Wide Range Of Loading Rates Research Articles

A high-speed vertical optical trap for the mechanical testing of living cells at piconewton forces

Although atomic force microscopy is often the method of choice to probe the mechanical response of (sub)micrometer sized biomaterials, the lowest force that can be reliably controlled is limited to ≈0.1 nN. For soft biological samples, like cells, such forces can already lead to a strain large enough to enter the non-elastic deformation regime. To be able to investigate the response of single cells at lower forces we developed a vertical optical trap. The force can be controlled down to single piconewtons and most of the advantages of atomic force microscopy are maintained, such as the symmetrical application of forces at a wide range of loading rates. Typical consequences of moving the focus in the vertical direction, like the interferometric effect between the bead and the coverslip and a shift of focus, were quantified and found to have negligible effects on our measurements. With a fast responding force feedback loop we can achieve deformation rates as high as 50 μm/s, which allow the investigation of the elastic and viscous components of very soft samples. The potential of the vertical optical trap is demonstrated by measuring the linearity of the response of single cells at very low forces and a high bandwidth of deformation rates.

Incrementally objective implicit integration of hypoelastic–viscoplastic constitutive equations based on the mechanical threshold strength model

The present paper focuses on the development of a fully implicit, incrementally objective integration algorithm for a hypoelastic formulation of \(J_{2}\)-viscoplasticity, which employs the mechanical threshold strength model to compute the material’s flow stress, taking into account its dependence on strain rate and temperature. Heat generation due to high-rate viscoplastic deformation is accounted for, assuming adiabatic conditions. The implementation of the algorithm is discussed, and its performance is assessed in the contexts of implicit and explicit dynamic finite element analysis, with the aid of example problems involving a wide range of loading rates. Computational results are compared to experimental data, showing very good agreement.

Rate effect and coupled evolution of atomic motions and potential landscapes

Since rate effect of materials plays a key role in impact engineering, the microscopic mechanism of rate effect is investigated at molecular level in this paper. The results show that rate effect on the strength of atomic system is closely related to the coupled evolution of atomic motions and potential landscapes. Accordingly, it becomes possible to develop a new algorithm of molecular simulation, which could properly and efficiently demonstrate strain rate effect under a wide range of loading rates and unveil the mechanisms underlying the strain rate effects.

Micromechanical model for the rate dependence of the fracture toughness anisotropy of Barre granite

Laboratory measurements of mode-I fracture toughness of Barre granite under a wide range of loading rates were carried out with an MTS machine and a split Hopkinson pressure bar (SHPB) system using the notched semi-circular bend (NSCB) specimen. The fracture toughness anisotropy was found to decrease with the increase of the loading rate. A micromechanics model is utilized in this work to understand this experimental observation, invoking crack–microcrack interactions. Two micromechanics models are constructed based on the microstructural investigation of Barre granite samples using the thin-section method. In both models, the rock material is assumed to be homogenous and isotropic. The main crack (i.e., the pre-crack in the NSCB specimen) and the closest microcracks are included in the numerical analysis. Numerical results show that stress shielding occurs in the model where the two microcracks form an acute angel with the main crack and the nominal fracture toughness is bigger than the intrinsic one, while stress amplification occurs in the model where the microcrack is collinear to the main crack and the nominal fracture toughness is smaller than the intrinsic one. Assuming that the intrinsic fracture toughness of the rock material has the usual loading rate dependency, we are able to reproduce the decreasing trend of the fracture toughness anisotropy as observed from experiments.

Strain Dependence of the Uniaxial Compression Response of Vegetable Shortening

AbstractMany soft food materials, including vegetable shortening, exhibit complex rheological behavior. For shortening, a precise determination of rheological behavior is necessary to understand its functionality as a food ingredient. Commercial vegetable shortening was subjected to monotonic and cyclic uniaxial compression tests at a wide range of loading rates. The elastic modulus determined from unloading was a function of strain, varying between 740 kPa in the shortening's strain hardening region to 220 kPa at large strain where perfect plasticity had developed. Visual analysis of shortening specimens during the compression process showed that a rate‐dependent stress overshoot was attributable to the development of a shear band following strain hardening. An elastoviscoplastic constitutive model was developed to define the complex rate‐dependent compression response of vegetable shortening. Using the fundamental parameters obtained from the different types of compression tests, the proposed model accurately predicted the uniaxial compression response of vegetable shortening over a wide range (three decades) of compression rates. A model with predictive capabilities of large strain properties is desirable because shortening is subject to large strain in essentially all applications.

Mechanical behavior of microstructure engineered multi-length-scale titanium over a wide range of strain rates

In this work, we studied the mechanical behavior of commercial purity Ti powder consolidates with an engineered microstructure containing multiple-length-scale features, over a wide range of loading rates. The microstructural length scales were engineered by mixing powders of different sizes, followed by either hot quasi-isostatic forging (QIF) or spark plasma sintering (SPS). We used electron backscatter diffraction and transmission electron microscopy to examine the microstructure of the Ti materials. A bimodal grain size distribution has been achieved for the majority of the QIFed samples, while those consolidated via SPS exhibit a near-equiaxed morphology. All samples synthesized with powders milled in liquid argon show considerable uniform plastic deformation under quasi-static compression, with no failure, and their strength values are considerably high when compared to those of commercial purity Ti. Moreover, the materials consolidated from milled powders exhibit adiabatic shear banding under high rate uniaxial compression via the Kolsky bar technique. Samples prepared from a preselected proportion of powders milled in liquid nitrogen showed quasi-static strength as high as 2000MPa, and dynamic peak stress as high as 2700MPa, comparable to the strength of high-strength steels. However, these super-strong Ti samples are brittle under both quasi-static and dynamic compression. The strengthening of these Ti materials with an engineered microstructure is primarily attributed to the presence of interstitials. Twins were observed in nanometer-sized grains in the strongest and brittle samples, along with evidence of the TiN phase, which was attributed to exposure to a high level of nitrogen introduced during milling in liquid nitrogen. The high rate behavior can be rationalized on the basis of an adiabatic shear band model that takes into account strain and strain rate hardening.

Temporal peculiarities of brittle fracture of rocks and concrete

When we want to compare the strength of two materials, we compare the table values of quasistatic strength. However results of some experiments show that the strength ratio of the materials can change with increase in rate of loading. Such of material strength at different strain rates is studied in this paper. It is shown that one material can have a lower dynamic strength for a higher static strength compared to the other material. Tests of two different materials, tests of mortar and concrete, and tests of concrete with different water content are considered. It is shown that load-carrying capacity of materials and the substitution effect of material strength in a wide range of loading rates can be predicted by the incubation time criterion.

Nanomechanical Properties of Proteins and Membranes Depend on Loading Rate and Electrostatic Interactions

Knowing the dynamic mechanical response of tissue, cells, membranes, proteins, nucleic acids, and carbohydrates to external perturbations is important to understand various biological and biotechnological problems. Atomic force microscopy (AFM)-based approaches are the most frequently used nanotechnologies to determine the mechanical properties of biological samples that range in size from microscopic to (sub)nanoscopic. However, the dynamic nature of biomechanical properties has barely been addressed by AFM imaging. In this work, we characterizethe viscoelastic properties of the native light-driven proton pump bacteriorhodopsin of the purple membrane of Halobacterium salinarum. Using force-distance curve (F-D)-based AFM we imaged purple membranes while force probing their mechanical response over a wide range of loading rates (from ∼0.5 to 100 μN/s). Our results show that the mechanical stiffness of protein and membrane increases with the loading rate up to a factor of 10 (from ∼0.3 to 3.2 N/m). In addition, the electrostatic repulsion between AFM tip and sample can alter the mechanical stiffness measured by AFM up to ∼60% (from ∼0.8 to 1.3 N/m).These findings indicate that the mechanical response of membranes and proteins and probably of other biomolecular systems should be determined at different loading rates to fully understand their properties.

Static and Dynamic Flexural Strength Anisotropy of Barre Granite

Granite exhibits anisotropy due to pre-existing microcracks under tectonic loadings; and the mechanical property anisotropy such as flexural/tensile strength is vital to many rock engineering applications. In this paper, Barre Granite is studied to understand the flexural strength anisotropy under a wide range of loading rates using newly proposed semi-circular bend tests. Static tests are conducted with a MTS hydraulic servo-control testing machine and dynamic tests with a split Hopkinson pressure bar (SHPB) system. Six samples groups are fabricated with respect to the three principle directions of Barre granite. Pulse shaping technique is used in all dynamic SHPB tests to facilitate dynamic stress equilibrium. Finite element method is utilized to build up equations calculating the flexural tensile strength. For samples in the same orientation group, a loading rate dependence of the flexural tensile strength is observed. The measured flexural tensile strength is higher than the tensile strength measured using Brazilian disc method at given loading rate and this scenario has been rationalized using a non-local failure theory. The flexural tensile strength anisotropy features obvious dependence on the loading rates, the higher the loading rate, the less the anisotropy and this phenomenon may be explained considering the interaction of the preferentially oriented microcracks.

Laboratory measurements of the rate dependence of the fracture toughness anisotropy of Barre granite

Barre granite exhibits strong anisotropy due to its pre-existing microcracks induced by long-term tectonic loading. The quantification of rock anisotropy in fracture properties such as mode-I fracture toughness under a wide range of loading rates is critical to a variety of rock engineering applications. To quantify fracture toughness of Barre granite, notched semi-circular bend (NSCB) fracture tests are conducted statically with an MTS hydraulic servo-control testing machine and dynamically with a split Hopkinson pressure bar (SHPB) system. Barre granite samples are prepared based on the three principal directions, resulting in six orientation sample groups. For dynamic tests, pulse shaping technique is used to achieve dynamic force balance. The finite element method is then implemented to formulate equations relating the failure load to the mode-I fracture toughness using an orthotropic elastic material model. For samples in the same orientation group, the fracture toughness shows clear loading rate dependence, with the fracture toughness increasing with the loading rate. The fracture toughness anisotropy is characterized by the ratio of the largest fracture toughness over the smallest one at a given loading rate. The mode-I fracture toughness anisotropy exhibits a pronounced rate dependence, being strong under static loading while diminishing as the loading rate increases. The mode-I fracture toughness anisotropy may be understood by considering the preferentially oriented microcracks, which will be fully explored in the future.

Uniaxial and biaxial failure behaviors of aluminum alloy foams

Combined shear–tensile test have been performed on a closed-cell aluminum alloy foams with three relative densities over a wide range of loading rates in order to probe their failure behaviors under biaxial loading conditions. Quasi-static uniaxial compressive and tensile tests have also been conducted to investigate uniaxial failure behaviors of the aluminum alloy foams. The materials exhibit uniaxial failure stress asymmetry due to different failure mechanism in the uniaxial tensile and compression. Comparison is made between three phenomenological failure criteria and the measured failure stresses under different loading conditions to verify these criteria. The experimental failure surfaces of the aluminum alloy foams provide support for the three phenomenological failure criteria when suitable Poisson’s ratio is employed. The shape of the experimental failure surface in principal stress plane was not significantly influenced by variation in the relative density. The slight expansion of the failure surfaces with loading rate happened to be isotropic for this investigated closed-cell aluminum alloy foams in combined shear–tensile testes.

Single-molecule force spectroscopy of G-protein-coupled receptors

The applicability of single-molecule force spectroscopy (SMFS) to characterize membrane proteins in vitro is developing rapidly and opening a wide range of fascinating possibilities to study how intra- and intermolecular interactions determine their structural stability and functional state. In particular, understanding how molecular interactions contribute to the functional state of G-protein-coupled receptors (GPCRs) is of importance because they mediate most of our physiological responses and act as therapeutic targets for a broad spectrum of diseases. In our review we focus on SMFS to characterize GPCRs embedded in their physiologically relevant membranes and exposed to physiologically relevant conditions. SMFS uses a molecularly sharp stylus to grasp the terminal end of a GPCR and to quickly unfold the receptor while recording interaction forces. The positional accuracy of SMFS localizes these interactions to structural segments of the GPCR whereas the sensitivity of SMFS enables their stabilizing interaction forces to be quantified. To further investigate the kinetic, energetic and mechanical properties of the structural segments, dynamic SMFS (DFS) probes their stability over a wide range of loading rates. These parameters provide insight into the energy landscape that provides information on the structural and functional properties of the GPCRs. Selected highlights exemplify the application of SMFS to characterize inter- and intramolecular interactions, which change the properties of GPCRs in relation to their functional state (e.g., ligand binding), diseased state (e.g., mutation), or lipid environment such as cholesterol.

A continuum glassy polymer model applicable to dynamic loading

A thermo-mechanical continuum model is proposed that is applicable to dynamically loaded glassy polymers. The underlying theory is based on an ansatz for the Helmholtz free energy where both the deviatoric and the volumetric terms in the free energy have non-equilibrium rate-dependent contributions. The requirement that the free energy is fully rate dependent arises from the desire to model the full range of dynamic conditions ranging from low-rate applications to those common in high-rate shock loading scenarios. A purely equilibrium equation of state (EOS) is found to be insufficient for this purpose. The resulting model suitably captures the thermo-mechanical behavior in both regimes. Polymethylmethacrylate (PMMA) is used as a representative polymer. Analysis is devoted to issues associated with a non-equilibrium equation of state. Because data are insufficient for the full determination of the model's non-equilibrium equation of state, several plausible conditions called the quasi-equilibrium hypothesis are put forth to complete the model. Comparisons of experimental and theoretical results over a wide-range of loading rates and conditions are reported.

Rate limit of protein elastic response is tether dependent

The elastic restoring force of tissues must be able to operate over the very wide range of loading rates experienced by living organisms. It is surprising that even the fastest events involving animal muscle tissues do not surpass a few hundred hertz. We propose that this limit is set in part by the elastic dynamics of tethered proteins extending and relaxing under a changing load. Here we study the elastic dynamics of tethered proteins using a fast force spectrometer with sub-millisecond time resolution, combined with Brownian and Molecular Dynamics simulations. We show that the act of tethering a polypeptide to an object, an inseparable part of protein elasticity in vivo and in experimental setups, greatly reduces the attempt frequency with which the protein samples its free energy. Indeed, our data shows that a tethered polypeptide can traverse its free-energy landscape with a surprisingly low effective diffusion coefficient D(eff) ~ 1,200 nm(2)/s. By contrast, our Molecular Dynamics simulations show that diffusion of an isolated protein under force occurs at D(eff) ~ 10(8) nm(2)/s. This discrepancy is attributed to the drag force caused by the tethering object. From the physiological time scales of tissue elasticity, we calculate that tethered elastic proteins equilibrate in vivo with D(eff) ~ 10(4)-10(6) nm(2)/s which is two to four orders magnitude smaller than the values measured for untethered proteins in bulk.

A Micromechanics Based Constitutive Model for Brittle Failure at High Strain Rates

The micromechanical damage mechanics formulated by Ashby and Sammis, 1990, “The Damage Mechanics of Brittle Solids in Compression,” Pure Appl. Geophys., 133(3), pp. 489–521, and generalized by Deshpande and Evans 2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model,” J. Mech. Phys. Solids, 56(10), pp. 3077–3100. has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated new crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces additional strain-rate sensitivity in the constitutive response. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from ∼10− 6to 103s− 1. Model parameters determined from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent.

Mode I Fracture Characterization of Bituminous Paving Mixtures at Intermediate Service Temperatures

This study presents an integrated approach combining experimental tests and numerical modeling to characterize mode I fracture behavior of bituminous paving mixtures subjected to a wide range of loading rates at intermediate temperature conditions. A simple experimental protocol is developed using the semi-circular bending (SCB) test geometry. The local fracture behavior at the initial notch tip of the SCB specimens is monitored using high-speed cameras with a digital image correlation (DIC) system. The DIC results of the SCB fracture tests are then simulated using a finite element method that is incorporated with material viscoelasticity and cohesive zone fracture. Fracture properties are obtained locally at the notch tip by identifying two cohesive zone fracture parameters (cohesive strength and fracture energy) that result in a good agreement between test results and numerical simulations. The results clearly present significant rate-dependent fracture characteristics of bituminous paving mixtures at intermediate service temperatures. This study further demonstrates that fracture properties of viscoelastic materials need to be characterized at the local fracture process zone when they present ductile fracture behavior.

Inertia effects on characterization of dynamic response of brain tissue

Modeling and simulation of traumatic brain injury (TBI) resulted from collision or blast loading requires characterization of mechanical response over a wide range of loading rates under valid testing conditions. In this study, mechanical response of fresh bovine brain tissue was studied using the two modified Kolsky bar techniques. Radial deformation behavior of annular specimens, which are typically used to characterize the dynamic uniaxial compressive response of biological tissues, was examined using a modified Kolsky bar and a high speed camera to collect images while the specimen deforms at an axial strain rate of 2000s−1. The high-speed images revealed inhomogeneous specimen deformation possibly brought about by radial inertia and causing a multi-axial stress state. To acquire valid stress–strain results that can be used to produce constitutive behavior of the soft materials, a novel torsion technique was developed to obtain pure shear response at dynamic loading rates. Experimental results show clear differences in the material response using the two methods. These results indicate that the previously demonstrated annular specimen geometry aimed at reducing inertia induced stress components for high rate soft materials uniaxial-compressive testing may still possess a significant component of radial inertia induced radial stress which consequently caused the observed inhomogeneous deformation in brain tissue test samples.

Rate effects on the mechanical response of magnesium aluminate spinel

The uniaxial compressive, biaxial flexural strength and fracture toughness of a polycrystalline transparent MgAl 2O 4 spinel were characterized over a wide range of loading rates. The flexural tests were carried out by means of ring-on-ring equibiaxial bending, while the fracture toughness was determined by four-point bending on samples with Chevron notch (CN) configuration. The surface crack (SC) method was also attempted in determining the fracture toughness. Quasi-static experiments were conducted on a servohydraulic testing machine, while the high-rate experiments were performed on a modified Kolsky bar. Results showed that both the failure strength and fracture toughness of the spinel were rate sensitive. Edge beveling in sample preparation did not affect the ring-on-ring flexural strength significantly, and the failure initiation sites were found to be inside the loading ring area regardless of edge conditions. Fracture toughness tests following ASTM standard were largely affected by the inherent coarse microstructure of this material.

Size of the Fracture Process Zone in High-Strength Concrete at a Wide Range of Loading Rates

Compared with the extensive research on properties of the fracture process zone (FPZ) under quasi-static loading conditions, much less information is available on its dynamic characterization, especially for high-strength concrete (HSC). This paper presents the very recent results of an experimental program aimed at disclosing the loading rate effect on the size and velocity of the (FPZ) in HSC. Eighteen three-point bending specimens were conducted under a wide range of loading rates from from 10-4 mm/s to 103 mm/s using either a servo-hydraulic machine or a self-designed drop-weight impact device. Four strain gauges mounted along the ligament of the specimen were used to measure the FPZ size. Surprisingly, the FPZ size remains almost constant (around 20 mm) when the loading rate varies seven orders of magnitude.

Effect of loading rate on fracture characteristics of rock

The three-point bending experiments were applied to investigating effects of loading rates on fracture toughness of Huanglong limestone. The fracture toughness of Huanglong limestone was measured over a wide range of loading rates from 9×10−4 to 1.537 MPa·m1/2/s. According to the approximate relationship between static and dynamic fracture toughness of Huanglong limestone, relationship between the growth velocity of crack and dynamic fracture toughness was obtained. The main conclusions are summarized as follows. (1) When the loading rate is higher than 0.027 MPa·m1/2/s, the fracture toughness of Huanglong limestone increases markedly with increasing loading rate. However, when loading rate is lower than 0.027 MPa·m1/2/s, fracture toughness slightly increases with an increase in loading rate. (2) It is found from experimental results that fracture toughness is linearly proportional to the logarithmic expression of loading rate. (3) For Huanglong limestone, when the growth velocity of crack is lower than 100 m/s, the energy release rate slightly decreases with increasing the growth velocity of crack. However, when the growth velocity of crack is higher than 1 000 m/s, the energy release rate dramatically decreases with an increase in the crack growth velocity.