Orthotropic cyclic stress-softening model for pure shear during repeated loading and unloading

We derive an orthotropic model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress-strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of strain-induced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the strain-induced anisotropy of the stress response is different in each of these three directions. We derive non-linear orthotropic models for the elastic response, stress relaxation and residual strain to model accurately the inelastic features associated with cyclic stress softening. We then develop an orthotropic version of the Arruda-Boyce eight-chain model of elasticity and then combine it with the ideas previously developed in this paper to produce an orthotropic constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed here includes the widely occurring effects of hysteresis, stress-relaxation and residual strain. The model is found to compare well with experimental data

On the complex singularities of the inverse Langevin function

We study the inverse Langevin function $\mathscr{L}^{-1}(x)$ because of its importance in modelling limited-stretch elasticity where the stress and strain energy become infinite as a certain maximum strain is approached, modelled here by $x\to1$. The only real singularities of the inverse Langevin function $\mathscr{L}^{-1}(x)$ are two simple poles at $x=\pm1$ and we see how to remove their effects either multiplicatively or additively. In addition, we find that $\mathscr{L}^{-1}(x)$ has an infinity of complex singularities. Examination of the Taylor series about the origin of $\mathscr{L}^{-1}(x)$ shows that the four complex singularities nearest the origin are equidistant from the origin and have the same strength; we develop a new algorithm for finding these four complex singularities. Graphical illustration seems to point to these complex singularities being of a square root nature. An exact analysis then proves these are square root branch points.Comment: 25 pages, 10 figures, 4 tables, 50 equations, 28 reference

Wave stability in anisotropic generalized temperature-rate-dependent thermoelasticity

Temperature-rate-dependent thermoelasticity is a theory of thermoelasticity in which two relaxation times are introduced into the equations of classical thermoelasticity. An important consequence of this theory is that heat now travels at a finite speed rather than the infinite speed implied by the diffusion equation. In an anisotropic temperature-rate-dependent thermoelastic material, it is found that four plane harmonic waves may propagate in any direction, all dispersive and attenuated, yet all are stable in the sense that their amplitudes remain bounded. An alternative theory that forces heat to travel at finite speed is generalized thermoelasticity in which the rate of change of heat flux also appears in the heat conduction equation, thereby introducing a relaxation time. Two different methods of combining the effects of temperature-rate-dependent thermoelasticity and generalized thermoelasticity are discussed, and it is found that at least some of the four waves become unstable

Stability in constrained temperature-rate-dependent thermoelasticity

In an anisotropic temperature-rate-dependent thermoelastic material four plane harmonic waves may propagate in any direction, all dispersive and attenuated, and all stable in the sense that their amplitudes remain bounded in the direction of travel. In this paper, the material is additionally assumed to suffer an internal constraint of the deformation-temperature type, i.e. the temperature is a prescribed function of the deformation gradient. In this constrained thermoelastic material four waves continue to propagate but instabilities are now found. Constrained temperature-rate-dependent thermoelasticity is then combined with generalized thermoelasticity in which the rate of change of heat flux also appears in the heat conduction equation. Four waves again propagate but instabilities are found as before. Anisotropic and isotropic materials are both considered

Mapping the sensitivity of split ring resonators using a localized analyte

Split ring resonator (SRR) based metamaterials have frequently been demonstrated for use as optical sensors of organic materials. This is made possible by matching the wavelength of the SRR plasmonic resonance with a molecular resonance of a specific analyte, which is usually placed on top of the metal structure. However, systematic studies of SRRs that identify the regions that exhibit a high electric field strength are commonly performed using simulations. In this paper we demonstrate that areas of high electric field strength, termed “hot-spots,” can be found by localizing a small quantity of organic analyte at various positions on or near the structure. Furthermore, the sensitivity of the SRR to the localized analyte can be quantified to determine, experimentally, suitable regions for optical sensing

Associations of Vitamin D with Inter- and Intra-Muscular Adipose Tissue and Insulin Resistance in Women with and without Polycystic Ovary Syndrome

Low vitamin D and insulin resistance are common in polycystic ovary syndrome (PCOS) and associated with higher inter- and intra-muscular adipose tissue (IMAT). We investigated associations between vitamin D, IMAT and insulin resistance in a cross-sectional study of 40 women with PCOS and 30 women without PCOS, and pre- and post-exercise in a 12-week intervention in 16 overweight participants (10 with PCOS and six without PCOS). A non-classical body mass index (BMI) threshold was used to differentiate lean and overweight women (BMI ≥ 27 kg/m²). Measurements included plasma 25-hydroxyvitamin D (25OHD), insulin resistance (glucose infusion rate (GIR; mg/m²/min), fasting glucose and insulin, and glycated haemoglobin), visceral fat, mid-thigh IMAT (computed tomography) and total body fat (dual-energy X-ray absorptiometry). Women with both PCOS and low 25OHD levels had the lowest GIR (all p < 0.05). Higher IMAT was associated with lower 25OHD (B = -3.95; 95% CI -6.86, -1.05) and GIR (B = -21.3; 95% CI -37.16, -5.44) in women with PCOS. Overweight women with pre-exercise 25OHD ≥30 nmol/L had significant increases in GIR, and decreases in total and visceral fat (all p < 0.044), but no associations were observed when stratified by PCOS status. Women with PCOS and low 25OHD levels have increased insulin resistance which may be partly explained by higher IMAT. Higher pre-training 25OHD levels may enhance exercise-induced changes in body composition and insulin resistance in overweight women

IL-13 Augments Compressive Stress–Induced Tissue Factor Expression in Human Airway Epithelial Cells

Tissue factor (TF) is best known as a cellular initiator of coagulation, but it is also a multifunctional protein that has been implicated in multiple pathophysiologic conditions, including asthma. In the lung, airway epithelial cells express TF, but it is unknown how TF expression is regulated by asthma-associated mediators. We investigated the role of IL-13, a type 2 cytokine, alone and in combination with compressive stress, which mimics asthmatic bronchoconstriction, on TF expression and release of TF-positive extracellular vesicles from primary normal human bronchial epithelial cells. Well-differentiated normal human bronchial epithelial cells were treated with IL-13 and compressive stress, alone and in combination. TF mRNA, protein and activity were measured in the cells and conditioned media. TF was also measured in the bronchoalveolar lavage (BAL) fluid of allergen-challenged mice and patients with asthma. IL-13 and compressive stress increased TF expression, but only compressive stress induced TF-positive extracellular vesicle release. Pretreatment with IL-13 augmented compressive stress–induced TF expression and release. TF protein and activity in BAL fluid were increased in allergen-sensitized and -challenged mice. TF was elevated in the BAL fluid of patients with mild asthma after an allergen challenge. Our in vitro and in vivo data indicate close cooperation between mechanical and inflammatory stimuli on TF expression and release of TF-positive extracellular vesicles in the lungs, which may contribute to pathophysiology of asthma