly significant dependences, were also found for spinnability and adhesivity. Elastic modulus, relaxation time and yield stress had no independent effect on cough clearance over the investigated range. The results indicate that, in the absence of airway surface liquid, cough-type clearance relates primarily with mucus gel viscosity. For a given viscosity, clearance is also impaired by spinnability, i.e. the capacity of the mucus to form threads. At constant viscosity and spinnability, clearance is further impaired by an increase in the adhesivity of the mucus. The negative dependence of each of these physical factors can be rationalized in terms of their inhibitory effect on wave formation in the mucus lining layer during high velocity airflow interaction.     

Probing single-cell micromechanics in vivo: the microrheology of C. elegans developing embryos

Cells are not directly accessible in vivo and therefore their mechanical properties cannot be measured by methods that require a direct contact between probe and cell. Here, we introduce a novel in vivo assay based on particle tracking microrheology whereby the extent and time-lag dependence of the mean squared displacements of thermally excited nanoparticles embedded within the cytoplasm of developing embryos reflect local viscoelastic properties. As a proof of principle, we probe local viscoelastic properties of the cytoplasm of developing Caenorhabditis elegans embryos. Our results indicate that unlike differentiated cells, the cytoplasm of these embryos does not exhibit measurable elasticity, but is highly viscous. Furthermore, the viscosity of the cytoplasm does not vary along the anterior-posterior axis of the embryo during the first cell division. These results support the hypothesis that the asymmetric positioning of the mitotic spindle stems from an asymmetric distribution of elementary force generators as opposed to asymmetric viscosity of the cytoplasm.     

Small angle X-ray scattering of wheat seed-storage proteins: alpha-, gamma- and omega-gliadins and the high molecular weight (HMW) subunits of glutenin

Small angle X-ray scattering in solution was performed on seed-storage proteins from wheat. Three different groups of gliadins (alpha-, gamma- and omega-) and a high molecular weight (HMW) subunit of glutenin (1Bx20) were studied to determine molecular size parameters. All the gliadins could be modelled as prolate ellipsoids with extended conformations. The HMW subunit existed as a highly extended rod-like particle in solution with a length of about 69 nm and a diameter of about 6.4 nm. Specific aggregation effects were observed which may reflect mechanisms of self-assembly that contribute to the unique viscoelastic properties of wheat dough.     

Manipulation of micro- and nanoparticles in viscoelastic fluid flows within microfluid systems

Manipulation of micro- and nanoparticles in complex biofluids is highly demanded in most biological and biomedical applications. A significant number of microfluidic platforms have been developed for inexpensive, rapid, accurate, and efficient particle manipulation. Due to the enormous potential of viscoelastic fluids (VEFs) for particle manipulation, various emerging microfluidic-based VEFs techniques have been presented over the last decade. This review provides an intuitive understanding of VEF physics for particle separation in different microchannel geometries. Besides, active and passive VEF methods are critically reviewed, highlighting the potential and practical challenges of each technique for particle/cell focusing, sorting, and separation. The outcome of this study could enable recognizing deliverable VEF technology with the promising prospect in the manipulation of submicron biological samples (e.g., exosomes, DNA, and proteins).     

Enhanced viscoelasticity of human cystic fibrotic sputum correlates with increasing microheterogeneity in particle transport

Current biochemical characterizations of cystic fibrosis (CF) sputum do not address the high degree of microheterogeneity in the rheological properties of the mucosal matrix and only provide bulk-average particle diffusion coefficients. The viscoelasticity of CF sputum greatly reduces the diffusion rates of colloidal particles, limiting the effectiveness of gene delivery to underlying lung cells. We determine diffusion coefficients of hundreds of individual amine-modified and carboxylated polystyrene particles (diameter 100-500 nm) embedded in human CF sputum with 5 nm and 33 ms of spatiotemporal resolution. High resolution multiple particle tracking is used to calculate the effective viscoelastic properties of CF sputum at the micron scale, which we relate to its macroscopic viscoelasticity. CF sputum microviscosity, as probed by 100- and 200-nm particles, is an order of magnitude lower than its macroviscosity, suggesting that nanoparticles dispersed in CF sputum are transported primarily through lower viscosity pores within a highly elastic matrix. Multiple particle tracking provides a non-destructive, highly sensitive method to quantify the high heterogeneity of the mucus pore network. The mean diffusion coefficient becomes dominated by relatively few but fast-moving particles as particle size is reduced from 500 to 100 nm. Neutrally charged particles with a diameter <200 nm undergo more rapid transport in CF sputum than charged particles. Treatment with recombinant human DNase (Pulmozyme) reduces macroviscoelastic properties of CF sputum by up to 50% and dramatically narrows the distribution of individual particle diffusion rates but surprisingly does not significantly alter the ensemble-average particle diffusion rate.     

Dynamical clustering of red blood cells in capillary vessels

We have modeled the dynamics of a 3-D system consisting of red blood cells (RBCs), plasma and capillary walls using a discrete-particle approach. The blood cells and capillary walls are composed of a mesh of particles interacting with harmonic forces between nearest neighbors. We employ classical mechanics to mimic the elastic properties of RBCs with a biconcave disk composed of a mesh of spring-like particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, translational and angular momenta. Realistic behavior of blood cells is modeled by considering RBCs and plasma flowing through capillaries of various shapes. Three types of vessels are employed: a pipe with a choking point, a curved vessel and bifurcating capillaries. There is a strong tendency to produce RBC clusters in capillaries. The choking points and other irregularities in geometry influence both the flow and RBC shapes, considerably increasing the clotting effect. We also discuss other clotting factors coming from the physical properties of blood, such as the viscosity of the plasma and the elasticity of the RBCs. Modeling has been carried out with adequate resolution by using 1 to 10 million particles. Discrete particle simulations open a new pathway for modeling the dynamics of complex, viscoelastic fluids at the microscale, where both liquid and solid phases are treated with discrete particles. Figure A snapshot from fluid particle simulation of RBCs flowing along a curved capillary. The red color corresponds to the highest velocity. We can observe aggregation of RBCs at places with the most stagnant plasma flow.     

Some viscoelastic properties of human erythrocyte spectrin networks end-linked in vitro

We have succeeded in making macroscopic networks of end-linked human erythrocyte spectrin. The network junctions were made using erythrocyte protein 4.1 irreversibly attached to 5 nm (diameter) colloidal gold particles. Rotary shadowing electron microscopy verifies that the protein 4.1-labelled colloidal gold particles bind only to the tail end of the spectrin molecules. Electron micrographs of protein 4.1-labelled colloidal gold particles incubated at 4 degrees C with spectrin dimers reveal that 1-5 spectrin dimers attach to each protein 4.1-labelled colloidal gold particle yielding a spider-like appearance of these complexes. Incubation with a low concentration of spectrin tetramers instead of dimers leads to extensive formation of spectrin microaggregates whereas use of spectrin concentrations higher than 3 mg/ml and a molar ratio between spectrin tetramers and protein 4.1/Au of 4 leads to formation of macroscopic spectrin networks. We have quantitated the viscoelastic properties of such end-linked macroscopic spectrin networks using a gravitational pendulum viscoelastometer. We find that in vitro end-linked spectrin networks can be described by linear viscoelastic theory. The dynamic storage modulus increases almost linearly with the spectrin-protein 4.1/gold particle concentration when the spectrin concentration exceeds about 3 mg/ml and the molar ratio between spectrin tetramers and protein 4.1/Au is 4. At a spectrin concentration of 6 mg/ml and the same ratio between spectrin and protein 4.1/Au, we find a dynamic storage modulus at low frequency of about 80 dyn/cm2. This is in adequate agreement with what is predicted by simple elastomer theory.     

A model of fracture testing of soft viscoelastic tissues

Fracture, or tear, toughness of soft tissues can be computed from the work of fracture divided by the area of new crack surface. For soft tissues without significant plastic deformation, total work, which can be measured experimentally, is composed of the sum of fracture and viscoelastic work. In order to deduce fracture work, a method is needed to estimate viscoelastic work.Two different methods (Ph.D. Dissertation, University of Minnesota, 2000; J. Mater. Sci.: Mater. Med. 12 (2001) 327) have been proposed to estimate viscoelastic work in a fracture test of a soft tissue. The relative merits of these methods are unknown because the true viscoelastic work in an experiment is unknown. In order to characterize the accuracy of these methods, a theoretical model of crack propagation of viscoelastic soft tissue in a tensile test is presented, from which the exact viscoelastic work is calculated. The material is assumed to obey the standard linear solid model.The "exact" solution for the viscoelastic work during the fracture is computed from the model and compared with the work estimated by the two methods. It was found that both methods tend to underestimate the viscoelastic work done, and thus overestimate the fracture work and fracture toughness, although the errors were greater with the Fedewa method. It was further found that low displacement rates can give rise to a "snap" effect, where rapid crack growth can cause a disproportionate amount of viscoelastic energy to be dissipated during unloading. This modeling approach may be useful in evaluating other experimental methods of soft tissue fracture.     

Remote Magnetic Actuation of Micrometric Probes for in situ 3D Mapping of Bacterial Biofilm Physical Properties

Bacterial adhesion and growth on interfaces lead to the formation of three-dimensional heterogeneous structures so-called biofilms. The cells dwelling in these structures are held together by physical interactions mediated by a network of extracellular polymeric substances. Bacterial biofilms impact many human activities and the understanding of their properties is crucial for a better control of their development — maintenance or eradication — depending on their adverse or beneficial outcome. This paper describes a novel methodology aiming to measure in situ the local physical properties of the biofilm that had been, until now, examined only from a macroscopic and homogeneous material perspective. The experiment described here involves introducing magnetic particles into a growing biofilm to seed local probes that can be remotely actuated without disturbing the structural properties of the biofilm. Dedicated magnetic tweezers were developed to exert a defined force on each particle embedded in the biofilm. The setup is mounted on the stage of a microscope to enable the recording of time-lapse images of the particle-pulling period. The particle trajectories are then extracted from the pulling sequence and the local viscoelastic parameters are derived from each particle displacement curve, thereby providing the 3D-spatial distribution of the parameters. Gaining insights into the biofilm mechanical profile is essential from an engineer''s point of view for biofilm control purposes but also from a fundamental perspective to clarify the relationship between the architectural properties and the specific biology of these structures.     

Investigation of electrorheological properties of biodegradable modified cellulose/corn oil suspensions

Considerable scientific and industrial interest is currently being focused on a class of materials known as electrorheological (ER) fluids, which display remarkable rheological behaviour, being able to convert rapidly and repeatedly from a liquid to solid when an electric field (E) is applied or removed. In this study, biodegradable cellulose was modified and converted to their carboxyl salts. Modified cellulose is characterised by Fourier transform infrared (FTIR) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, energy dispersive spectroscopy (EDS), thermogravimetric analysis (TGA) and conductivity measurements. Suspensions of cellulose (C) and modified cellulose (MC) were prepared in insulated corn oil (CO). The effects of electric field strength, shear rate, shear stress, temperature, etc. of these suspensions onto ER activity were determined. Rheological measurements were carried out via a rotational rheometer with a high-voltage generator to investigate the effects of electric field strength and particle concentration on ER performance.The results show that the ER properties are enhanced by increasing the particle concentration and electric field strength. Also the cellulose-based ER fluids exhibit viscoelastic behaviour under an applied electric field due to the chain formation induced by electric polarization between particles.     

Viscoelastic characterization of peripapillary sclera: material properties by quadrant in rabbit and monkey eyes

In this report we characterize the viscoelastic material properties of peripapillary sclera from the four quadrants surrounding the optic nerve head in both rabbit and monkey eyes. Scleral tensile specimens harvested from each quadrant were subjected to uniaxial stress relaxation and tensile ramp to failure tests. Linear viscoelastic theory, coupled with a spectral reduced relaxation function, was employed to characterize the viscoelastic properties of the tissues. We detected no differences in the stress-strain curves of specimens from the four quadrants surrounding the optic nerve head (ONH) below a strain of 4 percent in either the rabbit or monkey. While the peripapillary sclera from monkey eyes is significantly stiffer (both instantaneously and in equilibrium) and relaxes more slowly than that from rabbits, we detected no differences in the viscoelastic material properties (tested at strains of 0-1 percent) of sclera from the four quadrants surrounding the ONH within either species group.     

Motion and twisting of magnetic particles ingested by alveolar macrophages in the human lung: effect of smoking and disease

Background

Magnetic microparticles being ingested by alveolar macrophages can be used as a monitor for intracellular phagosome motions and cytoskeletal mechanical properties. These studies can be performed in the human lung after voluntary inhalation. The influence of cigarette smoking and lung diseases on cytoskeleton dependent functions was studied.

Methods

Spherical 1.3 μm diameter ferrimagnetic iron oxide particles were inhaled by 17 healthy volunteers (40 – 65 years), 15 patients with sarcoidosis (SAR), 12 patients with idiopathic pulmonary fibrosis (IPF), and 18 patients with chronic obstructive bronchitis (COB). The retained particles were magnetized and aligned in an external 100 mT magnetic field. All magnetized particles induce a weak magnetic field of the lung, which was detected by a sensitive SQUID (superconducting quantum interference device) sensor. Cytoskeletal reorganizations within macrophages and intracellular transport cause stochastic magnetic dipole rotations, which are reflected in a decay of the magnetic lung field, called relaxation. Directed phagosome motion was induced in a weak magnetic twisting field. The resistance of the cytoplasm to particle twisting was characterized by the viscosity and the stiffness (ratio between stress to strain) of the cytoskeleton.

Results

One week after particle inhalation and later macrophage motility (relaxation) and cytoskeletal stiffness was not influenced by cigarette smoking, neither in healthy subjects, nor in the patients. Patients with IPF showed in tendency a faster relaxation (p = 0.06). Particle twisting revealed a non-Newtonian viscosity with a pure viscous and a viscoelastic compartment. The viscous shear was dominant, and only 27% of the shear recoiled and reflected viscoelastic properties. In patients with IPF, the stiffness was reduced by 60% (p < 0.02). An analysis of the shear rate and stress dependence of particle twisting allows correlating the rheological compartments to cytoskeletal subunits, in which microtubules mediate the pure viscous (non-recoverable) shear and microfilaments mediate the viscoelastic (recoverable) behavior. The missing correlation between relaxation and particle twisting shows that both stochastic and directed phagosome motion reflect different cytoskeletal mechanisms.

Conclusion

Faster relaxation and a soft cytoskeleton in patients with IPF indicate alterations in cytoskeleton dependent functions of alveolar macrophages, which may cause dysfunction's in the alveolar defense, like a slower migration, a retarded phagocytosis, a disturbed phagosome lysosome fusion and an impaired clearance.

     

Intracellular microrheology of motile Amoeba proteus

The motility of Amoeba proteus was examined using the technique of passive particle tracking microrheology, with the aid of newly developed particle tracking software, a fast digital camera, and an optical microscope. We tracked large numbers of endogeneous particles in the amoebae, which displayed subdiffusive motion at short timescales, corresponding to thermal motion in a viscoelastic medium, and superdiffusive motion at long timescales due to the convection of the cytoplasm. Subdiffusive motion was characterized by a rheological scaling exponent of 3/4 in the cortex, indicative of the semiflexible dynamics of the actin fibers. We observed shear-thinning in the flowing endoplasm, where exponents increased with increasing flow rate; i.e., the endoplasm became more fluid-like. The rheology of the cortex is found to be isotropic, reflecting an isotropic actin gel. A clear difference was seen between cortical and endoplasmic layers in terms of both viscoelasticity and flow velocity, where the profile of the latter is close to a Poiseuille flow for a Newtonian fluid.     

Viscoelasticity of F-actin measured with magnetic microparticles

Dispersed submicroscopic magnetic particles were used to probe viscoelasticity for cytoplasm and purified components of cytoplasm. An externally applied magnetic field exerted force on particles in cells, in filamentous actin (F-actin) solutions, or in F-actin gels formed by the addition of the actin gelation factor, actin-binding protein (ABP). The particle response to magnetic torque can be related to the viscoelastic properties of the fluids. We compared data obtained on F-actin by the magnetic particle method with data obtained on F-actin by means of a sliding plane viscoelastometer. F-actin solutions had a significant elasticity, which increased by 20-fold when gels were formed by ABP addition. Both methods gave consistent results, but the dispersed magnetic particles indicated quantitatively greater rigidity than the viscoelastometer (two and six times greater for F-actin solutions and for F-actin plus ABP gels, respectively). These differences may be due to the fact that, compared with traditional microrheometers, dispersed particle measurements are less affected by long-range heterogeneity or domain-like structure. The magnetometric method was used to examine the mechanical properties of cytoplasm within intact macrophages; the application of the same magnetometric technique to both cells and well-defined, purified protein systems is a first step toward interpreting the results obtained for living cells in molecular terms. The magnetic particle probe system is an effective nonoptical technique for determining the motile and mechanical properties of cells in vitro and in vivo.     

Biphasic poroviscoelastic simulation of the unconfined compression of articular cartilage: II--Effect of variable strain rates

This study investigated the abilities of the linear biphasic poroviscoelastic (BPVE) model and the linear biphasic poroelastic (BPE) model to simulate the effect of variable ramp strain rates on the unconfined compression stress relaxation response of articular cartilage. Curve fitting of experimental data showed that the BPVE model was able to successfully account for the ramp strain rate-dependent viscoelastic behavior of articular cartilage under unconfined compression, while the BPE model was able to account for the complete viscoelastic response at a slow strain rate, but only the long-term viscoelastic response at faster strain rates. We concluded that the short-term viscoelastic behavior of articular cartilage, when subjected to a fast ramp strain rate, is primarily governed by a fluid flow-independent (intrinsic) viscoelastic mechanism, whereas the long-term viscoelastic behavior is governed by a fluid flow-dependent (biphasic) viscoelastic mechanism. Furthermore, a linear viscoelastic representation of the solid stress was found to be a valid model assumption for the simulation of ramp strain rate-dependent relaxation behaviors of articular cartilage within the range of ramp strain rates investigated.