Ring Strain Energy of Diheteropnictogeniranes El2 Pn (Pn=N, P, As, Sb)- Accurate versus Additive Approaches.

Accurate ring strain energy (RSE) values for sixty-six parent pnictogeniranes having two other identical p-block elements, El2 Pn, have been reported. A decrease in RSE was observed to correlate with an increase in the p character of the AO used in endocyclic bonds, which is particularly remarkable on descending the groups 15 and 16. The latter also parallels higher -NICS(1) values, which seems not to be related with an increase in aromaticity, as pointed out by other NICS-related criteria, but to atom-centred diatropic currents mostly arising from the presence of lone pairs. Only in case of pnictogenaditrieliranes Tr2 Pn (Tr=B, Al, Ga), the decrease of -NICS(1) is related to a lower Hückel-type 2π-electron aromaticity on descending group 13. The use of an additive methodology based on atom-strain contributions enables estimation of RSEs for a large majority of all possible three-membered rings containing group 13-16 elements with modest accuracy (RMSE=4.371 kcal/mol), that could be remarkably improved by using bond-strain contributions (RMSE=1.183 kcal/mol) instead.

Dots-on-Plots: A Web Application to Analyze Stress-Strain Curves From Tensile Tests of Soft Tissue.

The calculation of tensile mechanical properties from stress-strain curves is a fundamental step in characterizing material behavior, yet no standardized method exists to perform these calculations for soft tissue. To address this deficiency, we developed a free web application called Dots-on-Plots2 that fully automates the calculation of tensile mechanical properties from stress-strain curves. The analyzed mechanical properties include the strength, strain, and energy at four points of interest (transition, yield, ultimate, and rupture), and the linear modulus. Users of Dots-on-Plots can upload multiple files, view and download results, and adjust threshold settings. This study determined a threshold setting that minimized error when calculating the transition point, where the stress-strain curve "transitions" from a nonlinear "toe" region to a linear region. Using the optimal threshold (2% stress deviation from a linear region fit), Dots-on-Plots calculated the transition strains from twenty tensile experiments of human meniscus to be 0.049 ± 0.007, which nearly matched the known transition strain values of 0.050 ± 0.006 (determined using finite element parameter optimization). The sensitivity of the calculated transition strain to the shape of various stress-strain curves was analyzed using sets of model-generated synthetic data. This free web application offers a convenient and reliable tool to systematically enhance the speed, transparency, and consistency of mechanical analysis across biomedical research groups.

Theoretical Study of Si/C Equally Mixed Dodecahedrane Analogues.

To gain insight into the effect of Si/C arrangement on the molecular framework of strained polyhedral compounds, dodecahedrane analogues containing equal numbers of carbon and silicon (Si/C equally mixed dodecahedrane analogues) were investigated using the ab initio molecular orbital method. There are 1648 isomers for which the Si/C arrangement on the molecular framework is different. Based on the geometry optimization of all the isomers as well as the carbon and silicon analogues, the characteristics of the structure, relative energy, and strain energy of the Si/C equally mixed compounds are presented. Then, important factors controlling the relative energy, such as strain energy, are proposed through regression analysis. Also discussed is the correlation between the relative energy and the indices of Si/C dispersion, such as the number of skeletal C-Si single bonds and condensed five-membered rings constituting the polyhedral structure.

Strain Energy and Entropy Based Scaling of Buckling Modes.

A new utilization of entropy in the context of buckling is presented. The novel concept of connecting the strain energy and entropy for a pin-ended strut is derived. The entropy of the buckling mode is extracted through a surrogate model by decomposing the strain energy into entropy and virtual temperature. This concept rationalizes the ranking of buckling modes based on their strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all the modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of the buckling modes that coincide with the measurement of the initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for a given energy roughly decreases with the inverse square of the mode index. For practical engineering, this study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics.

Composite Correlated Molecular Orbital Theory Calculations of Ring Strain for Use in Predicting Polymerization Reactions.

Strained ring systems play an important role in synthesis and can be characterized by the ring strain energy (RSE). The RSE of 3, 4, 5, and 6 membered saturated and unsaturated ring systems containing N, O, P, and S heteroatoms and H, F, SiMe3 , and SO2 Me substituents were calculated at the G3(MP2) composite correlated molecular orbital theory level using up to 5 models to predict the RSE. Generally, the RSE decreased as ring size increased with a substantial decrease from 4 to 5 membered rings. Replacement of a ring CH2 with P or S reduced the RSE, consistent with less angle strain. The RSE for unsaturated systems were generally greater than for saturated systems due to increased angle strain. No general trends were found with respect to substituent effects. The RSE values suggest that 3-pyrroline and 2-pyrroline and their derivatives may be able to support ring opening metathesis polymerization and warrant further study.

Inside the coupling of ladybird beetle elytra: elastic setae can facilitate swift deployment.

The ladybird beetle (Coccinella septempunctata) is known for swift deployment of its elytra, an action that requires considerable power. However, actuation by thoracic muscles alone may be insufficient to deploy elytra at high speed because the maximum mechanical power that elytral muscles can produce is only 70% of that required for initiation of deployment. Nevertheless, the elytra open rapidly, within 3 ms in the initial phase, at a maximum angular velocity of 66.49±21.29 rad s-1, rivaling the strike velocity of ant lion (Myrmeleon crudelis) mandibles (65±21 rad s-1). Here, we hypothesize that elytra coupling may function as an energy storage mechanism that facilitates rapid opening by releasing elastic strain energy upon deployment. To test this hypothesis and better understand the biomechanics of elytra deployment, we combined micro-computed tomography and scanning electron microscopy to examine the microstructure of the coupling of paired elytra. We found that two rows of setae on the internal edges of the elytra coupling structure undergo elastic deformation when the elytra are locked together. Kinematics observations and mathematical modeling suggest that the elastic potential energy stored in the compressed setae generates 40% of the power required for deployment of elytra. Our findings broaden insights into how ladybirds actuate elytra opening by a strategy of using both muscles and elastic microstructures, and demonstrate a distributed pattern of actuation that adapts to geometrical constraints in elytra locking.

Elastic energy storage across speeds during steady-state hopping of desert kangaroo rats (Dipodomys deserti).

Small bipedal hoppers, including kangaroo rats, are not thought to benefit from substantial elastic energy storage and return during hopping. However, recent species-specific material properties research suggests that, despite relative thickness, the ankle extensor tendons of these small hoppers are considerably more compliant than had been assumed. With faster locomotor speeds demanding higher forces, a lower tendon stiffness suggests greater tendon deformation and thus a greater potential for elastic energy storage and return with increasing speed. Using the elastic modulus values specific to kangaroo rat tendons, we sought to determine how much elastic energy is stored and returned during hopping across a range of speeds. In vivo techniques were used to record tendon force in the ankle extensors during steady-speed hopping. Our data support the hypothesis that the ankle extensor tendons of kangaroo rats store and return elastic energy in relation to hopping speed, storing more at faster speeds. Despite storing comparatively less elastic energy than larger hoppers, this relationship between speed and energy storage offers novel evidence of a functionally similar energy storage mechanism, operating irrespective of body size or tendon thickness, across the distal muscle-tendon units of both small and large bipedal hoppers.

A generalized Ogden model for the compressibility of rubber-like solids.

The aim of this paper is to further demonstrate the advantages and effectiveness of the constitutive formulation proposed by Huang (Huang 2014 J. Appl. Mech. 59, 902-908 (doi:10.1115/1.2894059)). In this formulation, any strain-energy function for an incompressible material can be easily generalized to include the effect of material compressibility, in which only a few material parameters and material functions to be fitted with the experimental data are required. To this end, the Ogden model for incompressible rubber-like solids is chosen as the starting point. By means of this formulation, the generalized Ogden strain-energy function, which takes into account material compressibility, can conveniently be constructed so long as its incompressible counterpart is given. The obvious advantage shown in this paper is that only a few material parameters and material functions are needed, i.e. in addition to the material parameters used in the original Ogden model for incompressible solids, only one material function depending on the volume ratio is involved to characterize the effect of compressibility. Both the material parameters in the original Ogden model and the material function suggested in this paper can be determined by fitting the experimental data for uniaxially tensile test and hydrostatic deformation test of rubbers, respectively. The present model considering compressibility is general since it can be applied to predict the stress-strain responses of rubber-like materials and porous rubbers in various loading conditions. With the present formulation, the applicable range of the celebrated Ogden model can be further broadened, which should be of practical importance for accurately describing the mechanical behaviour of rubber-like solids. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Linear, weakly nonlinear and fully nonlinear models for soft tissues: which ones provide the most reliable estimations of the stiffness?

Benign and malignant lesions in tissues or organs can be detected by elastographic investigations in which pathological regions are spotted from local alterations of the stiffness. As is known, the shear modulus provides a measure of the stiffness of an elastic material. Based on the classical theory of linear elasticity, an elastogram yields estimations of the linear shear modulus from measurements of the speed of small-amplitude transverse waves propagating in the medium tested. In this paper, we show that the estimation of the shear modulus can be improved significantly by employing the fourth-order weakly nonlinear theory of elasticity (FOE), and indicate how the stiffness can be assessed more precisely with the use of FOE. We discuss also why FOE provides more reliable results than the fully nonlinear theory of elasticity. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Two-phase model of compressive stress induced on a surrounding hyperelastic medium by an expanding tumour.

In vitro experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an externally-supplied, diffusible nutrient (e.g., oxygen), affect the tumour's growth dynamics. In this article, we present a mathematical model that describes these in vitro experiments. We use the model to understand how tumour growth generates mechanical deformations in the hydrogel and how these deformations in turn influence the tumour's growth. The hydrogel is viewed as a nonlinear hyperelastic material and the tumour is modelled as a two-phase mixture, comprising a viscous tumour cell phase and an isotropic, inviscid interstitial fluid phase. Using a combination of numerical and analytical techniques, we show how the tumour's growth dynamics change as the mechanical properties of the hydrogel vary. When the hydrogel is soft, nutrient availability dominates the dynamics: the tumour evolves to a large equilibrium configuration where the proliferation rate of nutrient-rich cells on the tumour boundary balances the death rate of nutrient-starved cells in the central, necrotic core. As the hydrogel stiffness increases, mechanical resistance to growth increases and the tumour's equilibrium size decreases. Indeed, for small tumours embedded in stiff hydrogels, the inhibitory force experienced by the tumour cells may be so large that the tumour is eliminated. Analysis of the model identifies parameter regimes in which the presence of the hydrogel drives tumour elimination.

Cell mechanosensing is regulated by substrate strain energy rather than stiffness.

The ability of cells to perceive the mechanical identity of extracellular matrix, generally known as mechanosensing, is generally depicted as a consequence of an intricate balance between pulling forces actuated by the actin fibers on the adhesion plaques and the mechanical reaction of the supporting material. However, whether the cell is sensitive to the stiffness or to the energy required to deform the material remains unclear. To address this important issue, here the cytoskeleton mechanics of BALB/3T3 and MC3T3 cells seeded on linearly elastic substrates under different levels of deformation were studied. In particular, the effect of prestrain on cell mechanics was evaluated by seeding cells both on substrates with no prestrain and on substrates with different levels of prestrain. Results indicated that cells recognize the existence of prestrain, exhibiting a stiffer cytoskeleton on stretched material compared to cells seeded on unstretched substrate. Cytoskeleton mechanics of cells seeded on stretched material were, in addition, comparable to those measured after the stretching of the substrate and cells together to the same level of deformation. This observation clearly suggests that cell mechanosensing is not mediated only by the stiffness of the substrate, as widely assumed in the literature, but also by the deformation energy associated with the substrate. Indeed, the clutch model, based on the exclusive dependence of cell mechanics upon substrate stiffness, fails to describe our experimental results. By modifying the clutch model equations to incorporate the dependence on the strain energy, we were able to correctly interpret the experimental evidence.

Biomechanical constitutive modeling of the gastrointestinal tissues: a systematic review.

The gastrointestinal (GI) tract is a continuous channel through the body that consists of the esophagus, the stomach, the small intestine, the large intestine, and the rectum. Its primary functions are to move the intake of food for digestion before storing and ultimately expulsion of feces. The mechanical behavior of GI tissues thus plays a crucial role for GI function in health and disease. The mechanical properties are characterized by a biomechanical constitutive model, which is a mathematical representation of the relation between load and deformation in a tissue. Hence, validated biomechanical constitutive models are essential to characterize and simulate the mechanical behavior of the GI tract. Here, a systematic review of these constitutive models is provided. This review is limited to studies where a model of the strain energy function is proposed to characterize the stress-strain relation of a GI tissue. Several needs are identified for more advanced modeling including: 1) Microstructural models that provide actual structure-function relations; 2) Validation of coupled electro-mechanical models accounting for active muscle contractions; 3) Human data to develop and validate models. The findings from this review provide guidelines for using existing constitutive models as well as perspective and directions for future studies.

Dynamic patterns of cortical expansion during folding of the preterm human brain.

During the third trimester of human brain development, the cerebral cortex undergoes dramatic surface expansion and folding. Physical models suggest that relatively rapid growth of the cortical gray matter helps drive this folding, and structural data suggest that growth may vary in both space (by region on the cortical surface) and time. In this study, we propose a unique method to estimate local growth from sequential cortical reconstructions. Using anatomically constrained multimodal surface matching (aMSM), we obtain accurate, physically guided point correspondence between younger and older cortical reconstructions of the same individual. From each pair of surfaces, we calculate continuous, smooth maps of cortical expansion with unprecedented precision. By considering 30 preterm infants scanned two to four times during the period of rapid cortical expansion (28-38 wk postmenstrual age), we observe significant regional differences in growth across the cortical surface that are consistent with the emergence of new folds. Furthermore, these growth patterns shift over the course of development, with noninjured subjects following a highly consistent trajectory. This information provides a detailed picture of dynamic changes in cortical growth, connecting what is known about patterns of development at the microscopic (cellular) and macroscopic (folding) scales. Since our method provides specific growth maps for individual brains, we are also able to detect alterations due to injury. This fully automated surface analysis, based on tools freely available to the brain-mapping community, may also serve as a useful approach for future studies of abnormal growth due to genetic disorders, injury, or other environmental variables.

In Search of the Perfect Triple BB Bond: Mechanical Tuning of the Host Molecular Trap for the Triple Bond B≡B Fragment.

The coordination of the B2 fragment by two σ-donor ligands L: could lead to a diboryne compound with a formal triple bond L:→B≡B←:L. σ-Type coordination L:→B leads to an excess of electrons around the B2 central fragment, whereas π-back-donation from the B≡B moiety to ligand L has a compensation effect. Coordination of the σ-donor and π-acceptor ligand is accompanied by the lowering of the BB bond order. Here, we propose a new approach to obtain the perfect triple BB bond through the incorporation of the BB unit into a rigid molecular capsule. The idea is the replacement of π-back-donation, as the principal stabilization factor in the linear NBBN structure, with the mechanical stabilization of the BB fragment in the inert molecular capsule, thus preserving the perfect B≡B triple bond. Quantum-chemical calculations show that the rigid molecular capsule provided a linear NBBN structure and an unusually short BB bond of 1.36 Å. Quantum-chemical calculations of the proposed diboryne adducts show a perfect triple bond B≡B without π-back-donation from the B2 unit to the host molecule. Two mechanisms were tested for the molecular design of a diboryne adduct with a perfect B≡B triple bond: the elimination of π-back-donation and the construction of a suitable molecular trap for the encapsulation of the B2 unit. The second factor that could lead to the strengthening or stretching of a selected chemical bond is molecular strain produced by the rigid molecular host capsule, as was shown for B≡B and for C≡C triple bonds. Different derivatives of icosane host molecules exhibited variation in BB bond length and the corresponding frequency of the BB stretch. On the other hand, this group of molecules shows a perfect triple BB bond character and they all possess a similar level of HOMO.

Ligand Strain and Its Conformational Complexity Is a Major Factor in the Binding of Cyclic Dinucleotides to STING Protein.

STING (stimulator of interferon genes) is a key regulator of innate immunity that has recently been recognized as a promising drug target. STING is activated by cyclic dinucleotides (CDNs) which eventually leads to expression of type I interferons and other cytokines. Factors underlying the affinity of various CDN analogues are poorly understood. Herein, we correlate structural biology, isothermal calorimetry (ITC) and computational modeling to elucidate factors contributing to binding of six CDNs-three pairs of natural (ribo) and fluorinated (2'-fluororibo) 3',3'-CDNs. X-ray structural analyses of six {STING:CDN} complexes did not offer any explanation for the different affinities of the studied ligands. ITC showed entropy/enthalpy compensation up to 25 kcal mol-1 for this set of similar ligands. The higher affinities of fluorinated analogues are explained with help of computational methods by smaller loss of entropy upon binding and by smaller strain (free) energy.

First-Principles Calculations of Phonons and Thermodynamic Properties of Zr(Hf)S2 -Based Nanotubes.

Comparative hybrid density functional calculations on the structure, stability, and phonon frequencies of monolayers and single-walled nanotubes are performed for Zr(Hf)S2 disulfides. The first-principles calculations of HfS2 -based nanotubes are made for the first time. The symmetry analysis of infrared and Raman active vibrational modes in ZrS2 and HfS2 nanotubes is made using the induced representations of the isogonal point groups of line groups. It is shown that the number of infrared and Raman active modes is constant for NTs with the same chirality type. The correlation of the phonon modes of the nanotubes of relatively large diameters with those of monolayer is analyzed. The thermodynamic functions of monolayers and nanotubes with various chirality and diameters are calculated on the basis of the obtained phonon frequencies. It is established that the phonon contribution to the nanotube strain energy is small, but may be important for an accurate estimate of the stability of the nanotubes of small diameters. The calculated results show that the thermal contributions to Helmholtz free energy are positive; thereby they slightly reduce the stability of ZrS2 and HfS2 nanotubes at elevated temperatures. © 2019 Wiley Periodicals, Inc.

Spectroscopic Determination of Ice-Induced Interfacial Strain on Single-Layer Graphene.

Reliably determining the physical properties of ice (e.g., crystal structure, adhesion strength, interfacial state, and molecular orientation) has proven to be both challenging and highly dependent on experiment-specific conditions, including surface roughness, ice formation, water purity, and measurement method. Here, non-destructive measurements of single-layer graphene (SLG) interfaced with bulk ice are used to determine temperature-dependent, ice-induced strain and estimate ice-created strain elastic density in SLG. The use of SLG enables the precise study of interfacial strain by monitoring the 2D Raman mode. Upon ice formation, a clear, ≈2 cm-1 decrease in the 2D mode frequency is observed, which is ascribed to a 0.012% biaxial tensile shear strain at the ice-SLG interface. From this shear strain value, the ice-created SLG elastic strain energy density is estimated to be 2.4 µJ m-2 . In addition to these Raman strain measurements, intentionally ionized water is used to show that water-mediated charging of the SLG surface manifests itself in a distinctly different manner than ice-induced strain. Finally, the localized nature of the Raman probe is used to map SLG regions with and without ice, suggesting that this method cannot only determine ice-induced interfacial strain, but also correlate ice adhesion properties with surface roughness and topology.

Influence of a soft tissue layer covering the kidney upon blunt impact.

Blunt abdominal organ injury is an abundant and relevant topic in forensic medicine, yet comparatively few experimental studies have been performed to quantify organ injury threshold parameters. The goal of this study was to relate an impact to a kidney injury determining an energy threshold while taking account of the influence of the overlaying soft tissue thickness. A model consisting of ballistic gelatin with an embedded filled porcine kidney was made such that a gelatin layer of 2 or 4 cm thickness covered the organ. An impactor was dropped on this model from different heights and the resulting organ damage was categorized according to the abbreviated injury scale (AIS). The 50% energy threshold for damage and the 50% energy threshold causing injuries ≥ AIS 3 were determined for the two protecting soft layers to be 22 J and 32 J and 27 J and 36 J, respectively. A finite element model was created to determine the strain energy densities at the depth of the organ's surface for these energies. The strain energy densities for the 50% damage thresholds were 88.9 mJ/cm3 and 86.7 mJ/cm3 for 2 and 4 cm and for the injuries ≥ AIS 3104.2 mJ/cm3 and 98.7 mJ/cm3. For forensic cases, this means that the thickness of the abdominal layers must be taken into account when the severity of an injury is used to draw conclusions about the applied impact strength.

Gastrocnemius Medialis and Vastus Lateralis in vivo muscle-tendon behavior during running at increasing speeds.

This study combines in vivo ultrasound measurements of the Vastus Lateralis (VL) and Gastrocnemius Medialis (GM) muscles with electromyographic, kinematic, and kinetic measurements during treadmill running at different speeds (10, 13, and 16 km/h) to better understand the role of muscle and tendon behavior in two functionally different muscle-tendon units. In addition, the force-length and force-velocity relationships of VL and GM were experimentally assessed by combining dynamometry and EMG data with ultrasound measurements. With increasing running speed, the operating length of the fascicles in the stance phase shifted toward smaller lengths in the GM (P < .05; moving down the ascending limb of the F-L relationship) and longer lengths in the VL (P < .05; moving down the descending limb) at all speeds; however, both muscles contracted close to their optimal length L0 , where isometric force is maximal. Whereas the length of VL SEE did not change as a function of speed, GM SEE lengthened and shortened more at higher speeds. With increasing running speed, the contribution of elastic strain energy to the positive power generated by the MTU increased more for GM (from 0.75 to 1.56 W/kg) than for VL (from 0.62 to 1.02 W/kg). Notwithstanding these differences, these results indicate that, at increasing running speeds, both the VL and GM muscles produce high forces at low contraction velocities, and that the primary function of both muscle-tendon units is to enhance the storage and recovery of elastic strain energy.

An Optimization Method of Precision Assembly Process Based on the Relative Entropy Evaluation of the Stress Distribution.

The entropy evaluation method of assembly stress has become a hot topic in recent years. However, the current research can only evaluate the maximum stress magnitude and stress magnitude uniformity, and it cannot evaluate the stress position distribution. In this paper, an evaluation method of stress distribution characterized by strain energy density distribution is proposed. In this method, the relative entropy is used as the evaluation index of the stress distribution difference between the error model and the ideal model. It can evaluate not only the stress magnitude, but also the stress position. On this basis, an optimization method of the precise assembly process which takes the relative entropy as the optimization objective is proposed. The stress distributions of the optical lens are evaluated, and the assembly angle of the spacer in the process of the optical lens system assembly is optimized. By comparing the stress distribution of the optimized model and the ideal model, the validity of this method is proved.