Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods.

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

Blisters and Calluses from Rowing: Prevalence, Perceptions and Pain Tolerance.

Background and Objectives: Rowing is a sport that involves constant gripping, pulling/pushing, and rotational movements of the hands, in a cyclic periodic manner with every stroke, with hundreds of strokes being taken within a short period of time. Dermatological issues on rowers' hands (fingers and palms) in the form of blisters and calluses are common knowledge within the community, but their prevalence and the rower's perceptions and pain tolerance to them has never been systematically evaluated. This work addresses these lacunae. Materials and Methods: Analysis of data collected from a survey on a sample of competitive (117) and noncompetitive rowers (28) who row on-water (total 145). Results: It was found that approximately 69% of rowers participating in this study have calluses on their hands for most of their time (considered by them as not painful). The incidence of blisters was found to be lower (but perceived as more painful). Their incidence was found to be fairly independent of the frequency and intensity of training, but they seem to affect most rowers equally at the beginning of season or during a change of position (nonconditioned hands). Blisters and calluses were reported to be mainly located on the proximal phalanges and metacarpo-phalangeal joint area of both hands, i.e., on the lower parts of the fingers and the upper inner palms. Conclusions: Rowers demonstrated a sense of acceptance of these dermatological issues, even a sense of pride in what they represent. The incidence of blisters becoming infected was estimated to be so low that most rowers would not have encountered such serious, albeit rare, consequences.

The Multidirectional Auxeticity and Negative Linear Compressibility of a 3D Mechanical Metamaterial.

In this work, through the use of a theoretical model, we analyse the potential of a specific three-dimensional mechanical metamaterial composed of arrowhead-like structural units to exhibit a negative Poisson's ratio for an arbitrary loading direction. Said analysis allows us to assess its suitability for use in applications where materials must be able to respond in a desired manner to a stimulus applied in multiple directions. As a result of our studies, we show that the analysed system is capable of exhibiting auxetic behaviour for a broad range of loading directions, with isotropic behaviour being shown in some planes. In addition to that, we show that there are also certain loading directions in which the system manifests negative linear compressibility. This enhances its versatility and suitability for a number of applications where materials exhibiting auxetic behaviour or negative linear compressibility are normally implemented.

A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility.

Auxetics (negative Poisson's ratio) and materials with negative linear compressibility (NLC) exhibit the anomalous mechanical properties of getting wider rather than thinner when stretched and expanding in at least one direction under hydrostatic pressure, respectively. A novel mechanism-termed the 'triangular elongation mechanism'-leading to such anomalous behavior is presented and discussed through an analytical model. Amongst other things, it is shown that this novel mechanism, when combined with the well-known 'rotating squares' model, can generate giant negative Poisson's ratios when the system is stretched.

Filtration Properties of Auxetics with Rotating Rigid Units.

Auxetic structures and materials expand laterally when stretched. It has been argued that this property could be applied in the design of smart filters with tunable sieving properties. This work analyses the filtration properties of a class of auxetic structures which achieve their auxeticity through a rotating rigid unit mechanism, an archetypal mechanism known to be responsible for this behavior in a number of crystalline materials. In particular, mathematical expressions are derived for the space coverage of networks constructed from a variety of quadrilaterals, as well as the pore radius. The latter is indicative of the particle size that can pass through when the particle dimension is comparable to the pore size, whereas the space coverage is indicative of the rate of flow when the particles are of a much smaller dimension than the pore size. The expressions suggest that these systems offer a wide range of pore sizes and space coverages, both of which can be controlled through the way that the units are connected to each other, their shape and the angle between them.

On the dynamics and control of mechanical properties of hierarchical rotating rigid unit auxetics.

In this work, we investigate the deformation mechanism of auxetic hierarchical rotating square systems through a dynamics approach. We show how their deformation behaviour, hence their mechanical properties and final configuration for a given applied load, can be manipulated solely by altering the resistance to rotational motion of the hinges within the system. This provides enhanced tunability without necessarily changing the geometry of the system, a phenomenon which is not typically observed in other non-hierarchical unimode auxetic systems. This gives this hierarchical system increased versatility and tunability thus making it more amenable to be employed in practical application which may range from smart filtration to smart dressings.

Internal rib structure can be predicted using mathematical models: An anatomic study comparing the chest to a shell dome with application to understanding fractures.

The human rib cage resembles a masonry dome in shape. Masonry domes have a particular construction that mimics stress distribution. Rib cortical thickness and bone density were analyzed to determine whether the morphology of the rib cage is sufficiently similar to a shell dome for internal rib structure to be predicted mathematically. A finite element analysis (FEA) simulation was used to measure stresses on the internal and external surfaces of a chest-shaped dome. Inner and outer rib cortical thickness and bone density were measured in the mid-axillary lines of seven cadaveric rib cages using computerized tomography scanning. Paired t tests and Pearson correlation were used to relate cortical thickness and bone density to stress. FEA modeling showed that the stress was 82% higher on the internal than the external surface, with a gradual decrease in internal and external wall stresses from the base to the apex. The inner cortex was more radio-dense, P < 0.001, and thicker, P < 0.001, than the outer cortex. Inner cortical thickness was related to internal stress, r = 0.94, P < 0.001, inner cortical bone density to internal stress, r = 0.87, P = 0.003, and outer cortical thickness to external stress, r = 0.65, P = 0.035. Mathematical models were developed relating internal and external cortical thicknesses and bone densities to rib level. The internal anatomical features of ribs, including the inner and outer cortical thicknesses and bone densities, are similar to the stress distribution in dome-shaped structures modeled using FEA computer simulations of a thick-walled dome pressure vessel. Fixation of rib fractures should include the stronger internal cortex.

A hypothesis for reactivation of pulmonary tuberculosis: How thoracic wall shape affects the epidemiology of tuberculosis.

This study was aimed at determining the cause for the high incidence of tuberculosis (TB) reactivation occurring in males with a low body mass index (BMI). Current thinking about pulmonary TB describes infection in the lung apex resulting in cavitation after reactivation. A different hypothesis is put forward for TB infection, suggesting that this occurs in subclinical apical cavities caused by increased pleural stress due to a low BMI body habitus. A finite element analysis (FEA) model of a lung was constructed including indentations for the first rib guided by paramedian sagittal CT reconstructions, and simulations were conducted with varying antero-posterior (AP) diameters to mimic chests with a different thoracic index (ratio of AP to the transverse chest diameters). A Pubmed search was conducted about gender and thoracic index, and the effects of BMI on TB. FEA modeling revealed a tenfold increase in stress levels at the lung apex in low BMI chests, and a four-fold increase with a low thoracic index, r(2) = 0.9748 P < 0.001. Low thoracic index was related to BMI, P = 0.001. The mean thoracic index was statistically significantly lower in males, P = 0.001, and increased with age in both genders. This article is the first to suggest a possible mechanism linking pulmonary TB reactivation to low BMI due to the flattened thoracic wall shape of young male adults. The low thoracic index in young males may promote TB reactivation due to tissue destruction in the lung apex from high pleural stress levels.

External rib structure can be predicted using mathematical models: An anatomical study with application to understanding fractures and intercostal muscle function.

As ribs adapt to stress like all bones, and the chest behaves as a pressure vessel, the effect of stress on the ribs can be determined by measuring rib height and thickness. Rib height and thickness (depth) were measured using CT scans of seven rib cages from anonymized cadavers. A Finite Element Analysis (FEA) model of a rib cage was constructed using a validated approach and used to calculate intramuscular forces as the vectors of both circumferential and axial chest wall forces at right angles to the ribs. Nonlinear quadratic models were used to relate rib height and rib thickness to rib level, and intercostal muscle force to vector stress. Intercostal muscle force was also related to vector stress using Pearson correlation. For comparison, rib height and thickness were measured on CT scans of children. Rib height increased with rib level, increasing by 13% between the 3rd and 7th rib levels, where the 7th/8th rib was the widest part or "equator" of the rib cage, P < 0.001 (t-test). Rib thickness showed a statistically significant 23% increase between the 3rd and 7th ribs, P = 0.004 (t-test). Intercostal muscle force was significantly related to vector stress, Pearson correlation r = 0.944, P = 0.005. The three nonlinear quadratic models developed all had statistically significant parameter estimates with P < 0.03. External rib morphology, in particular rib height and thickness, can be predicted using statistical mathematical models. Rib height is significantly related to the calculated intercostal muscle force, showing that environmental factors affect external rib morphology.

Hierarchical auxetic mechanical metamaterials.

Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poisson's ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poisson's ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts.

Tailoring graphene to achieve negative Poisson's ratio properties.

Graphene can be made auxetic through the introduction of vacancy defects. This results in the thinnest negative Poisson's ratio material at ambient conditions known so far, an effect achieved via a nanoscale de-wrinkling mechanism that mimics the behavior at the macroscale exhibited by a crumpled sheet of paper when stretched.