The effect of strain rate on the mechanical properties of human cortical bone

Bone mechanical properties are typically evaluated at relatively low strain rates. However, the strain rate related to traumatic failure is likely to be orders of magnitude higher and this higher strain rate is likely to affect the mechanical properties. Previous work reporting on the effect of strain rate on the mechanical properties of bone predominantly used nonhuman bone. In the work reported here, the effect of strain rate on the tensile and compressive properties of human bone was investigated. Human femoral cortical bone was tested longitudinally at strain rates ranging between 0.14-29.1 s(-1) in compression and 0.08-17 s(-1) in tension. Young's modulus generally increased, across this strain rate range, for both tension and compression. Strength and strain (at maximum load) increased slightly in compression and decreased (for strain rates beyond 1 s(-1)) in tension. Stress and strain at yield decreased (for strain rates beyond 1 s(-1)) for both tension and compression. In general, there seemed to be a relatively simple linear relationship between yield properties and strain rate, but the relationships between postyield properties and strain rate were more complicated and indicated that strain rate has a stronger effect on postyield deformation than on initiation of yielding. The behavior seen in compression is broadly in agreement with past literature, while the behavior observed in tension may be explained by a ductile to brittle transition of bone at moderate to high strain rates.     

Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure

It is difficult to define the 'physiological' mechanical properties of bone. Traumatic failures in-vivo are more likely to be orders of magnitude faster than the quasistatic tests usually employed in-vitro. We have reported recently [Hansen, U., Zioupos, P., Simpson, R., Currey, J.D., Hynd, D., 2008. The effect of strain rate on the mechanical properties of human cortical bone. Journal of Biomechanical Engineering/Transactions of the ASME 130, 011011-1-8] results from tests on specimens of human femoral cortical bone loaded in tension at strain rates (epsilon ) ranging from low (0.08s(-1)) to high (18s(-1)). Across this strain rate range the modulus of elasticity generally increased, stress at yield and failure and strain at failure decreased for rates higher than 1s(-1), while strain at yield was invariant for most strain rates and only decreased at rates higher than 10s(-1). The results showed that strain rate has a stronger effect on post-yield deformation than on initiation of macroscopic yielding. In general, specimens loaded at high strain rates were brittle, while those loaded at low strain rates were much tougher. Here, a post-test examination of the microcracking damage reveals that microcracking was inversely related to the strain rate. Specimens loaded at low strain rates showed considerable post-yield strain and also much more microcracking. Partial correlation and regression analysis suggested that the development of post-yield strain was a function of the amount of microcracking incurred (the cause), rather than being a direct result of the strain rate (the excitation). Presumably low strain rates allow time for microcracking to develop, which increases the compliance of the specimen, making them tougher. This behaviour confirms a more general rule that the degree to which bone is brittle or tough depends on the amount of microcracking damage it is able to sustain. More importantly, the key to bone toughness is its ability to avoid a ductile-to-brittle transition for as long as possible during the deformation. The key to bone's brittleness, on the other hand, is the strain and damage localisation early on in the process, which leads to low post-yield strains and low-energy absorption to failure.     

Viscoelastic properties of collagen: synchrotron radiation investigations and structural model

Collagen type I is the most abundant structural protein in tendon, skin and bone, and largely determines the mechanical behaviour of these connective tissues. To obtain a better understanding of the relationship between structure and mechanical properties, tensile tests and synchrotron X-ray scattering have been carried out simultaneously, correlating the mechanical behaviour with changes in the microstructure. Because intermolecular cross-links are thought to have a great influence on the mechanical behaviour of collagen, we also carried out experiments using cross-link-deficient tail-tendon collagen from rats fed with beta-APN, in addition to normal controls. The load-elongation curve of tendon collagen has a characteristic shape with, initially, an increasing slope, corresponding to an increasing stiffness, followed by yielding and then fracture. Cross-link-deficient collagen produces a quite different curve with a marked plateau appearing in some cases, where the length of the tendon increases at constant stress. With the use of in situ X-ray diffraction, it was possible to measure simultaneously the elongation of the collagen fibrils inside the tendon and of the tendon as a whole. The overall strain of the tendon was always larger than the strain in the individual fibrils, which demonstrates that some deformation is taking place in the matrix between fibrils. Moreover, the ratio of fibril strain to tendon strain was dependent on the applied strain rate. When the speed of deformation was increased, this ratio increased in normal collagen but generally decreased in cross-link-deficient collagen, correlating to the appearance of a plateau in the force-elongation curve indicating creep. We proposed a simple structural model, which describes the tendon at a hierarchical level, where fibrils and interfibrillar matrix act as coupled viscoelastic systems. All qualitative features of the strain-rate dependence of both normal and cross-link-deficient collagen can be reproduced within this model. This complements earlier models that considered the next smallest level of hierarchy, describing the deformation of collagen fibrils in terms of changes in their molecular packing.     

Study of biodegradable polylactide/poly(butylene adipate-co-terephthalate) blends

Both polylactide (PLA) and poly(butylene adipate-co-terephthalate) (PBAT) are biodegradable polymers. They are thermoplastics which can be processed using most conventional polymer processing methods. PLA is high in strength and modulus (63 MPa and 3.4 GPa, respectively) but brittle (strain at break 3.8%) while PBAT is flexible and tough (strain at break approximately 710%). In view of their complementary properties, blending PLA with PBAT becomes a natural choice to improve PLA properties without compromising its biodegradability. In this study, PLA and PBAT were melt blended using a twin screw extruder. Melt elasticity and viscosity of the blends increased with the concentration of PBAT. Crystallization of the PLA component, phase morphology of the blend, mechanical properties, and toughening mechanism were investigated. The blend comprised an immiscible, two-phase system with the PBAT evenly dispersed in the form of approximately 300 nm domains within the PLA matrix. The PBAT component accelerated the crystallization rate of PLA but had little effect on its final degree of crystallinity. With the increase in PBAT content (5-20 wt %), the blend showed decreased tensile strength and modulus; however, elongation and toughness were dramatically increased. With the addition of PBAT, the failure mode changed from brittle fracture of the neat PLA to ductile fracture of the blend as demonstrated by tensile test and scanning electron microcopy (SEM) micrographs. Debonding between the PLA and PBAT domains induced large plastic deformation in PLA matrix ligaments.     

Increasing strain and strain rate strengthen transient stiffness but weaken the response to subsequent compression for articular cartilage in unconfined compression

Strain amplitude and strain rate dependent nonlinear behavior and load-induced mechanical property alterations of full-thickness bovine articular cartilage attached to bone were investigated in unconfined compression. A sequence of test compressions of finite deformation (ranging from 0.9% to 34.5% nominal strain) was performed at strain rates ranging from approximately 0.053%/s to 5.8%/s. Peak and equilibrium loads were analyzed to determine strain amplitude and strain rate dependence of linear versus nonlinear responses. The test protocol was designed to reveal changes in mechanical properties due to these finite deformations by interspersing small-amplitude witness ramps of approximately 1.1% deformation and approximately 0.44%/s strain rate between the test ramps ("witness" meaning to assess any mechanical property changes). We found that peak loads displayed high nonlinearity, stiffening with both increasing compression amplitude and more so with increasing strain rate. The response to witness ramps suggested that mechanical weakening occurred when compression amplitude reached 1.9-2.9% strain and beyond, and that weakening was much more significant at higher strain rate. These findings delineate regimes of linear versus nonlinear behavior of cartilage, and indicate the types of loads which can cause mechanical property alterations. Biological implications of this study are that strain amplitude and strain rate dependent stiffening may be essential to bear physiological loads and to protect cells and matrix from mechanical damage. Structural changes reflected by mechanical weakening at small compression could also initiate remodeling or disease processes.     

The mechanical behaviour of brain tissue: large strain response and constitutive modelling

The non-linear mechanical behaviour of porcine brain tissue in large shear deformations is determined. An improved method for rotational shear experiments is used, producing an approximately homogeneous strain field and leading to an enhanced accuracy. Results from oscillatory shear experiments with a strain amplitude of 0.01 and frequencies ranging from 0.04 to 16 Hz are given. The immediate loss of structural integrity, due to large deformations, influencing the mechanical behaviour of brain tissue, at the time scale of loading, is investigated. No significant immediate mechanical damage is observed for these shear deformations up to strains of 0.45. Moreover, the material behaviour during complex loading histories (loading-unloading) is investigated. Stress relaxation experiments for strains up to 0.2 and constant strain rate experiments for shear rates from 0.01 to 1 s(-1) and strains up to 0.15 are presented. A new differential viscoelastic model is used to describe the mechanical response of brain tissue. The model is formulated in terms of a large strain viscoelastic framework and considers non-linear viscous deformations in combination with non-linear elastic behaviour. This constitutive model is readily applicable in three-dimensional head models in order to predict the mechanical response of the intra-cranial contents due to an impact.     

Visualization of a phantom post-yield deformation process in cortical bone

A prominent opacity is evident in the process zone of notched thin wafers of bone loaded in tension. Being recoverable upon unloading, this opaque zone can be stained only when the sample is under load, unlike the classically reported forms of damage which take up the stain in the unloaded state. Furthermore, despite the stain uptake, microcracks are absent in the stained area examined by high magnification optical microscopy and atomic force microscopy (AFM). Therefore, the size scale and the electric charge of the features involved in the process zone were probed at the submicron level by using a wide range of fluorescent dyes of different molecular weights and charges. It was observed that negatively charged dyes penetrate the process zone and that dyes greater than 10 kDa (about 10–20 nm in size) were unable to label the process zone. Digital image correlation (DIC) measurements indicated that the opacity initiates at about 1% principal strain and the strain accumulates up to 14%. While the opacity was largely recoverable upon unloading, the core regions which experienced large strains had permanent residual strains up to 2%, indicating that the observed deformation phenomenon can be interlocked within bone matrix without the formation of microcracks. Based on the similarity of size and their known affinity for negatively charged species, exposure of mineral nanoplatelets is proposed as prime candidates. Therefore, the deformation process reported here may be associated with debonding of mineral crystals from the neighboring collagen molecules. Overall, post-yield deformation of bone at the micron scale takes place by large strain events which are accommodated in bone matrix by the generation of nanoscale positively charged interfaces.     

Mechanical properties of armchair silicene nanoribbons with edge cracks: a molecular dynamics study

Silicene has been proven to be a promising material with attractive electronic properties. During the synthesis of silicene, structural defects such as edge crack are likely to be generated and such defects in silicene have impacts on its properties. Herein, molecular dynamics simulations were performed to investigate the mechanical properties of the armchair silicene nanoribbons (ASiNRs) with edge cracks. Our results showed that the mechanical properties of the ASiNRs decrease because of the existence of edge crack. Both the pristine ASiNRs and the ASiNRs with edge cracks show brittle fracture behaviours. The crack length plays an important role in determining the critical strain and fracture strength of the ASiNRs. Moreover, we investigated the effects of strain rate and temperature on the mechanical properties of the ASiNRs with edge cracks. We observed that the increasing strain rate increases the critical strain and fracture strength while decreasing the Young’s modulus. Low-strain rates also changes the expanded directions of cracks in the ASiNRs. We also found that the increasing temperature could significantly decrease the mechanical properties of the ASiNRs with edge cracks.     

Mechanical properties of brain tissue in tension

This paper contains experimental results of in vitro, uniaxial tension of swine brain tissue in finite deformation as well as proposes a new hyper-viscoelastic constitutive model for the brain tissue. The experimental results obtained for two loading velocities, corresponding to strain rates of 0.64 and 0.64 x 10(-2)s(-1), are presented. We believe that these are the first ever experiments of this kind. The applied strain rates were similar to those applied in our previous study, focused on explaining brain tissue properties in compression. The stress-strain curves are convex downward for all extension rates. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. Swine brain tissue was found to be considerably softer in extension than in compression. Previously proposed in the literature brain tissue constitutive models, developed based on experimental data collected in compression are shown to be inadequate to explain tissue behaviour in tension. A new, non-linear, viscoelastic model based on the generalisation of the Ogden strain energy hyper-elastic constitutive equation is proposed. The new model accounts well for brain tissue deformation behaviour in both tension and compression (natural strain in <-0.3,0.2>) for strain rates ranging over five orders of magnitude.     

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.     

Effect of strain rate on the fracture behaviour of skin

The effect of strain rate on the stress-strain behaviour of skin is studied. It is observed that the plastic set in the skin is dependent on strain rate. The scanning electron micrographs of the fractured skin sample shows thicker fibrils and thinner one at low strain rates. The plastic flow is clearly brought out in the stress-strain curves at different strain rates. The stress relaxation behaviour at any given strain is clearly brought out in the 3-dimensional plot.     

Measurement of the circumferential mechanical properties of the umbilical vein: experimental and numerical analyses

Coronary artery disease is responsible for almost 30% of all deaths worldwide. The saphenous vein and umbilical vein (UV) are the most common veins using for treatment as a coronary artery bypass graft (CABG). The mechanical properties of UV belonging to its long-term patency for CABG are very important. However, there is a lack of knowledge on the linear elastic and nonlinear hyperelastic mechanical properties of the UV. In this study, three stress definitions (second Piola–Kichhoff stress, engineering stress and true stress) and four strain definitions (Almansi–Hamel strain, Green–St Venant strain, engineering strain and true strain) are used to determine the elastic modulus, maximum stress and strain of eight human UVs under circumferential loading. The nonlinear mechanical behaviour of the UV is computationally investigated using Mooney–Rivlin hyperelastic model. A numerical finite element analysis is also carried out to simulate the constitutive modelling versus its numerical results. The results show that the Almansi–Hamel strain definition overestimates the elastic modulus while Green–St Venant strain definition underestimates the elastic modulus at different stress definitions. The true stress–true strain definition, which gives more accurate measurements of the tissue's response using the instantaneous values, reveals the Young's modulus and maximum stress of 2.18 and 6.01 MPa, respectively. The Mooney–Rivlin material model is well represented by the nonlinear mechanical behaviour of the UV. The findings of this study could have implications not only for understanding the extension and rupture mechanism of UV but also for interventions and surgeries, including balloon angioplasty, bypass and stenting.     

High strain rate response of rabbit femur bones

Strain rate dependence of the mechanical response of hard tissues has led to a keen interest in their dynamic properties. The current study attempts to understand the high strain rate characteristics of rabbit femur bones. The testing was conducted using a split-Hopkinson pressure bar equipped with a high speed imaging system to capture the fracture patterns. The bones were also characterized under quasi-static compression to enable comparison with the high strain rate results. The quasi-static compressive moduli of the epiphyseal and diaphyseal regions were measured to be in the range of 2–3 and 5–7 GPa, respectively. Under high strain rate loading conditions the modulus is observed to increase with strain rate and attains values as high as 15 GPa for epiphyseal and 30 GPa for diaphyseal regions of the femur. The strength at high strain rate was measured to be about twice the quasi-static strength value. A large number of small cracks initiated on the specimen surface close to the incident bar. Coalescence of crack branches leading to fewer large cracks resulted in specimen fragmentation. In comparison, the quasi-static failure was due to shear cracking.     

Novel biobased nanocomposites from soybean oil and functionalized organoclay

Novel biobased nanocomposites have been prepared by the cationic polymerization of conjugated soybean oil (CSOY) or conjugated LoSatSoy oil (CLS) with styrene (ST) and divinylbenzene (DVB), and a reactive organomodified montmorillonite (VMMT) clay as a reinforcing phase. This filler has been prepared by the cationic exchange of sodium montmorillonite with (4-vinylbenzyl)triethylammonium chloride in aqueous solution. The nanostructures of the nanocomposites have been determined by using wide-angle X-ray diffraction (WAXD) and transmission electron microscopy (TEM), respectively. The results from WAXD and TEM indicate that a heterogeneous structure consisting of intercalation and partial exfoliation or an intercalation structure exists in the nanocomposites, depending on the amount of VMMT in the polymer matrix. The thermal, mechanical, and organic vapor barrier properties of the nanocomposites have been evaluated by dynamic thermal analysis, thermogravimetric analysis, mechanical testing, and toluene absorption. A significant improvement is observed in the thermal stability, the dynamic bending storage modulus, the compressive modulus, the compressive strength, the compressive strain at failure, and the vapor barrier performance for the CSOY-- and CLS-based nanocomposites with 1-2 wt % VMMT loading, where some individual exfoliated silicate platelets occur. For example, the CLS-based nanocomposite with 1-2 wt % VMMT exhibits increases of 100-128%, 86-92%, and 5-7% in compressive modulus, compressive strength, and compressive strain at failure, respectively. CLS with higher unsaturation and reactivity affords nanocomposites with higher thermal stability and higher mechanical properties than CSOY.     

An inverse approach for the mechanical characterisation of vascular tissues via a generalised rule of mixtures

Mechanical factors such as stresses and strains play a major role in the growth and remodelling of soft biological tissues. The main constituents of tissue undergo different processes reacting to mechanical stimulus. Thereby, the characterisation of growth and remodelling requires an accurate estimation of the stresses and strains of their main components. Many soft tissues can be considered as composite materials and can be analysed using an appropriate rule of mixtures. Particularly, arterial tissue can be modelled as an isotropic soft matrix reinforced with preferentially oriented collagen fibres. An inverse approach to obtain the mechanical characterisation of each main component is proposed in this work. The procedure is based on a rule of mixtures raised in a finite deformation framework and generalised to include kinematics and compatibility equations for serial–parallel behaviour. This methodology allows obtaining the stress–strain relationship of the components fitting experimental data.     

Molecular dynamics simulations of structural instability of fullerene family under tension force

Fullerene molecules are cage-like nanoscopic structures with pentagonal and hexagonal faces. In practical applications such as fullerene-reinforced nanocomposites (FRNCs), these structures may be subjected to tension force. In this research, we employ molecular dynamics (MD) simulation to compute the behaviour and deformation of different fullerene molecules, ranging from C₆₀ to C₂₀₀₀, under tension force. To model the interactions between carbon atoms in the MD simulations, the adaptive intermolecular reactive bond order (AIREBO) force field is used. The displacement–force and the displacement–strain energy curves are obtained. It is observed that a new type of structural instability occurs in the fullerene molecules when the applied tension force increases. This abnormal structural instability in the fullerenes is investigated for the first time in the literature. The critical tensile forces and the corresponding mode shapes are determined for different fullerenes. The results indicate that the critical forces and deformations strongly depend upon the number of carbon atoms.     

Deformation mechanisms in nanotwinned γ-TiAl by molecular dynamics simulation

ABSTRACT

In this work, the plastic deformation mechanisms and fracture toughness of nanotwinned γ-TiAl with different twin boundary (TB) spacing are investigated by using molecular dynamics simulation. The simulation results reveal that there are pronounced shifts in the mechanical behaviour of nanotwinned γ-TiAl when the TB spacing is 3.50, 4.20 and 4.90?nm. In addition, the variation of the dislocation density with strain at these three TB spacing illustrates that a smaller TB spacing induces a higher dislocation density. Different TB spacing has an influence on the dislocation behaviour. The dislocation pile-up, dislocation–dislocation, dislocation–twin and twin–twin reactions, hierarchical twins including their generation and density, step formation, dislocation emission from steps and TB migration are the main plastic deformation mechanisms. The results also show that TB migration, twinning formation and interaction of crack and TB dominate the deformation mechanism of nanotwinned γ-TiAl with crack. The generation of hierarchical twins, lower distance between crack surface plane and twin plane, dislocation–twin, twin–twin interaction and crack deflection increase the fracture toughness of nanotwinned γ-TiAl.     

Poroelastic Mechanical Effects of Hemicelluloses on Cellulosic Hydrogels under Compression

Hemicelluloses exhibit a range of interactions with cellulose, the mechanical consequences of which in plant cell walls are incompletely understood. We report the mechanical properties of cell wall analogues based on cellulose hydrogels to elucidate the contribution of xyloglucan or arabinoxylan as examples of two hemicelluloses displaying different interactions with cellulose. We subjected the hydrogels to mechanical pressures to emulate the compressive stresses experienced by cell walls in planta. Our results revealed that the presence of either hemicellulose increased the resistance to compression at fast strain rates. However, at slow strain rates, only xyloglucan increased composite strength. This behaviour could be explained considering the microstructure and the flow of water through the composites confirming their poroelastic nature. In contrast, small deformation oscillatory rheology showed that only xyloglucan decreased the elastic moduli. These results provide evidence for contrasting roles of different hemicelluloses in plant cell wall mechanics and man-made cellulose-based composite materials.     

A molecular dynamics investigation on the compression of cross-linked epoxy resins

Molecular dynamics method is employed to simulate the compression deformation of the polymer materials for electronic packaging. The effects of moisture content, conversion degree, strain rate and temperature on the mechanical properties of epoxy resin are investigated. The stress–strain curves, Young's modulus and Poisson ratio are compared with existing experimental data. The results show that mechanical properties of epoxy resin decrease obviously with increasing moisture content and temperature. However, the high cross-linking conversion and strain rate enhance the mechanical properties of resin.     

Mechanical properties of a mature biofilm from a wastewater system: from microscale to macroscale level

A fundamental understanding of biofilm mechanical stability is critical in order to describe detachment and develop biofouling control strategies. It is thus important to characterise the elastic deformation and flow behaviour of the biofilm under different modes of applied force. In this study, the mechanical properties of a mature wastewater biofilm were investigated with methods including macroscale compression and microscale indentation using atomic force microscopy (AFM). The mature biofilm was found to be mechanically isotropic at the macroscale level as its mechanical properties did not depend on the scales and modes of loading. However, the biofilm showed a tendency for mechanical inhomogeneity at the microscale level as indentation progressed deeper into the matrix. Moreover, it was observed that the adhesion force had a significant influence on the elastic properties of the biofilm at the surface, subjected to microscale tensile loading. These results are expected to inform a damage-based model for biofilm detachment.