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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., Competing Interests: Competing interests statement:The authors declare no competing interest.

Compaction of hot mix asphalt (HMA) requires high temperatures in the range of 125 to 145 °C to ensure the fluidity of asphalt binder and, therefore, the workability of asphalt mixtures. The high temperatures are associated with high energy consumption, and higher NOx emissions, and can also accelerate the aging of asphalt binders. In previous research, the authors have developed two approaches for improving the compactability of asphalt mixtures: (1) addition of Graphite Nanoplatelets (GNPs), and (2) optimizing aggregate packing. This research explores the effects of these two approaches, and the combination of them, on reducing compaction temperatures while the production temperature is kept at the traditional levels. A reduction in compaction temperatures is desired for prolonging the paving window, extending the hauling distance, reducing the energy consumption for reheating, and for reducing the number of repairs and their negative environmental and safety effects, by improving the durability of the mixtures. A Superpave asphalt mixture was chosen as the control mixture. Three modified mixtures were designed, respectively, by (1) adding 6% GNP by the weight of binder, (2) optimizing aggregate packing, and (3) combining the two previous approaches. Gyratory compaction tests were performed on the four mixtures at two compaction temperatures: 135 °C (the compaction temperature of the control mixture) and 95 °C. A method was proposed based on the gyratory compaction to estimate the compaction temperature of the mixtures. The results show that all the three methods increase the compactability of mixtures and thus significantly reduce the compaction temperatures. Method 3 (combining GNP modification and aggregate packing optimization) has the most significant effect, followed by method 1 (GNP modification), and method 2 (aggregate packing optimization).

The failure probability of engineering structures such as aircraft, bridges, dams, nuclear structures, and ships, as well as microelectronic components and medical implants, must be kept extremely low, typically <10(-6). The safety factors needed to ensure it have so far been assessed empirically. For perfectly ductile and perfectly brittle structures, the empirical approach is sufficient because the cumulative distribution function (cdf) of random material strength is known and fixed. However, such an approach is insufficient for structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared with the structure size. The reason is that the strength cdf of quasibrittle structure varies from Gaussian to Weibullian as the structure size increases. In this article, a recently proposed theory for the strength cdf of quasibrittle structure is refined by deriving it from fracture mechanics of nanocracks propagating by small, activation-energy-controlled, random jumps through the atomic lattice. This refinement also provides a plausible physical justification of the power law for subcritical creep crack growth, hitherto considered empirical. The theory is further extended to predict the cdf of structural lifetime at constant load, which is shown to be size- and geometry-dependent. The size effects on structure strength and lifetime are shown to be related and the latter to be much stronger. The theory fits previously unexplained deviations of experimental strength and lifetime histograms from the Weibull distribution. Finally, a boundary layer method for numerical calculation of the cdf of structural strength and lifetime is outlined.

Ensuring a small enough failure probability is important for the design and selection of restorative dental ceramics. For this purpose, the two-parameter Weibull distribution, which is based on the weakest link model with infinitely many links, is usually adopted to model the strength distribution of dental ceramics. This distribution has been thoroughly validated for perfectly brittle materials. However, dental ceramics are generally quasibrittle because the inhomogeneity size is not negligible compared to the size of the ceramic part. For such materials, the experimental histograms of many quasibrittle materials have been shown to exhibit strong deviations from the two-parameter Weibull distribution. As a remedy, the three-parameter Weibull distribution, which has a nonzero threshold, has been proposed. However, the improvement of the fits of histograms of quasibrittle materials has been only partial. Instead of making the threshold non-zero, the correct remedy is to consider the weakest link model to have a finite number of links, each of them representing one finite-size representative volume element of material. This model has recently been justified on the basis of the probability of random jumps of atomic lattice cracks over the activation energy barriers on the free energy potential of the lattice. It is shown that, in similarity to other quasibrittle materials, this new model allows excellent fits of the experimental strength histograms of various types of dental ceramics.