Failure mechanism of hollow tree trunks due to cross-sectional flattening

Designing Bioinspired Composite Structures via Genetic Algorithm and Conditional Variational Autoencoder

Designing composite materials with tailored stiffness and toughness is challenging due to the massive number of possible material and geometry combinations. Although various studies have applied machine learning techniques and optimization methods to tackle this problem, we still lack a complete understanding of the material effects at different positions and a systematic experimental procedure to validate the results. Here we study a two-dimensional (2D) binary composite system with an edge crack and grid-like structure using a Genetic Algorithm (GA) and Conditional Variational Autoencoder (CVAE), which can design a composite with desired stiffness and toughness. The fitness of each design is evaluated using the negative mean square error of their predicted stiffness and toughness and the target values. We use finite element simulations to generate a machine-learning dataset and perform tensile tests on 3D-printed specimens to validate our results. We show that adding soft material behind the crack tip, instead of ahead of the tip, tremendously increases the overall toughness of the composite. We also show that while GA generates composite designs with slightly better accuracy (both methods perform well, with errors below 20%), CVAE takes considerably less time (~1/7500) to generate designs. Our findings may provide insights into the effect of adding soft material at different locations of a composite system and may also provide guidelines for conducting experiments and Explainable Artificial Intelligence (XAI) to validate the results.

Exploring the mechanical and morphological rationality of tree branch structure based on 3D point cloud analysis and the finite element method

Trees are thought to have acquired a mechanically optimized shape through evolution, but a scientific methodology to investigate the mechanical rationality of tree morphology remains to be established. The aim of this study was to develop a new method for 3D reconstruction of actual tree shape and to establish a theoretical formulation for elucidating the structure and function of tree branches. We obtained 3D point cloud data of tree shape of Japanese zelkova (Zelkova serrata) and Japanese larch (Larix kaempferi) using the NavVis Lidar scanner, then applied a cylinder structure extraction from point cloud data with error estimation. We then formulated the mechanical stress of branches under gravity using the elastic theory, and performed finite element method simulations to evaluate the mechanical characteristics. Subsequently, we constructed a mechanics-based theoretical formulation of branch development that ensures constant bending stress produces various branching patterns depending on growth properties. The derived theory recapitulates the trade-off among branch growth anisotropy, stress-gravity length, and branch shape, which may open the quantitative way to evaluate mechanical and morphological rationality of tree branches.

The quest for a unified theory on biomechanical palm risk assessment through theoretical analysis and observation

Several methodologies related to the biomechanical risk assessment and the uprooting and breaking potential of palms are reviewed and evaluated in this study. Also a simple mathematical model was designed, to simulate the results of critical wind speed predictions for a tall coconut palm by using classic beam theory and Brazier buckling. First, the review presents arguments that assess the applicability of some influential claims and tree and palm risk assessment methods that have been amply marketed in the last 20 years. Then, the analysis goes beyond the classical procedures and theories that have influenced the arboricultural industry and related press so far. And afterwards, rationale behind several postulated ideas are presented, that are hoped to be fruitful in the path towards a new biomechanical theory for the biomechanical risk assessment of palms. The postulated model envisages the palm stem as a viscoelastic and hollow cylinder that is not only prone to buckling, ovalization and kinking, but also fatigue, shear, splitting and crack propagation. This envisaging was also the main reason why simple Brazier buckling formulation was experimentally applied to simulate the breaking risk of a cocostem. This study also enables a better understanding of the wide range of factors that may influence the mechanical behaviour of trees and palms under (wind) loading.

Elastic Moduli of Avian Eggshell

We analyze 700 freshly-laid eggs from 58 species (22 families and 13 orders) across three orders of magnitude in egg mass. We study the elastic moduli using three metrics: (i) effective Young's modulus, EFEM, by a combined experimental and numerical method; (ii) elastic modulus, Enano, by nanoindentation, and (iii) theoretical Young's modulus, Etheory. We measure the mineral content by acid-base titration, and crystallographic characteristics by electron backscatter diffraction (EBSD), on representative species. We find that the mineral content ranges between 83.1% (Zebra finch) and 96.5% (ostrich) and is positively correlated with EFEM-23.28 GPa (Zebra finch) and 47.76 GPa (ostrich). The EBSD shows that eggshell is anisotropic and non-homogeneous, and different species have different degrees of crystal orientation and texture. Ostrich eggshell exhibits strong texture in the thickness direction, whereas chicken eggshell has little. Such anisotropy and inhomogeneity are consistent with the nanoindentation tests. However, the crystal characteristics do not appear to correlate with EFEM, as EFEM represents an overall "average" elasticity of the entire shell. The experimental results are consistent with the theoretical prediction of linear elasticity. Our comprehensive investigation into the elastic moduli of avian eggshell over broad taxonomic scales provides a useful dataset for those who work on avian reproduction.

Investigating the Underlying Effect of Thermal Modification on Shrinkage Behavior of Bamboo Culm by Experimental and Numerical Methods

This study probes into the root cause of split in thermally modified bamboo culm by investigating the underlying effect of thermal contraction with respect to its orthotropic nature by experimental and numerical methods while concurrently monitoring the chemical variation of its structure by Fourier transformed infrared spectroscopy (FTIR). In first part of this study, a non-linear increase in dimensional and weight changes of small clear bamboo specimens were observed with increasing temperature. The dimensional changes in the radial and tangential directions significantly exceeded that in the longitudinal direction. From FTIR results, shrinkage effect between 150 °C to 200 °C was associated with weight loss engendered by reduction in weakly bound water and increase in desorption of water content while alteration of its mechanical properties was attributed to changes in cellulose, hemicellulose, and lignin. From results of finite element method (FEM), the graded variation in thermal expansion coefficient, which showed the formation of a narrowed region of strain concentration corresponding to longitudinal crack propagation, was associated with the inducement of internal forces, namely tensile and compressive forces, at specific regions along the culm length. The results of this study can be useful to achieve optimized durability in modified bamboo for construction.

Investigation of the Effect of Inhomogeneous Material on the Fracture Mechanisms of Bamboo by Finite Element Method

Bamboo is a remarkably strong and sustainable material available for construction. It exhibits optimized mechanical characteristics based on a hollow-inhomogeneous structure which also affects its fracture behavior. In this study, the aim is to investigate the effect of material composition and geometrical attributes on the fracture mechanisms of bamboo in various modes of loading by the finite element method. In the first part of the investigation, the optimized transverse isotropy of bamboo to resist transverse deformation was numerically determined to represent its noticeable orthotropic characteristics which prevail in the axial direction. In the second part of this study, a numerical investigation of fracture mechanisms in four fundamental modes of loading, namely bending, compression, torsion, and shear, were conducted by considering the failure criterion of maximum principal strain. A crack initiation stage was simulated and compared by implementing an element erosion technique. Results showed that the characteristics of bamboo’s crack initiation differed greatly from solid geometry and homogeneous material-type models. Splitting patterns, which were discerned in bending and shear modes, differed in terms of location and occurred in the outside-center position and inside-lowermost position of the culm, respectively. The results of this study can be useful in order to achieve optimized strength in bamboo-inspired bionic designs.

Mechanism of cracking failure in curved stems due to transverse stress under a bending moment

It is essential to understand the failure modes and the failure moments of curved stems since trees could be damaged and may cause severe loss of life and property in urban. In our previous papers, the cracking failure mechanism of hollow erect and curved trunks under bending moment was clarified and we also found that the mechanism of cracking failure of solid trunk is different from the hollow one. While the existing equation to calculate the transverse stress of a solid curved stem under a bending moment is approximate and may cause considerable errors when the initial curvature of stem is small. To solve this problem, a series of novel equations were derived in this study. Among these newly derived equations, 3 of them are especially practical in the assessment of the risk of urban tree for both safety and environment management which are M_c, c_minR and c_criR. The equation of M_c is to calculate the bending moment for a solid curved trunk at which the cracking failure is initiated and this equation is more accurate than the existing equation. The equation of c_minR is to calculate the minimum cR (c: curvature, R: radius of trunk) below which cracking failure will not occur, and the equation of c_criR is to calculate the critical cR which represents equal opportunities for cracking and bending failure of the stem to occur. To exert our model to practice, the equations derived in this paper were applied to literature data (Wood handbook, 1999). From the data of 41 species of softwood and 48 species of hardwood, statistically, hardwoods have larger average values of c_minR and c_criR than softwoods which means that hardwoods are more resistant to cracking failure than softwoods.

Cracking failure of curved hollow tree trunks

Understanding the failure modes of curved hollow tree trunks is essential from both safety and conservation perspectives. Despite extensive research, the underlying mechanism that determines the cracking failure of curved hollow tree trunks remains unclear due to the lack of theoretical analysis that considers both the initial curvature and orthotropic material properties. Here we derive new mathematical expressions for predicting the bending moment, M _crack, at which the cracking failure occurs. The failure mode of a tree species is then determined, as a function of t/R and cR, by comparing M _crack with M _bend, where t, R and c are, respectively, the trunk wall thickness, outer radius and initial curvature; M _bend is the bending moment for conventional bending failure. Our equation shows that M _crack is proportional to the tangential tensile strength of wood σ_T , increases with t/R, and decreases with the final cR. We analyse 11 tree species and find that hardwoods are more likely to fail in conventional bending, whereas softwoods tend to break due to cracking. This is due to the softwoods' much smaller tangential tensile strength, as observed from the data of 66 hardwoods and 43 softwoods. For larger cR, cracking failure is easier to occur in curvature-decreasing bending than curvature-increasing due to additional normal tensile force F acting on the neutral cross-section; on the other hand, for smaller cR, bending failure is easier to occur due to decreased final curvature. Our formulae are applicable to other natural and man-made curved hollow beams with orthotropic material properties. Our findings provide insights for those managing trees in urban situations and those managing for conservation of hollow-dependent fauna in both urban and rural settings.

Mechanics of the Microtubule Seam Interface Probed by Molecular Simulations and in Vitro Severing Experiments

Microtubules (MTs) are structural components essential for cell morphology and organization. It has recently been shown that defects in the filament's lattice structure can be healed to create stronger filaments in a local area and ultimately cause global changes in MT organization and cell mobility. The ability to break, causing a defect, and heal appears to be a physiologically relevant and important feature of the MT structure. Defects can be created by MT severing enzymes and are target sites for complete severing or for healing by newly incorporated dimers. One particular lattice defect, the MT lattice ''seam" interface, is a location often speculated to be a weak site, a site of disassembly, or a target site for MT binding proteins. Despite seams existing in many MT structures, very little is known about the seam's role in MT function and dynamics. In this study, we probed the mechanical stability of the seam interface by applying coarse-grained indenting molecular dynamics. We found that the seam interface is as structurally robust as the typical lattice structure of MTs. Our results suggest that, unlike prior results that claim the seam is a weak site, it is just as strong as any other location on the MT, corroborating recent mechanical measurements.

Microtubules soften due to cross-sectional flattening

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasingdeformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effect in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.