Generalized Hooke's law for isotropic second gradient materials

In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortun\'e & Vall\'ee. Linear isotropic constitutive relations for stress and hyperstress in terms of strain and strain-gradient are then obtained proving that these materials are characterized by seven elastic moduli and generalizing previous studies by Toupin, Mindlin and Sokolowski. Using a suitable decomposition of the strain-gradient, it is found a necessary and sufficient condition, to be verified by the elastic moduli, assuring positive definiteness of the stored elastic energy. The problem of warping in linear torsion of a prismatic second gradient cylinder is formulated, thus obtaining a possible measurement procedure for one of the second gradient elastic moduli.Comment: 20 page

A phase field model for partially saturated geomaterials describing fluid–fluid displacements. Part I: The model and one-dimensional analysis

A model describing immiscible fluid-fluid displacements in partially saturated porous media is presented. This is based on a phase field approach that interprets the mixture of wetting (liquid water) and non-wetting (air) fluids within the pore space as a single saturating non-uniform pore fluid characterized by a phase field parameter, which is considered to be the saturation degree of the wetting fluid. While the standard retention curve provides for the retention properties of the pore walls, a Cahn-Hilliard like double-well energy is employed to describe the possible co-existence of the immiscible fluid phases. An enhanced description of the macroscopic surface tension between the fluid phases is obtained naturally within the phase field framework due to a regularization that depends on the spatial gradient of the water content. A generalized Darcy's law is used to describe dissipation due to fluid flow driven by the gradient of a generalized chemical potential. Thus, in the context of soil hydrology this model is interpreted as an extension to the classical Richards equation governing the spatio-temporal evolution of the phase field parameter. Employing a convex-concave flux function it is shown, using one-dimensional analysis, that both imbibition and drainage fronts can be modeled in this phase field framework. The non-monotonicities observed in the resolved solutions are explained using a combination of asymptotic matching techniques and dynamical systems analysis

Variational Approach to Damage Induced by Drainage in Partially Saturated Granular Geomaterials

Within the context of immiscible biphasic flow in porous media, when the nonwetting fluid invades the pore spaces which are a priori saturated with the wetting fluid, capillary forces dominate if the pore network is formed by fine-grained soils. Owing to the cohesion-less frictional behavior of such soils, a capillary force-driven fracturing phenomenon has been put forward by some researchers. Unlike the purely mechanistic tensile force-driven mode-I fracturing that typically has been attributed to the formation of desiccation cracks in soils, attempts to model this alternate capillarity-driven mechanism have not yet been realized at a continuum scale. However, the macro-scale counterpart of the capillary energy associated with the various pore-scale menisci is well-established as the interfacial energy characterized by the soil-water retention curve. An investigation of the possible contribution of this interfacial energy in supplying the dissipation related to fracture initiation is the essence of this work, inspired by the vast literature on gradient damage modeling

Can the intraprostatic concentration of epidermal growth factor influence the variance of serum prostate specific antigen levels in patients with benign prostatic hyperplasia?

Purpose: Except for prostate volume, little is known about the factors influencing serum prostate specific antigen (PSA) levels. Considering that dihydrotestosterone and epidermal growth factor are regulators of the proliferation and differentiation in the epithelial component of human prostate tissue and that PSA is produced only by the epithelial cells of the gland, studies were performed on patients with a histological diagnosis of benign prostatic hyperplasia (BPH) to establish whether a significant association exists between the intraprostatic concentration of dihydrotestosterone or epidermal growth factor and serum PSA levels. Materials and Methods: A total of 20 patients with BPH who had not been previously treated were part of a larger study on the correlation among PSA, prostate volume and age, and were evaluated according to the algorithm in the guidelines of the international consultation on BPH. All men underwent open suprapubic prostatectomy to enucleate the entire adenoma and in each case sections were made in the periurethral, subcapsular and intermediate zones of the BPH tissue. Dihydrotestosterone and epidermal growth factor concentrations were evaluated by radioimmunoassay in the periurethral zone and in total BPH tissue. Results: In these 20 patients with BPH serum PSA levels were significantly associated with epidermal growth factor but not with dihydrotestosterone concentrations in total BPH tissue (r = 0.7762, p = 0.00002836 and r = 0.3923, p = 0.0956307, respectively). A stronger association was found between PSA levels and the periurethral concentration of epidermal growth factor and dihydrotestosterone (r = 0.8117, p = 0.000005 and r = 0.5656, p = 0.0098326, respectively). On the contrary, epidermal growth factor and dihydrotestosterone were not significantly associated with prostate volume (p = 0.957415 and p = 0.531439, respectively). Conclusions: To our knowledge this study is the first report in the literature to demonstrate an association between serum PSA, and dihydrotestosterone and epidermal growth factor levels, particularly in the periurethral zone of human BPH tissue. These data suggest the importance of epidermal growth factor and dihydrotestosterone in influencing serum PSA levels

Fingering and strain localization in porous media during imbibition processes

Fingered infiltration of a wetting fluid through a porous network is a widely studied subject in the field of fluid mechanics. However, the effect of this heterogeneous percolation on the response of granular materials, in particular fine-grained soils, is a poorly investigated and badly understood topic which deserves deep analysis, considering, among others, possible applications in soil remediation and underground energy storage. This paper presents a first application of a new formulation of unsaturated poromechanics based on a phase field approach that allows to characterize on the one hand the occurrence of fingering hydraulic instabilities and on the other one to capture their effects on the irreversible, and possible unstable, deformation of the solid skeleton. The envisaged application concerns the behavior of fine-grained soils whose dilatant/contractant behavior is more and more attracting the interest of the scientific community both in the fields of experimental research and numerical modeling

Thermal and Structural Analysis of Helicopter Transmission Housings Using NASTRAN

The application of NASTRAN to improve the design of helicopter transmission housings is described. A finite element model of the complete forward rotor transmission housing for the Boeing Vertol CH-47C helicopter was used to study thermal distortion and stress, stress and deflection due to static and dynamic loads, load paths, and design optimization by the control of structural energy distribution. The analytical results are correlated with test data and used to reduce weight and to improve strength, service life, failsafety, and reliability. The techniques presented, although applied herein to helicopter transmissions, are sufficiently general to be applicable to any power transmission system