Still rethinking the value of high wood density

? Premise of the study: In a previous paper, we questioned the traditional interpretation of the advantages and disadvantages of high wood density (Functional Ecology 24: 701-705). Niklas and Spatz (American Journal of Botany 97: 1587-1594) challenged the biomechanical relevance of studying properties of dry wood, including dry wood density, and stated that we erred in our claims regarding scaling. ? Methods: We first present the full derivation of our previous claims regarding scaling. We then examine how the fresh modulus of rupture and the elastic modulus scale with dry wood density and compare these scaling relationships with those for dry mechanical properties, using almost exactly the same data set analyzed by Niklas and Spatz. ? Key results: The derivation shows that given our assumptions that the modulus of rupture and elastic modulus are both proportional to wood density, the resistance to bending is inversely proportional to wood density and strength is inversely proportional with the square root of wood density, exactly as we previously claimed. The analyses show that the elastic modulus of fresh wood scales proportionally with wood density (exponent 1.05, 95% CI 0.90-1.11) but that the modulus of rupture of fresh wood does not, scaling instead with the 1.25 power of wood density (CI 1.18-1.31). ? Conclusions: The deviation from proportional scaling for modulus of rupture is so small that our central conclusion remains correct: for a given construction cost, trees with lower wood density have higher strength and higher resistance to bending.     

Theoretical Prediction and Experimental Testing of Mechanical Properties for 3D Printed Silk Fibroin-Type II Collagen Scaffolds for Cartilage Regeneration

Silk fibroin-typeⅡcollagen scaffold was made by 3D printing technique and freeze-drying method, and its mechanical properties were studied by experiments and theoretical prediction. The results show that the three-dimensional silk fibroin-typeⅡ collagen scaffold has good porosity and water absorption, which is (89.3%+3.26%) and (824.09%+93.05%), respectively. With the given strain value, the stress of scaffold decreases rapidly firstly and then tends to be stable during the stress relaxation. Both initial and instantaneous stresses increase with increase of applied strain value. The creep strains of scaffold with different stress levels show the two stages: the rapidly increasing stage and the second stable stage. It is noted that the scaffold with compressive stress of less than 35 kPa can recover when the compressive stress is removed. However when the compressive stress is higher than 50 kPa, the scaffold is damaged and its structure is destroyed. Not only the compressive property but tensile property of scaffold are dependent on the applied displacement rate or strain rate. Its compressive elastic modulus and tensile modulus increase with increase of strain rate or displacement rate. The nonlinear relaxation model and creep model were constructed respectively and applied to predict the stress relaxation behavior and creep behavior of scaffold. It is found that there are good agreements between the experimental data and predictions, which mean that the built theoretical model can predict the mechanical behavior of scaffold.     

Continuum damage mechanics (CDM) modelling demonstrates that ligament fatigue damage accumulates by different mechanisms than creep damage

Ligaments can be subjected to creep and fatigue damage when loaded to higher than normal stresses due to injury of a complementary joint restraint. Continuum damage mechanics (CDM) assumes that diffuse damage accumulates in a material, thereby reducing the effective cross-sectional area and leading to eventual rupture. The objective of this study was to apply CDM modelling to ligament creep and fatigue to reveal mechanisms of damage. Fatigue was modelled by cyclically varying the stress in the creep model. A few novel approaches were used. First, area reduction was not assumed equal to modulus reduction; thus, allowing damaged fibres to potentially contribute to load-bearing through the extracellular matrix. Modulus ratio was related to area reduction using residual strength. Second, damage rate was not assumed constant but rather was determined directly from the modulus ratio change with respect to time. Third, modulus ratio was normalized to maximum modulus to avoid artificial calculation of negative damage. With this approach, the creep time-to-rupture was predicted with -4% error at 60% UTS and -13% error at 30% UTS. At 15% UTS, no test was undertaken experimentally for a duration as long as the 24 days predicted theoretically. Oscillating the time-dependent damage in the creep model could not completely explain the fatigue behaviour because the fatigue time-to-rupture was predicted with over 1300% error at all stresses. These results suggest that a cycle-dependent damage mechanism, in addition to a time-dependent one, was responsible for fatigue rupture. Cycle-dependent damage may be an important consideration for rehabilitation activities following injury of a complementary ligament restraint.     

On the sensitivity of wall stresses in diseased arteries to variable material properties

Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.     

Atomistic Simulations of Uniaxial Tensile Behaviors of Single-walled Carbon Nanotubes

Atomistic simulations, using the second-generation reactive empirical bond order (REBO) potential, are performed to investigate the uniaxial tensile behaviors of single-walled carbon nanotubes (SWCNTs). It is found that the effect of the nanotube diameters on the elastic modulus, the tensile strength and the stress vs. strain relation of SWCNTs is small yet noticeable. However, the effect of the degree of helicity is significant.     

Mechanical properties of the dog renal capsule.

The renal capsule is an important determinant of whole kidney volume/pressure relationships. To gain further insights into its possible role we examined the mechanical properties of the dog renal capsule using standard materials testing procedures. From each of four locations on the kidney surface, the following mechanical properties of the renal capsule were determined: elastic modulus (force/unit of cross-sectional area theoretically required to double the length of the specimen), tensile stiffness (force/unit width theoretically required to double the length of the specimen), ultimate strength (stress at time of fracture of the specimen), and maximum strain (percent strain at time of the fracture of the specimen). We found that the elastic modulus of the renal capsule from all capsular sites was substantially greater than values previously reported for dog aorta. The stiffness of the capsule covering the anterior-posterior surface of the kidney was found to be about 50% greater than the stiffness of the capsule covering the lateral and polar surfaces of the kidney. The ultimate strength of the anterior-posterior capsule was significantly greater than that of the lateral or polar capsule. This finding may explain the clinical observation that the spontaneous rupture of the renal capsule and parenchyma associated with the acute swelling of transplant rejection is confined almost exclusively to the lateral and polar portions of the renal capsule and cortex. The mean maximum strain at each capsular site was about 35%. This degree of circumferential expansion corresponds to about a doubling of kidney volume. Thus, this observation suggests that the renal capsule is at risk to undergo spontaneous rupture when renal volume increases of this magnitude are observed.     

Stress transfer in collagen fibrils reinforcing connective tissues: effects of collagen fibril slenderness and relative stiffness

Unlike engineering fibre composite materials which comprise of fibres that are uniform cylindrical in shape, collagen fibrils reinforcing the proteoglycan-rich (PG) gel in the extra-cellular matrices (ECMs) of connective tissues are taper-ended (paraboloidal in shape). In an earlier paper we have discussed how taper of a fibril leads to an axial stress up-take which differs from that of a uniform cylindrical fibre and implications for fibril fracture. The present paper focuses on the influence of fibre aspect ratio, q (slenderness), and Young's modulus (stiffness), relative to that of the gel phase, E(R), on the magnitude of the axial tensile stresses generated within a fibril and wider implications on failure at tissue level. Fibre composite models were evaluated using finite element (FE) and mathematical analyses. When the applied force is low, there is elastic stress transfer between the PG gel and a fibril. FE modelling shows that the stress in a fibril increases with E(R) and q. At higher applied forces, there is plastic stress transfer. Mathematical modelling predicts that the stress in a fibril increases linearly with q. For small q values, fibrils may be regarded as fillers with little ability to provide tensile reinforcement. Large q values lead to high stress in a fibril. Such high stresses are beneficial provided they do not exceed the fracture stress of collagen. Modulus difference regulates the strain energy release density, u, for interfacial rupture; large E(R) not only leads to high stress in a fibril but also insures against interfacial rupture by raising the value of u.     

Rheological properties and mechanical stability of new gel-entrapment systems applied in bioreactors

The mechanical stability of gels applied for entrapment and retention of biocatalysts in bioreactors is of crucial importance for successful scale-up applications. Gel abrasion in agitated reactors will depend on liquid shear, bubble shear, and wall shear, as well as collisions between the gel particles. As a simplified standardized model system, abrasion of gel beads was studied in 1-m-high bubble columns with controlled aeration, and quantified by measuring the loss of gel material into solution. Gel beads were also taken out to measure stress-strain response during controlled compression. More general rheological properties of different gels were studied by applying a variety of regimes of controlled compression of standardized gel cylinders: Gel strength was measured by recording the fracture properties and the Young's modulus. Viscoelastic properties were revealed by recording creep during compression as well as recovery after compression. Oscillation tests up to 1000 cyclic compressions were applied to compare the fatigue of different gels. Results obtained for Ca-alginate gels, gels of chemically modified polyvinyl alcohol with stilbazolium groups (PVA-SbQ) as well as mixed gels of Ca-alginate and PVA-SbQ are compared with previously published data for kappa-carrageenan, agar, and polyethylene glycol (PEG) gels. It is concluded that material fatigue rather than mechanical properties such as stiffness or fracture stress should be considered when selecting a suitable gel material on the basis of abrasion resistance. The very soft and superelastic PVA-SbQ gel showed no significant fatigue in mechanical tests and no abrasion was detected in the standardized model system used. Ca-alginate gels, however, showed severe irreversible changes due to fatigue at oscillating loads and creep at constant load. Due to their similarities with kappa-carrageenan gels in mechanical tests, it is likely that Ca-alginate would also be sensitive to abrasion. Mixed gels of Ca-alginate and PVA-SbQ represent a complex system with intermediate properties, showing significant fatigue and creep, but elastic properties from the PVA-SbQ gel make it less sensitive than the pure Ca-alginate gel.     

Kinetics of the Multistep Rupture of Fibrin ‘A-a’ Polymerization Interactions Measured Using Atomic Force Microscopy

Fibrin, the structural scaffold of blood clots, spontaneously polymerizes through the formation of ‘A-a’ knob-hole bonds. When subjected to external force, the dissociation of this bond is accompanied by two to four abrupt changes in molecular dimension observable as rupture events in a force curve. Herein, the configuration, molecular extension, and kinetic parameters of each rupture event are examined. The increases in contour length indicate that the D region of fibrinogen can lengthen by ∼50% of the length of a fibrin monomer before rupture of the ‘A-a’ interaction. The dependence of the dissociation rate on applied force was obtained using probability distributions of rupture forces collected at different pull-off velocities. These distributions were fit using a model in which the effects of the shape of the binding potential are used to quantify the kinetic parameters of forced dissociation. We found that the weak initial rupture (i.e., event 1) was not well approximated by these models. The ruptured bonds comprising the strongest ruptures, events 2 and 3, had kinetic parameters similar to those commonly found for the mechanical unfolding of globular proteins. The bonds ruptured in event 4 were well described by these analyses, but were more loosely bound than the bonds in events 2 and 3. We propose that the first event represents the rupture of an unknown interaction parallel to the ‘A-a’ bond, events 2 and 3 represent unfolding of structures in the D region of fibrinogen, and event 4 is the rupture of the ‘A-a’ knob-hole bond weakened by prior structural unfolding. Comparison of the activation energy obtained via force spectroscopy measurements with the thermodynamic free energy of ‘A-a’ bond dissociation indicates that the ‘A-a’ bond may be more resistant to rupture by applied force than to rupture by thermal dissociation.     

Influence of odd and even number of Stone–Wales defects on the fracture behaviour of an armchair single-walled carbon nanotube under axial and torsional strain

Using Brenner's bond-order potential to represent the interaction of the in-plane C–C bond, an armchair (8,8) single-walled carbon nanotube is investigated by molecular dynamics simulation under axial loading and twist, both for perfect and imperfect lattices introducing an increasing number of Stone–Wales (SW) defects. The Young modulus, shear modulus, tensile strength, shear strength, ductility, stiffness and toughness are computed. All the mechanical characteristics are found to change appreciably by the inclusion of SW defects. Two distinct patterns of fracture mode are observed with odd and even numbers of defects. A clear evidence of the defect–defect interaction is observed when more than one defect is included.     

Experimental study in rat metatarsals to determine whether callus vascularity is an indicator of the mechanical strength of healing fractures

Changes in the mechanical properties and percentage area of blood vessels of healing fracture callus were followed using rat metatarsals. By 24 weeks after fracture the mean ultimate tensile stress and elastic modulus were still less than half that of the contralateral unfractured bone, whereas the mean torsional modulus had almost reached that of the unfractured bone. The percentage area of blood vessels declined from five days post-fracture and showed no changes which coincided with the increases in mechanical strength or moduli. We conclude that studies of vascularity would not justify a prediction of the strength of a healing fracture.     

Effects of multiple-bond ruptures on kinetic parameters extracted from force spectroscopy measurements: revisiting biotin-streptavidin interactions

Force spectroscopy measurements of the rupture of the molecular bond between biotin and streptavidin often results in a wide distribution of rupture forces. We attribute the long tail of high rupture forces to the nearly simultaneous rupture of more than one molecular bond. To decrease the number of possible bonds, we employed hydrophilic polymeric tethers to attach biotin molecules to the atomic force microscope probe. It is shown that the measured distributions of rupture forces still contain high forces that cannot be described by the forced dissociation from a deep potential well. We employed a recently developed analytical model of simultaneous rupture of two bonds connected by polymer tethers with uneven length to fit the measured distributions. The resulting kinetic parameters agree with the energy landscape predicted by molecular dynamics simulations. It is demonstrated that when more than one molecular bond might rupture during the pulling measurements there is a noise-limited range of probe velocities where the kinetic parameters measured by force spectroscopy correspond to the true energy landscape. Outside this range of velocities, the kinetic parameters extracted by using the standard most probable force approach might be interpreted as artificial energy barriers that are not present in the actual energy landscape. Factors that affect the range of useful velocities are discussed.     

Molecular friction in an actomyosin molecular machine

In muscle contraction, it has been widely recognized that a binding state exists between myosin and actin in the presence of Mg-ATP. To estimate the magnitude of binding strength, I introduce a concept of frictional phenomena which occurs between two sliding bodies in contact each other. In such cases, the sliding speed can be formulated as a function of the actin-myosin bond strength. In order to validate this, the present theory is applied for the two movement assay systems with no external load; one movement assay of Phalloidin Rhodamine bound F-actin on a myosin coated hydrophobic cover glass and another assay of myosin coated beads along actin cables of Nitella. If a coefficient of 0.005 is applied to the kinetic friction, 1pN for the sliding force per cross-bridge and 10 microns sec-1 for the sliding speed, it is found that the bond strength between actin and one myosin head is about 200 pN in the contracting state.     

Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles

Both elastic modulus and fracture stress are known to increase with the amount of mineral deposited within collagen fibrils. Current mechanical models of mineralized fibrils, where mineral platelets are arranged in parallel arrays, reproduce the first effect but fail to predict an increase in fracture stress. Here, we propose a model with a staggered array of platelets that is in better agreement with results on molecular packing in collagen fibrils and that accounts for an increase of both elastic modulus and fracture stress with the amount of mineral in the fibril. Finally, we explore the dependence of the mechanical properties within the model, when the degree of mineralization and the thickness of the platelets as well as their distance varies.     

Is callus calcium content an indicator of the mechanical strength of healing fractures? An experimental study in rat metatarsals

Changes in the mechanical properties and the calcium content of healing fracture callus were followed, using rat metatarsals. By 24 weeks post-fracture the mean ultimate tensile stress and elastic modulus were still less than half that of the contralateral unfractured bone, whereas the mean torsional modulus had almost reached that of the unfractured bone. The calcium content of the callus formed immediately between the fractured ends of the bone showed changes which coincided with the increases in mechanical strength and the moduli, thus measurement of callus calcium content would enable the prediction of the strength of a healing fracture.     

Coupling field theory with mesoscopic dynamical simulations of multicomponent lipid bilayers

A method for simulating a two-component lipid bilayer membrane in the mesoscopic regime is presented. The membrane is modeled as an elastic network of bonded points; the spring constants of these bonds are parameterized by the microscopic bulk modulus estimated from earlier atomistic nonequilibrium molecular dynamics simulations for several bilayer mixtures of DMPC and cholesterol. The modulus depends on the composition of a point in the elastic membrane model. The dynamics of the composition field is governed by the Cahn-Hilliard equation where a free energy functional models the coupling between the composition and curvature fields. The strength of the bonds in the elastic network are then modulated noting local changes in the composition and using a fit to the nonequilibrium molecular dynamics simulation data. Estimates for the magnitude and sign of the coupling parameter in the free energy model are made treating the bending modulus as a function of composition. A procedure for assigning the remaining parameters in the free energy model is also outlined. It is found that the square of the mean curvature averaged over the entire simulation box is enhanced if the strength of the bonds in the elastic network are modulated in response to local changes in the composition field. We suggest that this simulation method could also be used to determine if phase coexistence affects the stress response of the membrane to uniform dilations in area. This response, measured in the mesoscopic regime, is already known to be conditioned or renormalized by thermal undulations.     

Effects of wall calcifications in patient-specific wall stress analyses of abdominal aortic aneurysms

It is generally acknowledged that rupture of an abdominal aortic aneurysm (AAA) occurs when the stress acting on the wall over the cardiac cycle exceeds the strength of the wall. Peak wall stress computations appear to give a more accurate rupture risk assessment than AAA diameter, which is currently used for a diagnosis. Despite the numerous studies utilizing patient-specific wall stress modeling of AAAs, none investigated the effect of wall calcifications on wall stress. The objective of this study was to evaluate the influence of calcifications on patient-specific finite element stress computations. In addition, we assessed whether the effect of calcifications could be predicted directly from the CT-scans by relating the effect to the amount of calcification present in the AAA wall. For 6 AAAs, the location and extent of calcification was identified from CT-scans. A finite element model was created for each AAA and the areas of calcification were defined node-wise in the mesh of the model. Comparisons are made between maximum principal stress distributions, computed without calcifications and with calcifications with varying material properties. Peak stresses are determined from the stress results and related to a calcification index (CI), a quantification of the amount of calcification in the AAA wall. At calcification sites, local stresses increased, leading to a peak stress increase of 22% in the most severe case. Our results displayed a weak correlation between the CI and the increase in peak stress. Additionally, the results showed a marked influence of the calcification elastic modulus on computed stresses. Inclusion of calcifications in finite element analysis of AAAs resulted in a marked alteration of the stress distributions and should therefore be included in rupture risk assessment. The results also suggest that the location and shape of the calcified regions--not only the relative amount--are considerations that influence the effect on AAA wall stress. The dependency of the effect of the wall stress on the calcification elastic modulus points out the importance of determination of the material properties of calcified AAA wall.     

A hybrid approach to theoretical analysis of bovine pancreatic trypsin inhibitor.

A static analysis of bovine pancreatic trypsin inhibitor (BPTI) is presented based on a new discrete/continuum approach to modeling the dynamics of biomolecules. This hybrid method utilizes knowledge of the intramolecular potential and molecular configuration to generate a field of elastic modulus tensors. These tensors, which relate the local stress and strain for each atom in the biomolecule, can be used to judge the local rigidity as well as indicate regions of high stress. Comparing the tensor fields for an unrelaxed and a relaxed configuration, the microscopic structure of BPTI is found to be anisotropic and to have regions of stress even when it is relaxed in the potential field. However, when these fields are averaged over the whole protein or over individual residues the structure becomes more isotropic and the stressed regions vanish. Using these averaged tensors, we calculated bulk properties such as Young's modulus and the Lamé constants and they agreed with previously reported values.