Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios

Experimental measurements of the Poisson's ratio in tendon and ligament tissue greatly exceed the isotropic limit of 0.5. This is indicative of volume loss during tensile loading. The microstructural origin of the large Poisson's ratios is unknown. It was hypothesized that a helical organization of fibrils within a fiber would result in a large Poisson's ratio in ligaments and tendons, and that this helical organization would be compatible with the crimped nature of these tissues, thus modeling their classic nonlinear stress–strain behavior. Micromechanical finite element models were constructed to represent crimped fibers with a super-helical organization, composed of fibrils embedded within a matrix material. A homogenization procedure was performed to determine both the effective Poisson's ratio and the Poisson function. The results showed that helical fibril organization within a crimped fiber was capable of simultaneously predicting large Poisson's ratios and the nonlinear stress–strain behavior seen experimentally. Parametric studies revealed that the predicted Poisson's ratio was strongly dependent on the helical pitch, crimp angle and the material coefficients. The results indicated that, for physiologically relevant parameters, the models were capable of predicting the large Poisson's ratios seen experimentally. It was concluded that helical organization within a crimped fiber can produce both the characteristic nonlinear stress–strain behavior and large Poisson's ratios, while fiber crimp alone could only account for the nonlinear stress–strain behavior.     

Poisson's ratio of bovine meniscus determined combining unconfined and confined compression

Poisson's ratio has not been experimentally measured earlier for meniscus in compression. It is however an important intrinsic material property needed in biomechanical analysis and computational models. In this study, equilibrium Poisson's ratio of bovine meniscus (n = 6) was determined experimentally by combining stress-relaxation measurements in unconfined and confined compression geometries. The average Young's modulus, aggregate modulus and Poisson's ratio were 0.182 ± 0.086 MPa, 0.252 ± 0.089 MPa and 0.316 ± 0.040, respectively. These moduli are consistent with previously determined values, but the Poisson’s ratio is higher than determined earlier for meniscus in compression through biomechanical modelling analysis. This new experimentally determined Poisson’s ratio value could be used in the analysis of biomechanical data as well as in computational finite element analysis when the Poisson’s ratio is needed as an input for the analysis.     

Modelling of the mechanical and mass transport properties of auxetic molecular sieves: an idealised inorganic (zeolitic) host–guest system

Force field based simulations have been employed to model the structure, and mechanical and mass transport properties of the all-silica zeolite MFI (ZSM5—Si₉₆O₁₉₂). Undeformed and deformed MFI subject to uniaxial loading in each of the three principal directions were investigated. The mechanical properties are predicted to include negative on-axis Poisson's ratios (auxetic behaviour) in the x ₁–x ₃ plane of the undeformed structure, and are strain-dependent. Transformation from positive-to-negative Poisson's ratio behaviour, and vice versa, is predicted for most on-axis Poisson's ratios at critical loading strains. Simulations of the simultaneous sorption of neopentane and benzene guest molecules onto the undeformed host MFI framework indicate a low neopentane-to-benzene loading ratio, consistent with experimental observation. The sorption of these two molecular species onto deformed MFI is Poisson's ratio- and strain-dependent. Uniaxial tensile loading along a direction containing a negative on-axis Poisson's ratio leads to an increase in the loading of the larger neopentane molecules with respect to benzene, strongly correlated with the increase in volume associated with auxetic behaviour.     

The role of particle softness in determining the value of Poisson's ratio for soft sphere solids

The influence of particle softness on the Poisson's ratio of model solids has been investigated. We have used the repulsive inverse power potential (～r ^? n for particle separations, r) between the particles, which is conveniently characterised by one adjustable parameter, ? = 1/n. For large ?, the interaction is soft whereas in the ? → 0 limit the particles approach hard spheres. The pressure and elastic constants of the solid phase have been calculated at various densities with constant temperature molecular dynamics (MD) simulation for a range of the softness parameter in the range, n>12. Density-softness surfaces of these quantities were determined which revealed hitherto unrecorded trends in the behaviour of the elastic moduli and Poisson's ratio. It was found that the pressure and some elastic properties, e.g. the C₁₂ elastic constant and the bulk modulus, manifest a maximum value or ‘ridge’ on this surface. The height of the maximum increases with density and interaction steepness (small ?). The Poisson's ratio varies essentially linearly with softness and is relatively insensitive to density. However, at higher densities and for larger steepness a considerable lowering of the Poisson's ratio is observed. In order to identify possible mechanisms for reducing the value of Poisson's ratio, ν, the fluctuation and Born-Green contributions were analysed. Changes in the Poisson's ratio are mainly determined by the fluctuation contribution which can cause a considerable decrease as well as increase of its value.     

New resource for the computation of cartilage biphasic material properties with the interpolant response surface method

Cartilage material properties are important for understanding joint function and diseases, but can be challenging to obtain. Three biphasic material properties (aggregate modulus, Poisson's ratio and permeability) can be determined using an analytical or finite element model combined with optimisation to find the material properties values that best reproduce an experimental creep curve. The purpose of this study was to develop an easy-to-use resource to determine biphasic cartilage material properties. A Cartilage Interpolant Response Surface was generated from interpolation of finite element simulations of creep indentation tests. Creep indentation tests were performed on five sites across a tibial plateau. A least-squares residual search of the Cartilage Interpolant Response Surface resulted in a best-fit curve for each experimental condition with corresponding material properties. These sites provided a representative range of aggregate moduli (0.48–1.58 MPa), Poisson's ratio (0.00–0.05) and permeability (1.7 × 10^? 15–5.4 × 10^? 15 m⁴/N s) values found in human cartilage. The resource is freely available from https://simtk.org/home/va-squish.     

Sensitivity of tissue differentiation and bone healing predictions to tissue properties

Computational models are employed as tools to investigate possible mechano-regulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The aim was to clarify the importance of the assumed tissue material properties in a computational model of tissue differentiation during bone healing. An established mechano-biological model was employed together with a statistical approach. The model included an adaptive 2D finite element model of a fractured long bone. Four outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at specific time points, (3) total time until healing, and (4) mechanical stability at specific time points. Statistical analysis based on fractional factorial designs first involved a screening experiment to identify the most significant tissue material properties. These seven properties were studied further with response surface methodology in a three-level Box–Behnken design. Generally, the sequential events were not significantly influenced by any properties, whereas rate-dependent outcome criteria and mechanical stability were significantly influenced by Young's modulus and permeability. Poisson's ratio and porosity had minor effects. The amount of bone formation at early, mid and late phases of healing, the time until complete healing and the mechanical stability were all mostly dependent on three material properties; permeability of granulation tissue, Young's modulus of cartilage and permeability of immature bone. The consistency between effects of the most influential parameters was high. To increase accuracy and predictive capacity of computational models of bone healing, the most influential tissue mechanical properties should be accurately quantified.     

Molecular mechanics studies on the conformations of 2',3'-dideoxy-2',3'-didehydroguanine nucleoside, D4G.

Conformational energy calculations have been presented on guanine nucleoside in which the furanose ring is replaced by 2',3'-dideoxy-2',3'-didehydrofuran using molecular mechanics and conformational analysis. Conformational energies have been evaluated using the MM2 and AMBER94 force field parameters at two different dielectric constants. The results are presented in terms of isoenergy contours in the conformational space of the glycosidic (chi) and C4'-C5' (gamma) bonds torsions. In general, the chi-gamma interrelationships differ from the corresponding plots for unmodified nucleosides and nucleotides, reported previously. Consistency of the calculated preferred conformations with the x-ray data is sensitive to the force field employed.     

Temperature and configurational effects on the Young’s modulus of poly (methyl methacrylate): a molecular dynamics study comparing the DREIDING,AMBER and OPLS force fields

The effects of the configuration and temperature on the Young’s modulus of poly (methyl methacrylate) (PMMA) have been studied using molecular dynamics simulations. For the DREIDING force field under ambient temperatures, increasing the number of monomers significantly increases the modulus of isotactic and syndiotactic PMMA while the isotactic form has a greater modulus. The effects of temperature on the modulus of isotactic PMMA have been simulated using the DREIDING, AMBER, and OPLS force fields. All these force fields predict the effects of temperature on the modulus from 200 to 350 K that are in close agreement with experimental values, while at higher temperatures the moduli are greater than those measured. The glass transition temperature determined by the force fields, based on the variation of the modulus with temperature, is greater than the experimental values, but when obtained from a plot of the volume as a function of the temperature, there is closer agreement. The Young’s moduli calculated in this study are in closer agreement to the experimental data than those reported by previous simulations.     

Influence of material properties on the mechanical behaviour of the L5-S1 intervertebral disc in compression: a nonlinear finite element study

A simple finite element model of the L₅-S₁ intervertebral disc body has been constructed; it is circular and symmetrical about the sagittal plane. The annulus fibrosus of the model was idealized as an inhomogeneous composite of an isotropic ground substance, reinforced by helically oriented collagen fibres so that the model has six different structural components namely: cortical bone, cancellous bone, cartilaginous endplates, nucleus pulposus, ground substance and collagen fibres. A sensitivity analysis of the material properties of each structural component was carried out by varying those properties for one structural component at a time and evaluating the changes in the biomechanical response to compressive displacements. Experimentally available relations between the applied compressive force and the vertical displacements, the nucleus pulposus pressure increase and the disc lateral bulge were used to evaluate the biomechanical responses for each set of material properties. Results showed that both the Poisson's ratio and the Young's modulus of the ground substance play an important role in the prediction of the biomechanical response.     

Hydraulic permeability and compressive properties of porcine and human synovium

The synovium is a multilayer connective tissue separating the intra-articular spaces of the diarthrodial joint from the extra-synovial vascular and lymphatic supply. Synovium regulates drug transport into and out of the joint, yet its material properties remain poorly characterized. Here, we measured the compressive properties (aggregate modulus, Young's modulus, and Poisson's ratio) and hydraulic permeability of synovium with a combined experimental-computational approach. A compressive aggregate modulus and Young's modulus for the solid phase of synovium were quantified from linear regression of the equilibrium confined and unconfined compressive stress upon strain, respectively (H_A = 4.3 ± 2.0 kPa, E_s = 2.1 ± 0.75, porcine; H_A = 3.1 ± 2.0 kPa, E_s = 2.8 ± 1.7, human). Poisson's ratio was estimated to be 0.39 and 0.40 for porcine and human tissue, respectively, from moduli values in a Monte Carlo simulation. To calculate hydraulic permeability, a biphasic finite element model's predictions were numerically matched to experimental data for the time-varying ramp and hold phase of a single increment of applied strain (k = 7.4 ± 4.1 × 10^?15 m⁴/N.s, porcine; k = 7.4 ± 4.3 × 10^?15 m⁴/N.s, human). We can use these newly measured properties to predict fluid flow gradients across the tissue in response to previously reported intra-articular pressures. These values for material constants are to our knowledge the first available measurements in synovium that are necessary to better understand drug transport in both healthy and pathological joints.     

Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine "dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution

We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.     

Dynamic simulations of potentially auxetic liquid-crystalline polymers incorporating swivelling mesogens

Dynamic simulations under stress were carried out on a series of main-chain polymers containing two types of mesogen. One mesogen is orientated in-line with the chain (end-to-end) and the second (swivelling) has the main chain passing at right angles through it. Under strain the swivelling mesogens are expected to rotate, pushing apart the neighbouring chains. Polymers incorporating 50% of both mesogens showed a reduced Poisson's ratio. In particular, swivelling mesogens of seven rings length produced a negative Poisson's ratio, and thus should be auxetic. In contrast, polymers containing only end-to-end mesogens had relatively high Poisson's ratios of 0.53–0.59.     

Computational study of IR,Raman, and NMR spectra of 4-methylmethcathinone drug

In the current study, the elastic and plastic properties of the 2 × 2 and 3 × 3 pristine and transition metal (TM)-doped antimonene are studied through DFT calculations. Sc, Ti, V, Cr, Fe, Co, Ni, Cu, and Zn atoms are selected as the doping atoms. It was observed that Young’s and bulk moduli of both 2 × 2 and 3 × 3 pristine structure would decrease while affected by the doping atoms. The highest reduction in the Young’s and bulk moduli of the 2 × 2 nanosheets has occurred in the Cr- and Ti-doped structures, respectively, while the same reduction was observed in the V- and Ti-doped structures in the 3 × 3 nanosheets. In addition, it was shown that all of the investigated structures express isotropic behavior since the obtained Young’s moduli of these nanostructures have negligible difference along armchair and zigzag directions. Finally, the loading is further increased to investigate the plastic behavior of these structures. The results showed that except for 2 × 2 Sc-doped structure under biaxial loading, the yield strain of all doped nanosheets would decrease under uniaxial and biaxial loadings. The highest reduction in the yield strain of the 2 × 2 nanosheets under biaxial loading has been observed in Cu-doped nanosheet while in 3 × 3 nanosheets, the highest reduction has occurred in Cu-, Fe-, and Zn-doped nanosheets under the same condition. As for the yield strain of the doped 2 × 2 nanosheets while affected by the uniaxial loading, Cu- and Zn-doped nanosheets experienced the highest reduction while in 3 × 3 nanosheets, the highest reduction has been observed for Cr-doped nanosheet under the same condition.

     

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.     

Nanomechanical properties of mineralised collagen microfibrils based on finite elements method: biomechanical role of cross-links

Hierarchical structures in bio-composites such as bone tissue have many scales or levels and synergic interactions between the different levels. They also have a highly complex architecture in order to fulfil their biological and mechanical functions. In this study, a new three-dimensional (3D) model based on the finite elements (FEs) method was used to model the relationship between the hierarchical structure and the properties of the constituents at the sub-structure scale (mineralised collagen microfibrils) and to investigate their apparent nanomechanical properties. The results of the proposed FE simulations show that the elastic properties of microfibrils depend on different factors such as the number of cross-links, the mechanical properties and the volume fraction of phases. The results obtained under compression loading at a small deformation < 2% show that the microfibrils have a Young's modulus (E_f) ranging from 0.4 to 1.16 GPa and a Poisson's ratio ranging from 0.26 to 0.3. These results are in excellent agreement with experimental data (X-ray, AFM and MEMS) and molecular simulations.     

Ultrathin MoS2 Nanosheets as Anode Materials for Sodium‐Ion Batteries with Superior Performance

Few‐layer MoS₂ nanosheets are successfully synthesized using a simple and scalable ultrasonic exfoliation technique. The thicknesses of the MoS₂ nanosheets ares about 10 nm as measured by scanning electron microscopy (SEM) and atomic force microscopy (AFM). The unique nanosheet architecture renders the high‐rate transportation of sodium ions due to the short diffusion paths provided by ultrathin thickness and the large interlayer space within the MoS₂ crystal structure (d₍₀₀₂₎ = 6.38 Å). When applied as anode materials in sodium‐ion batteries, MoS₂ nanosheets exhibit a high, reversible sodium storage capacity and excellent cyclability. The MoS₂ nanosheets also demonstrate good electrochemical performance at high current densities.     

Molecular Mechanics: The Conjugate Nitro Group Parameters in the MM2 Force Field

The conjugated nitro group has been included in the π system calculation within the MM2 force field. New parameters have been estimated by a statistical process from X-ray molecular structures recorded in the C.S.D.S. Comparison of the corresponding results with those given by the MM2(91) force field parameters show a clear improvement for dihedral and bond angles. For N-O and C-N bond lengths a slight global improvement is also observed. A closer examination of the results for the latter bond shows that sometimes MM2(91) gives better results for six membered ring nitro compounds. By contrast the parameters proposed here are more adapted to five membered ring derivatives. The derived linear relations permit the study of molecules over a wider range of π indices. The introduction of a correction factor to the calculated molecular π dipole moment in conjunction with a necessary reestimation of some σ-bond dipole moments also leads to improved total molecular dipole moments.     

A simple method of estimating the stress acting on a bilaterally symmetric abdominal aortic aneurysm

We extended a method of estimating the stress acting on an axisymmetric abdominal aortic aneurysm (AAA) under a load in vivo (Elger, D. F., Blackketter, D. M., Budwig, R. S., Johansen, K. H. (1996) The influence of shape on the stresses in model abdominal aortic aneurysms, Journal of Biomechanical Engineering, 118, pp. 326-32.) to bilaterally-symmetric AAAs, which are symmetric about the sagittal plane. Stresses were calculated along the anterior and posterior median lines of the AAA wall. Of the two force equilibrium equations, the Laplace equation held in this study. The longitudinal equilibrium was extended to hold by approximating the meridional tension and the directional cosine of the wall surface as constants along the circumference. The estimated stresses were compared with the results of a finite element analysis. Comparisons showed that the maximal principal stress, usually the circumferential stress or sometimes the meridional stress depending on location, sufficiently represented the wall stress. The proposed method provides a reasonable index for evaluating the rupture risk using the peak value of the maximal principal stress and its location without using the stress-free geometry and constitutive equation.     

Modelling of auxetic networked polymers built from calix[4]arene building blocks

Auxetic materials (i.e. materials with a negative Poisson's ratio) expand laterally when stretched and become thinner when compressed. This unusual yet very useful property arises from the way by which the nano or microstructure of the material deforms when subjected to uniaxial mechanical loads. This paper discusses a novel class of molecular-level auxetic (networked polymers) built from calix[4]arene building blocks. These calix[4]arene subunits are connected in such a way that they mimic the shape of a “folded macrostructure” which is known to exhibit auxetic behaviour. We confirm through force-field based simulations that these newly proposed networked polymers exhibit negative Poisson's ratios, the magnitudes of which can be changed by introducing slight variations in the molecular structure of these polymers. We also develop simple geometry-based models which explain the values of the Poisson's ratios obtained through the force-field based simulations, and which give an insight into the features of the molecular structure that are responsible for the auxetic effect.