Uncovering the dual role of dimensionless radius in buckling of spherical shells with random geometric imperfections.

Localized deformation and randomly shaped imperfections are salient features of buckling-type instabilities in thin-walled load-bearing structures. However, it is generally agreed that their complex interactions in response to mechanical loading are not yet sufficiently understood, as evidenced by buckling-induced catastrophic failures which continue to today. This study investigates how the intimate coupling between localization mechanisms and geometric imperfections combine to determine the statistics of the pressure required to buckle (the illustrative example of) a hemispherical shell. The geometric imperfections, in the form of a surface, are defined by a random field generated over the nominally hemispherical shell geometry, and the probability distribution of the buckling pressure is computed via stochastic finite element analysis. Monte-Carlo simulations are performed for a wide range of the shell's radius to thickness ratio, as well as the correlation length of the spatial distribution of the imperfection. The results show that over this range, the buckling pressure is captured by the Weibull distribution. In addition, the analyses of the deformation patterns observed during the simulations provide insights into the effects of certain characteristic lengths on the local buckling that triggers global instability. In light of the simulation results, a probabilistic model is developed for the statistics of the buckling load that reveals how the dimensionless radius plays a dual role which remained hidden in previous deterministic analyses. The implications of the present model for reliability-based design of shell structures are discussed.

Tension tests on mammalian collagen fibrils.

A brief overview of isolated collagen fibril mechanics testing is followed by presentation of the first results testing fibrils isolated from load-bearing mammalian tendons using a microelectromechanical systems platform. The in vitro modulus (326 ± 112 MPa) and fracture stress (71 ± 23 MPa) are shown to be lower than previously measured on fibrils extracted from sea cucumber dermis and tested with the same technique. Scanning electron microscope images show the fibrils can fail with a mechanism that involves circumferential rupture, whereas the core of the fibril stays at least partially intact.

Viscoelastic properties of isolated collagen fibrils.

Understanding the viscoelastic behavior of collagenous tissues with complex hierarchical structures requires knowledge of the properties at each structural level. Whole tissues have been studied extensively, but less is known about the mechanical behavior at the submicron, fibrillar level. Using a microelectromechanical systems platform, in vitro coupled creep and stress relaxation tests were performed on collagen fibrils isolated from the sea cucumber dermis. Stress-strain-time data indicate that isolated fibrils exhibit viscoelastic behavior that could be fitted using the Maxwell-Weichert model. The fibrils showed an elastic modulus of 123 ± 46 MPa. The time-dependent behavior was well fit using the two-time-constant Maxwell-Weichert model with a fast time response of 7 ± 2 s and a slow time response of 102 ± 5 s. The fibrillar relaxation time was smaller than literature values for tissue-level relaxation time, suggesting that tissue relaxation is dominated by noncollagenous components (e.g., proteoglycans). Each specimen was tested three times, and the only statistically significant difference found was that the elastic modulus is larger in the first test than in the subsequent two tests, indicating that viscous properties of collagen fibrils are not sensitive to the history of previous tests.

Interface toughness of carbon nanotube reinforced epoxy composites.

Traditional single-fiber pull-out type experiments were conducted on individual multiwalled carbon nanotubes (MWNT) embedded in an epoxy matrix using a novel technique. Remarkably, the results are qualitatively consistent with the predictions of continuum fracture mechanics models. Unstable interface crack propagation occurred at short MWNT embedments, which essentially exhibited a linear load-displacement response prior to peak load. Deep embedments, however, enabled stable crack extension and produced a nonlinear load-displacement response prior to peak load. The maximum pull-out forces corresponding to a wide range of embedments were used to compute the nominal interfacial shear strength and the interfacial fracture energy of the pristine MWNT-epoxy interface.

In vitro fracture testing of submicron diameter collagen fibril specimens.

Mechanical testing of collagenous tissues at different length scales will provide improved understanding of the mechanical behavior of structures such as skin, tendon, and bone, and also guide the development of multiscale mechanical models. Using a microelectromechanical-systems (MEMS) platform, stress-strain response curves up to failure of type I collagen fibril specimens isolated from the dermis of sea cucumbers were obtained in vitro. A majority of the fibril specimens showed brittle fracture. Some displayed linear behavior up to failure, while others displayed some nonlinearity. The fibril specimens showed an elastic modulus of 470 ± 410 MPa, a fracture strength of 230 ± 160 MPa, and a fracture strain of 80% ± 44%. The fibril specimens displayed significantly lower elastic modulus in vitro than previously measured in air. Fracture strength/strain obtained in vitro and in air are both significantly larger than those obtained in vacuo, indicating that the difference arises from the lack of intrafibrillar water molecules produced by vacuum drying. Furthermore, fracture strength/strain of fibril specimens were different from those reported for collagenous tissues of higher hierarchical levels, indicating the importance of obtaining these properties at the fibrillar level for multiscale modeling.

Deformation micromechanisms of collagen fibrils under uniaxial tension.

Collagen, an essential building block of connective tissues, possesses useful mechanical properties due to its hierarchical structure. However, little is known about the mechanical properties of collagen fibril, an intermediate structure between the collagen molecule and connective tissue. Here, we report the results of systematic molecular dynamics simulations to probe the mechanical response of initially unflawed finite size collagen fibrils subjected to uniaxial tension. The observed deformation mechanisms, associated with rupture and sliding of tropocollagen molecules, are strongly influenced by fibril length, width and cross-linking density. Fibrils containing more than approximately 10 molecules along their length and across their width behave as representative volume elements and exhibit brittle fracture. Shorter fibrils experience a more graceful ductile-like failure. An analytical model is constructed and the results of the molecular modelling are used to find curve-fitted expressions for yield stress, yield strain and fracture strain as functions of fibril structural parameters. Our results for the first time elucidate the size dependence of mechanical failure properties of collagen fibrils. The associated molecular deformation mechanisms allow the full power of traditional material and structural engineering theory to be applied to our understanding of the normal and pathological mechanical behaviours of collagenous tissues under load.

Stress-strain experiments on individual collagen fibrils.

Collagen, a molecule consisting of three braided protein helices, is the primary building block of many biological tissues including bone, tendon, cartilage, and skin. Staggered arrays of collagen molecules form fibrils, which arrange into higher-ordered structures such as fibers and fascicles. Because collagen plays a crucial role in determining the mechanical properties of these tissues, significant theoretical research is directed toward developing models of the stiffness, strength, and toughness of collagen molecules and fibrils. Experimental data to guide the development of these models, however, are sparse and limited to small strain response. Using a microelectromechanical systems platform to test partially hydrated collagen fibrils under uniaxial tension, we obtained quantitative, reproducible mechanical measurements of the stress-strain curve of type I collagen fibrils, with diameters ranging from 150-470 nm. The fibrils showed a small strain (epsilon < 0.09) modulus of 0.86 +/- 0.45 GPa. Fibrils tested to strains as high as 100% demonstrated strain softening (sigma(yield) = 0.22 +/- 0.14 GPa; epsilon(yield) = 0.21 +/- 0.13) and strain hardening, time-dependent recoverable residual strain, dehydration-induced embrittlement, and susceptibility to cyclic fatigue. The results suggest that the stress-strain behavior of collagen fibrils is dictated by global characteristic dimensions as well as internal structure.