Lung parenchyma surrounding an atelectatic region is thought to be subjected to increased stress compared with the rest of the lung. Using 37 hexagonal cells made of linear springs, Mead et al. (1970) measured a stress concentration greater than 30% in the springs surrounding a stiffer central cell. We re-examine the problem using a 2D finite element model of 500 cells made of thin filaments with a non-linear stress-strain relationship. We study the consequences of increasing the central stiff region from one to nine contiguous cells in regular hexagonal honeycombs and random Voronoi honeycombs. The honeycomb structures were uniformly expanded with strains of 15%, 30%, 45% and 55% above their resting, non-deformed geometry. The curve of biaxial stress vs. fractional area change has a similar shape to that of the pressure-volume curve of the lung, showing an initial regime with relatively flat slope and a final regime with decreasing slope, tending toward an asymptote. Regular honeycombs had little variability in the maximum stress in radially oriented filaments adjacent to the central stiff region. In contrast, some filaments in random Voronoi honeycombs were subjected to stress concentration approximately 16 times the average stress concentration in the radially oriented filaments adjacent to the stiff region. These results may have implications in selecting the appropriate strategy for mechanical ventilation in ARDS and defining a "safe" level of alveolar pressure for ventilating atelectatic lungs.

Both creep and crack growth contribute to the reduction in modulus associated with fatigue loading in bone. Here we simulate crack growth and subsequent strut failure in fatigue in an open-cell, three-dimensional Voronoi structure which is similar to that of low density, osteoporotic bone. The model indicates that sequential failure of struts leads to a precipitous drop in modulus: the failure of 1% of the struts leads to about a 10% decrease in modulus. A parametric study is performed to assess the influence of normalized stress range, relative density, initial crack size, crack shape and cell geometry on the fatigue life. The fatigue life is most sensitive to the relative density and the initial crack length. The results lead to a quantitative expression for the fatigue life associated with crack growth. Data for the fatigue life of trabecular bone are compared with the crack growth model described in this paper as well as with a previous model for creep of a three-dimensional Voronoi structure. In our models, creep dominates the fatigue behavior in low cycle fatigue while crack growth dominates in high cycle fatigue, consistent with previous observations on cortical bone. The large scatter in the trabecular bone fatigue data make it impossible to identify a transition between creep dominated fatigue and crack growth dominated fatigue. The parametric study of the crack growth model indicates that variations in relative density among specimens, initial crack size within trabeculae and crack shape could easily produce such variability in the test results.

A pivotal process in the loss of phonological quantity in West Germanic languages is what is traditionally known as Open Syllable Lengthening. Existing accounts have found no explanation for why languages such as English apply this change in less than 50% of the relevant cases. This paper presents the results of a corpus investigation of four West Germanic languages showing that whether Open Syllable Lengthening occurs in more than 50% of predicted cases correlates with the ratio of closed syllables with short vowels to open syllables with long vowels. We interpret this as the result of frequency effects that have markedly shaped the application of Open Syllable Lengthening in West Germanic. This has implications for phonological change in general, as well as for the relationship between stress and syllable structure in West Germanic languages.*

This work presents a new philosophy for optimisation of composite structures in relation to lightweight design. It is based on Michell optimum lay-out theory, which uses orthogonal mesh structures disposed in the direction of principal stress trajectories, associated with an absolutely uniform distribution of stress in the fibres. The fibres in the composite component micro structure are disposed orthogonally like the minimum weight Michell structures, with voids filled with resin. This is the same mechanical principle which governs the optimisation of natural composites such as bones, hom, trees etc. Based on this natural rule, a procedure to find the optimum topology for the design of optimum composite mechanical components has been developed. A CAD-CAE software system based on finite element analysis using ABAQUS produces interactively on a screen the structure of optimum topology where the optimum fibre arrangement will be made.