Analytical continuum mechanics \`a la Hamilton-Piola: least action principle for second gradient continua and capillary fluids

In this paper a stationary action principle is proven to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard. Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both material and spatial description and the corresponding Euler-Lagrange bulk and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation tensor. When particularized to energies which characterize fluid materials, the capillary fluid evolution conditions (see e.g. Casal or Seppecher for an alternative deduction based on thermodynamic arguments) are recovered. A version of Bernoulli law valid for capillary fluids is found and, in the Appendix B, useful kinematic formulas for the present variational formulation are proposed. Historical comments about Gabrio Piola's contribution to continuum analytical mechanics are also presented. In this context the reader is also referred to Capecchi and Ruta.Comment: 52 page

Band gaps in the relaxed linear micromorphic continuum

In this note we show that the relaxed linear micromorphic model recently proposed by the authors can be suitably used to describe the presence of band-gaps in metamaterials with microstructures in which strong contrasts of the mechanical properties are present (e.g. phononic crystals and lattice structures). This relaxed micromorphic model only has 6 constitutive parameters instead of 18 parameters needed in Mindlin- and Eringen-type classical micromorphic models. We show that the onset of band-gaps is related to a unique constitutive parameter, the Cosserat couple modulus $\mu_{c}$ which starts to account for band-gaps when reaching a suitable threshold value. The limited number of parameters of our model, as well as the specific effect of some of them on wave propagation can be seen as an important step towards indirect measurement campaigns

Propagation of Acoustic Waves in Porous Media and their Reflection and Transmission at a Pure Fluid/Porous Medium Permeable Interface

International audienceWe find a sufficient condition of hyperbolicity for a differential system governing the motion of a onedimensional porous medium, so ensuring the existence of a solution for the associated Cauchy problem. We study propagation of linear waves impacting at a pure-fluid/porous-medium interface and we deduce novel expressions for the reflection and transmission coefficients in terms of the spectral properties of the governing differential system. We show three dimensional plots drawing reflection and transmission coefficients as functions of Biot's parameters. In such a way we propose an indirect method for measuring Biot's parameters when the measurement of the reflection and transmission coefficients associated to the traveling waves is possible

The bias-extension test for the analysis of in-plane shear properties of textile composite reinforcements and prepregs: a review

The bias-extension test is a rather simple experiment aiming to determine in-plane shear properties of textile composite reinforcements. However the mechanics during the test involves fibrous material at large shear strains and large rotations of the fibres. Several aspects are still being studied and are not yet modeled in a consensual manner. The standard analysis of the test is based on two assumptions: inextensibility of the fibers and rotations at the yarn crossovers without slippage. They lead to the development of zones with constant fibre orientations proper to the bias-extension test. Beyond the analysis of the test within these basic assumptions, the paper presents studies that have been carried out on the lack of verification of these hypothesis (slippage, tension in the yarns, effects of fibre bending). The effects of temperature, mesoscopic modeling and tension locking are also considered in the case of the bias-extension test

Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements

Inspired by some composite fiber reinforcements used in aeronautical engineering and by the need of conceiving new metamaterials, some discrete models including (quasi-) inextensible elasticae are considered. A class of continuum models approximately describing the macroscopic mechanical behavior of introduced structures is then heuristically proposed. Some of these continuum models can be regarded as a special kind of second-gradient elastic media, in which the higher-gradient elasticity is conferred by the flexural stiffnesses of elasticae constituting the microscopic lattice. The discrete models are studied by means of suitably tailored numerical codes designed to avoid numerical instabilities and locking and a comparison of discrete versus continuum models is attempted. The obtained results show that the theory of generalized continua may be useful in some engineering applications and it plays a relevant role in the mechanics of woven composites. The introduced discrete and continuum models are used to describe the so-called bias extension test on woven fabrics and it is shown that a good choice to correctly reproduce the targeted phenomenology is to use a second gradient continuum theory. However, as discussed throughout the paper, in the context of rigorous micro-macro identification procedures there still remain many open problems to be solved, especially when dealing with systems subjected to particular constraints, such as inextensibility. © 2014 Elsevier Ltd

Left atrial trajectory impairment in hypertrophic cardiomyopathy disclosed by geometric morphometrics and parallel transport

The analysis of full Left Atrium (LA) deformation and whole LA deformational trajectory in time has been poorly investigated and, to the best of our knowledge, seldom discussed in patients with Hypertrophic Cardiomyopathy. Therefore, we considered 22 patients with Hypertrophic Cardiomyopathy (HCM) and 46 healthy subjects, investigated them by three-dimensional Speckle Tracking Echocardiography, and studied the derived landmark clouds via Geometric Morphometrics with Parallel Transport. Trajectory shape and trajectory size were different in Controls versus HCM and their classification powers had high AUC (Area Under the Receiving Operator Characteristic Curve) and accuracy. The two trajectories were much different at the transition between LA conduit and booster pump functions. Full shape and deformation analyses with trajectory analysis enabled a straightforward perception of pathophysiological consequences of HCM condition on LA functioning. It might be worthwhile to apply these techniques to look for novel pathophysiological approaches that may better define atrio-ventricular interaction

Long-Term Outcome of Repetitive Transcranial Magnetic Stimulation in a Large Cohort of Patients With Cocaine-Use Disorder: An Observational Study

Background: Cocaine is a psychostimulant drug used as performance enhancer throughout history. The prolonged use of cocaine is associated with addiction and a broad range of cognitive deficits. Currently, there are no medications proven to be effective for cocaine-use disorder (CocUD). Previous preliminary clinical work suggests some benefit from repetitive transcranial magnetic stimulation (rTMS) stimulating the prefrontal cortex (PFC), involved in inhibitory cognitive control, decision-making and attention. All published studies to date have been limited by small sample sizes and short follow-up times. Methods: This is a retrospective observational study of 284 outpatients (of whom 268 were men) meeting DSM-5 criteria for CocUD. At treatment entry, most were using cocaine every day or several times per week. All patients underwent 3 months of rTMS and were followed for up to 2 years, 8 months. Self-report, reports by family or significant others and regular urine screens were used to assess drug use. Results: Median time to the first lapse (resumption of cocaine use) since the beginning of treatment was 91 days. For most patients, TMS was re-administered weekly, then monthly, throughout follow-up. The decrease in frequency of rTMS sessions was not accompanied by an increase in lapses to cocaine use. Mean frequency of cocaine use was <1·0 day/month (median 0), while serious rTMS-related adverse events were infrequent, consistent with published reports from smaller studies. Conclusions: This is the first follow-up study to show that rTMS treatment is accompanied by long-lasting reductions in cocaine use in a large cohort