Tensile material instabilities in elastic beam lattices lead to a bounded stability domain.

Homogenization of the incremental response of grids made up of preloaded elastic rods leads to homogeneous effective continua which may suffer macroscopic instability, occurring at the same time in both the grid and the effective continuum. This instability corresponds to the loss of ellipticity in the effective material and the formation of localized responses as, for instance, shear bands. Using lattice models of elastic rods, loss of ellipticity has always been found to occur for stress states involving compression of the rods, as usually these structural elements buckle only under compression. In this way, the locus of material stability for the effective solid is unbounded in tension, i.e. the material is always stable for a tensile prestress. A rigorous application of homogenization theory is proposed to show that the inclusion of sliders (constraints imposing axial and rotational continuity, but allowing shear jumps) in the grid of rods leads to loss of ellipticity in tension so that the locus for material instability becomes bounded. This result explains (i) how to design elastic materials subject to localization of deformation and shear banding for all radial stress paths; and (ii) how for all these paths a material may fail by developing strain localization and without involving cracking. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

Liquid Crystal Elastomer Lattices with Thermally Programmable Deformation via Multi-Material 3D Printing.

An integrated design, modeling, and multi-material 3D printing platform for fabricating liquid crystal elastomer (LCE) lattices in both homogeneous and heterogeneous layouts with spatially programmable nematic director order and local composition is reported. Depending on their compositional topology, these lattices exhibit different reversible shape-morphing transformations upon cycling above and below their respective nematic-to-isotropic transition temperatures. Further, it is shown that there is good agreement between their experimentally observed deformation response and model predictions for all LCE lattice designs evaluated. Lastly, an inverse design model is established and the ability to print LCE lattices with the predicted deformation behavior is demonstrated. This work opens new avenues for creating architected LCE lattices that may find potential application in energy-dissipating structures, microfluidic pumping, mechanical logic, and soft robotics.

Radial width of the temporal horn: a sensitive measure in Alzheimer disease.

BACKGROUND AND PURPOSE: Atrophy in the medial temporal lobe (MTL) structures depicted with brain imaging is one of the most accurate markers of Alzheimer disease (AD), but practical considerations have thus far limited their routine clinical use. The aim of this study was to explore the validity of a CT- and MR-based measure of MTL atrophy that would be feasible for routine clinical use. METHODS: We acquired brain CT scans in the temporal lobe plane with thin sections in 42 patients with AD and in 29 control patients without dementia. We also acquired MR images (according to a 3D magnetization-prepared rapid gradient-echo protocol) in 28 patients with AD and in 28 control subjects without dementia. The radial width of the temporal horn (rWTH) of the lateral ventricle was measured with a precision caliper at the tip of the horn on CT scans or high-quality MR images. The validity of the rWTH variable was assessed by test-retest and interrater reliability, convergent and discriminant validity compared with progressively distant brain regions, and known-group validity (accuracy of the separation of patients with AD from control subjects). Convergent and discriminant validity compared with volumetric measures was tested in the patients who underwent MR imaging. RESULTS: Intraclass correlation coefficients for inter- and intrarater reliability were between 0.94 and 0.98. On CT scans, Pearson's correlation of the rWTH with the transverse width of the temporal horn was between 0.60 and 0.79; with Jobst's minimum thickness of the MTL, between 0.63 and 0.78 (interuncal distance approximately 0.50); and with an index of frontal atrophy, between 0.35 and 0.42. On MR images, the correlation with volumetric MR measures was 0.80 in the temporal horn, 0.74 in the hippocampus, 0.68 in the temporal lobe, 0.58 in the entorhinal cortex, and 0.49 in the frontal lobe. On CT scans (cutoff value for AD, >5.3 mm; age range of subjects, 50-90 y), the rWTH measure was a sensitive marker for AD in 39 of 42 patients with AD (sensitivity, 93%) and was a specific marker in 28 of the 29 control patients (specificity, 97%). On MR images (cutoff 3.6-6.7 mm; age range of subject, 50-90 y), the rWTH was a sensitive marker for AD in 21 of 28 patients with AD (sensitivity, 75%) and was a specific marker in 26 of 28 control subjects (specificity, 93%). The accuracy of other linear CT-based measures of MTL atrophy and linear and volumetric MR-based measures was lower. With specificity set to 95%, sensitivity ranged from 57% to 74% for CT-based measures and from 52% to 74% for MR-based measures. CONCLUSION: The rWTH is an accurate marker of AD that could be used in routine clinical settings.