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Stinger-like structures in living organisms evolved convergently across taxa for both defensive and offensive purposes, with the main goal being penetration and damage. Our observations over a broad range of taxa and sizes, from microscopic radiolarians to narwhals, reveal a self-similar geometry of the stinger extremity: the diameter (d) increases along the distance from the tip (x) following a power law [Formula: see text] , with the tapering exponent varying universally between 2 and 3. We demonstrate, through analytical and experimental mechanics involving three-dimensional (3D) printing, that this geometry optimizes the stinger's performance; it represents a trade-off between the propensity to buckle, for n smaller than 2, and increased penetration force, for n greater than 3. Moreover, we find that this optimal tapering exponent does not depend on stinger size and aspect ratio (base diameter over length). We conclude that for Nature's stingers, composed of biological materials with moduli ranging from hundreds of megapascals to ten gigapascals, the necessity for a power-law contour increases with sharpness to ensure sufficient stability for penetration of skin-like tissues. Our results offer a solution to the puzzle underlying this universal geometric trait of biological stingers and may provide a new strategy to design needle-like structures for engineering or medical applications.

Stinger-like structures in living organisms evolved convergently across taxa for both defensive and offensive purposes, with the main goal being penetration and damage. Our observations over a broad range of taxa and sizes, from microscopic radiolarians to narwhals, reveal a self-similar geometry of the stinger extremity: the diameter (d) increases along the distance from the tip (x) following a power law x ~ dn, with the tapering exponent varying universally between 2 and 3. We demonstrate, through analytical and experimental mechanics involving three-dimensional (3D) printing, that this geometry optimizes the stinger's performance; it represents a trade-off between the propensity to buckle, for n smaller than 2, and increased penetration force, for n greater than 3. Moreover, we find that this optimal tapering exponent does not depend on stinger size and aspect ratio (base diameter over length). We conclude that for Nature's stingers, composed of biological materials with moduli ranging from hundreds of megapascals to ten gigapascals, the necessity for a power-law contour increases with sharpness to ensure sufficient stability for penetration of skin-like tissues. Our results offer a solution to the puzzle underlying this universal geometric trait of biological stingers and may provide a new strategy to design needle-like structures for engineering or medical applications. [ABSTRACT FROM AUTHOR]

Vascular tortuosity may impede blood flow, occlude the lumen, and ultimately lead to ischemia or even infarction. Mechanical loads like blood pressure, axial force, and also torsion are key factors participating in this complex mechanobiological process. The available studies on arterial torsion instability followed computational or experimental approaches, yet single available theoretical study had modeled the artery as isotropic linear elastic. This paper aim is to validate a theoretical model of arterial torsion instability against experimental data. The artery is modeled as a single-layered, nonlinear, hyperelastic, anisotropic solid, with parameters calibrated from experiment. Linear bifurcation analysis is then performed to predict experimentally measured stability margins. Uncertainties in geometrical parameters and in measured mechanical response were considered. Also, the type of rate (incremental) boundary conditions (RBCs) impact on the results was examined (e.g., dead load, fluid pressure). The predicted critical torque and twist angle followed the experimentally measured trends. The closest prediction errors in the critical torque and twist rate were 22% and 67%, respectively. Using the different RBCs incurred differences of up to 50% difference within the model predictions. The present results suggest that the model may require further improvements. However, it offers an approach that can be used to predict allowable twist levels in surgical procedures (like anastomosis and grafting) and in the design of stents for arteries subjected to high torsion levels (like the femoropopliteal arteries). It may also be instructive in understanding biomechanical processes like arterial tortuosity, kinking, and coiling. [ABSTRACT FROM AUTHOR]

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Despite all technological innovations in esophageal stent design over the past 20 years, the association between the stent design’s mechanical behavior and its effect on the clinical outcome has not yet been thoroughly explored. A parametric numerical model of a commercially available esophageal bioresorbable polymeric braided wire stent is set up, accounting for stent design aspects such as braiding angle, strut material, wire thickness, degradation and friction between the wires comprising a predictive tool on the device’s mechanical behavior. Combining this tool with complex multilayered numerical models of the pathological in vivo stressed, actively contracting and buckling esophagus could provide clinicians and engineers with a patient-specific window into the mechanical aspects of stent-based esophageal intervention. This study integrates device and soft tissue mechanics in one computational framework to potentially aid in the understanding of the occurrence of specific symptoms and complications after stent placement. [ABSTRACT FROM AUTHOR]

Many studies have measured the global compressive properties of tissue engineered (TE) cartilage grown on porous scaffolds. Such scaffolds are known to exhibit strain softening due to local buckling under loading. As matrix is deposited onto these scaffolds, the global compressive properties increase. However the relationship between the amount and distribution of matrix in the scaffold and local buckling is unknown. To address this knowledge gap, we studied how local strain and construct buckling in human TE constructs changes over culture times and GAG content. Confocal elastography techniques and digital image correlation (DIC) were used to measure and record buckling modes and local strains. Receiver operating characteristic (ROC) curves were used to quantify construct buckling. The results from the ROC analysis were placed into Kaplan-Meier survival function curves to establish the probability that any point in a construct buckled. These analysis techniques revealed the presence of buckling at early time points, but bending at later time points. An inverse correlation was observed between the probability of buckling and the total GAG content of each construct. This data suggests that increased GAG content prevents the onset of construct buckling and improves the microscale compressive tissue properties. This increase in GAG deposition leads to enhanced global compressive properties by prevention of microscale buckling. [ABSTRACT FROM AUTHOR]

Legs in dipteran pupae are tightly packed in a zigzag configuration. Changes in the shape or configuration of long podomeres during eclosion have been overlooked because they occur rapidly (in a few minutes) and the legs are hidden inside a tight opaque confinement: the puparium in the Cyclorrhapha, the obtect pupa in mosquitoes. We fixed insects at different times during eclosion and obtained a temporal description of changes in leg shape. At the start of eclosion in Calliphora vicina and Drosophila melanogaster , femora are buckled in between the joints. Later, the chain of podomeres straightened, pointing posterad. Initial deformation and further stretching were passive, exerted by forces external to the legs. The prerequisites for this are pliability of the tubular podomeres and anchoring of the tarsi to the confinement. Each femur was strongly crooked instead of buckled in the mosquito Aedes cantans . The site of bending shifted distad in the course of eclosion: a sort of peeling. In contrast, other insects (the moth Bombyx mori , the ants Formica polyctena and Formica rufa , the honey bee Apis mellifera ) left their tight confinements without any change in the initial zigzag leg configuration and without transient deformations of initially straight femora and tibiae. [ABSTRACT FROM AUTHOR]

Veins are often subjected to torsion and twisted veins can hinder and disrupt normal blood flow but their mechanical behavior under torsion is poorly understood. The objective of this study was to investigate the twist deformation and buckling behavior of veins under torsion. Twist buckling tests were performed on porcine internal jugular veins (IJVs) and human great saphenous veins (GSVs) at various axial stretch ratio and lumen pressure conditions to determine their critical buckling torques and critical buckling twist angles. The mechanical behavior under torsion was characterized using a two-fiber strain energy density function and the buckling behavior was then simulated using finite element analysis. Our results demonstrated that twist buckling occurred in all veins under excessive torque characterized by a sudden kink formation. The critical buckling torque increased significantly with increasing lumen pressure for both porcine IJV and human GSV. But lumen pressure and axial stretch had little effect on the critical twist angle. The human GSVs are stiffer than the porcine IJVs. Finite element simulations captured the buckling behavior for individual veins under simultaneous extension, inflation, and torsion with strong correlation between predicted critical buckling torques and experimental data ( R 2 = 0.96). We conclude that veins can buckle under torsion loading and the lumen pressure significantly affects the critical buckling torque. These results improve our understanding of vein twist behavior and help identify key factors associated in the formation of twisted veins. [ABSTRACT FROM AUTHOR]

Looping of the initially straight embryonic gut tube is an essential aspect of intestinal morphogenesis, permitting proper placement of the lengthy small intestine within the confines of the body cavity. The formation of intestinal loops is highly stereotyped within a given species and results from differential-growth–driven mechanical buckling of the gut tube as it elongates against the constraint of a thin, elastic membranous tissue, the dorsal mesentery. Although the physics of this process has been studied, the underlying biology has not. Here, we show that BMP signaling plays a critical role in looping morphogenesis of the avian small intestine. We first exploited differences between chicken and zebra finch gut morphology to identify the BMP pathway as a promising candidate to regulate differential growth in the gut. Next, focusing on the developing chick small intestine, we determined that Bmp2 expressed in the dorsal mesentery establishes differential elongation rates between the gut tube and mesentery, thereby regulating the compressive forces that buckle the gut tube into loops. Consequently, the number and tightness of loops in the chick small intestine can be increased or decreased directly by modulation of BMP activity in the small intestine. In addition to providing insight into the molecular mechanisms underlying intestinal development, our findings provide an example of how biochemical signals act on tissue-level mechanics to drive organogenesis, and suggest a possible mechanism by which they can be modulated to achieve distinct morphologies through evolution. [ABSTRACT FROM AUTHOR]

Strong regions and physical barriers in soils may slow root elongation, leading to reduced water and nutrient uptake and decreased yield. In this study, the biomechanical responses of roots to axial mechanical forces were assessed by combining 3D live imaging, kinematics and a novel mechanical sensor. This system quantified Young’s elastic modulus of intact poplar roots (32 MPa), a rapid <0.2 mN touch-elongation sensitivity, and the critical elongation force applied by growing roots that resulted in bending. Kinematic analysis revealed a multiphase bio-mechanical response of elongation rate and curvature in 3D. Measured critical elongation force was accurately predicted from an Euler buckling model, indicating that no biologically mediated accommodation to mechanical forces influenced bending during this short period of time. Force applied by growing roots increased more than 15-fold when buckling was prevented by lateral bracing of the root. The junction between the growing and the mature zones was identified as a zone of mechanical weakness that seemed critical to the bending process. This work identified key limiting factors for root growth and buckling under mechanical constraints. The findings are relevant to crop and soil sciences, and advance our understanding of root growth in heterogeneous structured soils. [ABSTRACT FROM AUTHOR]

This paper investigated buckling phenomena of the spine induced by the growth of vertebral bodies that have potential to cause idiopathic scoliosis. In the previous study, we presented a hypothesis that idiopathic scoliosis is a buckling phenomena induced by the growth of vertebral bodies based on the similarity of the clinical single and double-major curves with the results of the fourth and sixth buckling modes, respectively, as analyzed by the finite-elements method using linear buckling theory. However, this theory is valid for infinitesimal deformation and is not applicable to estimation of stability for post-buckling behavior. In this study, we developed a program to analyze deformation histories caused by the growth of vertebral bodies considering the geometrical nonlinearity and investigated buckling phenomena. We assumed that growth represents generation of non-elastic bulk strain. To exclude modes correctable by posture change, we considered constraints at the cervical spine. Using the developed program, we analyzed deformation histories induced by the growth of vertebral bodies and obtained deformation histories including buckling phenomena with side-bending modes similar to clinical curves. However, the magnitudes of deformations were in the sub-millimeter order that is too small for the etiology of idiopathic scoliosis by itself. Based on the results, we suggested that participation of other phenomena, such as bone remodeling caused by the stresses at the side-bending deformations, will be necessary.

The present paper describes the numerical results by the finite-element method of unstable phenomena of the spine induced by the growth of vertebral bodies in order to investigate the cause of the idiopathic scoliosis. In the previous study, through the linear buckling analysis using simple plate models, we confirmed the existence of the buckling phenomena, and made clear the region of geometrical parameters in which the buckling phenomena occur. These results support the buckling hypothesis as a cause of initiation of the idiopathic scoliosis. However, this theory is valid for infinitesimal deformation and is not applicable to estimate the stability for post-buckling behavior. In this study, we conduct post-buckling simulations caused by the growth of vertebral bodies considering the geometrical nonlinearity using the simple plate model and spine models with full width and half width. From the results, the existence of the non-linear buckling phenomena are confirmed in the simple plate model and the spine model with half width. Moreover, after the non-linear buckling phenomena, stable deformations are obtained excepting each one case in the simple plate model and the spine model with half width. However, the magnitudes of the post-buckling deformations are too small to explain the pathogenesis of the severe deformity observed in patients of idiopathic scoliosis.

The present paper presents the numerical results of a finite-element analysis of the role of a linear buckling phenomena in the etiology of idiopathic scoliosis. In a previous study, we assumed that idiopathic scoliosis is a buckling phenomenon induced by the growth of vertebral bodies, and we used the finite-element method with a spine model to demonstrate the results of linear buckling. However, a program based on the theory of nonlinear buckling did not produce clear buckling modes that were similar to the observed clinical modes. In this study, we return to the starting point and use rather simple models to confirm the existence of a buckling phenomenon that has various geometrical properties. We assumed that the growth of the vertebral bodies can be modeled by the generation of a non-elastic bulk strain. We use the finite-element method to analyze linear buckling modes caused by the growth deformation, and we confirm the existence of the buckling phenomena and clarify the range of the geometrical parameters in which this buckling occurs. By a comparison of different models, we investigate the influence of the region of the buckling phenomena on the physiological curvature of the spine and the intervertebral articulation. Our results support Dickson's hypothesis that a flattening or reversal of normal thoracic kyphosis at the apex of the curvature of the spine causes the buckling phenomenon.

Cervical spine injuries continue to be a costly societal problem. Future advancements in injury prevention depend on improved physical and computational models, which are predicated on a better understanding of the neck response during dynamic loading. Previous studies have shown that the tolerance of the neck is dependent on its initial position and its buckling behavior. This study uses a computational model to examine three important factors hypothesized to influence the loads experienced by vertebrae in the neck under compressive impact: muscle activation, torso constraints, and pre-flexion angle of the cervical spine. Since cadaver testing is not practical for large scale parametric analyses, these factors were studied using a previously validated computational model. On average, simulations with active muscles had 32% larger compressive forces and 25% larger shear forces—well in excess of what was expected from the muscle forces alone. In the short period of time required for neck injury, constraints on torso motion increased the average neck compression by less than 250 N. The pre-flexion hypothesis was tested by examining pre-flexion angles from neutral (0°) to 64°. Increases in pre-flexion resulted in the largest increases in peak loads and the expression of higher-order buckling modes. Peak force and buckling modality were both very sensitive to pre-flexion angle. These results validate the relevance of prior cadaver models for neck injury and help explain the wide variety of cervical spine fractures that can result from ostensibly similar compressive loadings. They also give insight into the mechanistic differences between burst fractures and lower cervical spine dislocations. [ABSTRACT FROM AUTHOR]

Female insects of diverse orders bore into substrates to deposit their eggs. Such insects must overcome several biomechanical challenges to successfully oviposit, which include the selection of suitable substrates through which the ovipositor can penetrate without itself fracturing. In many cases, the insect may also need to steer and manipulate the ovipositor within the substrate to deliver eggs at desired locations before rapidly retracting her ovipositor to avoid predation. In the case of female parasitoid ichneumonid wasps, this process is repeated multiple times during her lifetime, thus testing the ability of the ovipositioning apparatus to endure fracture and fatigue. What specific adaptations does the ovipositioning apparatus of a female ichneumonoid wasp possess to withstand these challenges? We addressed this question using a model system composed of parasitoid and pollinator fig wasps. First, we show that parasitoid ovipositor tips have teeth-like structures, preferentially enriched with zinc, unlike the smooth morphology of pollinator ovipositors. We describe sensillae present on the parasitoid ovipositor tip that are likely to aid in the detection of chemical species and mechanical deformations and sample microenvironments within the substrate. Second, using atomic force microscopy, we show that parasitoid tip regions have a higher modulus compared with regions proximal to the abdomen in parasitoid and pollinator ovipositors. Finally, we use videography to film wasps during substrate boring and analyse buckling of the ovipositor to estimate the forces required for substrate boring. Together, these results allow us to describe the biomechanical principles underlying substrate boring in parasitoid ichneumonid wasps. Such studies may be useful for the biomimetic design of surgical tools and in the use of novel mechanisms to bore through hard substrates [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study was to compare the morphologic change of the posterior cruciate ligament (PCL) on magnetic resonance imaging (MRI) in chronic anterior cruciate ligament (ACL) tear before and after reconstruction. Materials and Methods: On the MRI image after ACL reconstruction, a base line (BL) was drawn between the femoral and tibial insertion sites of the PCL. Point A was established as the vertically farthest point from BL. Line 1 and 2 were drawn respectively between point A and the insertions of PCL. The angles between BL and Line1 and 2 were defined as angle a and angle b. Correlations between the preoperative anterior knee instability assessed with the KT 1000 arthrometer and the parameters were evaluated. Results: The average angle a was 52.3°±7.1° preoperatively and 30.1°±3.4° postoperatively, and the average angle b was 28.95°±4.62° preoperatively and 22°±2.9° postoperatively (p<0.05). The preoperative manual maximal side-to-side difference was 7.2±2.3 mm, which had no significant correlation with angle b. Conclusions: The preoperative buckling of PCL in the case of chronic ACL injury disappeared after ACL reconstruction. The degree of PCL buckling had no correlation with the degree of preoperative anterior instability. [ABSTRACT FROM AUTHOR]

Abstract: The performance of cellular solids in biomedical applications relies strongly on a detailed understanding of the effects of pore topology on mechanical properties. This study aims at characterizing the failure mechanism of scaffolds based on nodal connectivity (number of struts that meet in joints) and geometry of the pores. Plastic models of scaffolds having the same relative density but different cubic and trigonal unit cells were designed and then fabricated via three dimensional (3-D) printing. Unit cells were repeated in different arrangements in 3-D space. An in-situ imaging technique was utilized to study the progressive deformation of the scaffold models. Different nodal connectivities resulted in a wide range of compressive behaviors in scaffold models, from elastic-plastic to fully brittle. The Maxwell necessary criterion for rigidity was used to explain mechanical behavior of the scaffolds. Nodal connectivity of 4 satisfied Maxwell''s criterion for rigidity in the examined structures. In a stress–strain curve of scaffolds with cubic unit cells and nodal connectivities of 3 and 4, pore deformation was observed after yielding. On the other hand, scaffolds with trigonal unit cells and nodal connectivities of 4 and 6, exhibited brittle behavior in the absence of pore deformation. These results highlight the role of nodal connectivity on failure mechanism and subsequently mechanical performance of scaffolds. This study reveals that appropriate pore geometry can provide sufficient condition for rigidity when Maxwell''s necessary condition is satisfied. In addition, this study demonstrates that Maxwell''s criterion can be used in pre-designing of pore geometries for scaffolds with distinct nodal connectivities. [Copyright &y& Elsevier]

Abstract: The human spine has an elaborate system of muscles and ligaments which serve to actuate this complex biomechanical system. In this paper, the buckling instabilities of the ligamentous spine are explored using a model based on Euler''s elastica. The model features the intrinsic curvature and self-weight of the spine. With the help of nonlinear stability criteria, the stability of the spine and its buckled states are analyzed. Our main novel results demonstrate that the ligamentous spine in the sagittal plane remains stable under its self-weight and a terminal vertical load, and, following a pitchfork bifurcation, an unstable configuration of the spine is possible which is close to the unloaded spine. [Copyright &y& Elsevier]

Abstract: This paper deals with the buckling analysis of cracked beam-columns. The crack is modelled with a unilateral elastic bending-stiffness behaviour, represented by a unilateral rotational spring. This model takes into account the crack closure effect associated with the phenomenon of breathing crack. The rotational spring may model a one-sided crack (or a unilateral joint for other applications in biomechanics or civil engineering). The unilateral elastic constitutive law of the crack is introduced from a variational procedure based on energy arguments. It is shown that this constitutive law can be formulated as a function of a physically-based damage parameter. A one-crack and a two-crack hinged-hinged beam-column are theoretically investigated to illustrate the unilateral effect of the crack behaviour on the buckling load. It is shown that the open crack analogy can be adopted for the one-crack beam-column, whereas this simplified assumption cannot be retained for the two-crack beam-column. In this last case, the crack closure effect strongly affects the buckling load, with respect to the open crack analogy of the same problem. More specifically, the crack-closure phenomenon tends to increase the buckling load, with respect to the open crack assumption mainly retained in the literature. [Copyright &y& Elsevier]

Background/purpose: The mechanical aspects of wrinkle formation were studied in the dorsal skin of hairless mice. Methods: Wrinkles were induced by irradiating with ultraviolet (UV) B for 10 weeks, while observing skin deformation during wrinkle formation. Changes in skin dimensions were also observed during the specimen excision process. Wrinkle depth and interval were measured before and after removal of the cutaneous muscle layer. Local deformation of wrinkled skin during uniaxial stretch was also measured. Changes in curvature of skin specimens upon muscle layer removal were then observed to determine the force balance in skin layers. Results: The skin showed spontaneous contraction in response to UV irradiation. Wrinkled skin showed a marked decrease in the wrinkle depth and a slight increase in wrinkle interval following muscle layer removal, a peculiar mechanical response that cannot be explained by homogeneous deformation of the skin. This response was due to compressive deformations of dermal tissue caused by the muscle layer and concentrated at valleys of the wrinkles. Curvature measurements indicated that the muscle layer compressed the dermal tissue predominantly in the craniocaudal direction. Morphological observations showed that the wrinkles coincided with rows of pores and sulci cutis, where the structural stiffness of the horny layer was relatively low. The horny layer showed significant thickening. Conclusion: Taken together, we propose the following hypothetical mechanisms of wrinkle formation during UV irradiation: spontaneous contraction of the dermis while maintaining or increasing the epidermal area induces buckling of the epidermis into the dermis at mechanically weak lines, namely, the rows of pores and sulci cutis, and buckling may be amplified by the axial compression of the dermis by the muscle layer. [ABSTRACT FROM AUTHOR]

Vertebral compression fractures are a potentially severe injury, which is characteristic to osteoporotic elderly. Despite being a significant healthcare problem, the etiology of compression fractures is not fully understood, and there are no biomechanical models in the literature that describe the development of these fractures based on cancellous bone failure accumulation. The objective of this study was therefore to develop a computational model of tissue-level failure accumulation in vertebral cancellous bone, which eventually leads to compression fractures. The model predicts the accumulated percentage of broken trabeculae δ in a vertebral region of interest (ROI) over 60 years, by employing Euler's theory for elastic buckling. The accumulated failure δ is calculated as function of the daily activity characteristics and rate of annual bone loss (RABL) with aging. An RABL of unity represents the normal bone loss attributed to aging per se, whereas RABL>1 is assumed to represent pathological bone metabolism such as osteoporosis. Simulations were conducted for a range of RABLs, to determine the effect of changes in bone metabolism on the accumulation of bone failure. Results showed that bone failure rapidly increased with RABL. Generally, trabecular failure was shown to become more severe for RABL>4. Total failure was exhibited at RABL = 7.5 for the central ROI, and at RABL = 8.5 for the sub-endplate ROI. We concluded that vertebral compression fractures advance monotonically between the age of 50-55 years and 70 years, and may accelerate thereafter if RABL is high (∼8). Additionally, the model identified weight lifting as the action that most dramatically accelerated the destruction of osteoporotic spinal cancellous bone. The present biomechanical model is useful for understanding the etiology of compression fractures, and potentially, depending on further experimental characterization of RABL, for considering the effects of medications that influence bone metabolism on patient prognosis. [ABSTRACT FROM AUTHOR]

Fracture mechanics concepts are applied to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. The discussions in this paper are organized around the following questions: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material? (4) The strength question: how does nature balance the widely different strengths of protein and mineral? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures? What is the role of structural hierarchy? A complete analysis of these questions taking into account the full biological complexities is far beyond the scope of this paper. The intention here is only to illustrate some of the basic mechanical design principles of bone-like materials using simple analytical and numerical models. With this objective in mind, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. The follow-up analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. The staggered nanostructure is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. Finally, the question on structural hierarchy is discussed via a model hierarchical material consisting of multiple levels of self-similar composite structures mimicking the nanostructure of bone. We show that the resulting “fractal bone”, a model hierarchical material with different properties at different length scales, can be designed to tolerate crack-like flaws of multiple length scales. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the vibration, buckling and dynamic instability behavior of laminated composite, cross-ply, doubly-curved panels with a central circular hole subjected to in-plane static and periodic compressive loads. A generalized shear deformable Sanders' theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. Bolotin's approach is used for studying the dynamic instability regions of doubly-curved panels. The effects of non-uniform edge loads, curvature with different cutout ratios, static and dynamic load factors, and lamination parameters on curved panels are investigated with the results discussed. [ABSTRACT FROM AUTHOR]