Approach à la Piola for the equilibrium problem of bodies with second gradient energies. Part II: Variational derivation of second gradient equations and their transport

After the wide premise of Part I, where the equations for Cauchy’s continuum were retrieved through the energy minimization and some differential geometric perspectives were specified, the present paper as Part II outlines the variational derivation of the equilibrium equations for second gradient materials and their transformation from the Eulerian to the Lagrangian form. Volume, face and edge contributions to the inner virtual work were provided through integration by parts and by repeated applications of the divergence theorem extended to curved surfaces with border. To sustain double forces over the faces and line forces along the edges, the role of the third rank hyperstress tensor was highlighted. Special attention was devoted to the edge work, and to the evaluation of the variables discontinuous across the edge belonging to the contiguous boundary faces. The detailed expression of the contact pressures was provided, including multiple products of normal vector components, their gradient and a combination of them: in particular, the dependence on the local mean curvature was shown. The transport of the governing equations from the Eulerian to the Lagrangian configuration was developed according to two diverse strategies, exploiting novel differential geometric formulae and revealing a coupling of terms transversely to the involved domains

Third gradient continua: nonstandard equilibrium equations and selection of work conjugate variables

This paper outlines the variational derivation of the Lagrangian equilibrium equations for the third-gradient materials, stemming from the minimization of the total potential energy functional, and the selection of suitable dual variables to represent the inner work in the Eulerian configuration. Volume, face, edge and wedge contributions were provided through integration by parts of the inner virtual work and by repeated applications of the divergence theorem extended to embedded submanifolds with codimension one and two. Detailed expressions were provided for the contact pressures and the edge loading, revealing the complex dependence on the face normals and on the mean curvature. Relationships were specified among the Lagrangian (hyper-)stress tensors of rank lower or equal to four, and their Eulerian counterparts

Deformation induced coupling of the generalized external actions in third-gradient materials

In this study, diverse typologies of external actions are outlined, which turn out to be admissible for the thirdgradient modeling of elastic materials. It is shown how such loading, when prescribed over the boundary surface, along the border edges and at the wedges of a deformable body in the Eulerian configuration, can be transformed into the Lagrangian description generating multiple interactions, with a surprising deformation-induced coupling. Such a phenomenon becomes more and more important at increasing the order of the β-forces, specified by duality as covectors expending work on the βth normal derivative of the virtual displacements, being herein at most β = 2. Insights are provided into the true nature of such generalized forces, resting on the differential geometric features of the deformation proces

Extended Identification of Mechanical Parameters and Boundary Conditions by Digital Image Correlation

Abstract This paper represents a further contribution to the study of identification procedures for material mechanics resting on kinematic measurements provided by 2D Digital Image Correlation (DIC) at the microscale. Reference is made to non-conventional experiments on adhesively bonded assemblies industrially manufactured for aerospace applications. For calibration purposes a local approach is considered under plane stress conditions, focusing on a small sub-domain on the sample surface, in which mixed mode debonding is monitored. As a novelty, both the (cohesive) mechanical parameters of the interface and the actual boundary conditions prescribed at different time instants during the test are considered as unknowns to be estimated on the basis of full-field data. In this way, data smoothing and parameter identification procedures, so far usually performed in a sequence, are tackled simultaneously in a coupled framework. Since the inverse problem generalized as mentioned above turns out to be severely ill-posed, suitable regularizing provisions are applied, concerning the a priori regularity of (kinematic) displacement fields, from which boundary data are sampled, and the equilibrium (Neumann) conditions along the cracked part of the interface

Limit analysis assessment of experimental behavior of arches reinforced with GFRP materials

In this paper, a comparison between results furnished by a 3D FE upper bound limit analysis and experimental results for some reinforced masonry arches tested at the University of Minho (Portugal) is provided. While the delamination from arches support can be modelled only in an approximate way within limit analysis, the aim of the paper is to accurately reproduce the change in the failure mechanism observed in experimentation, due to the introduction of strengthening elements. Both experimental and numerical results showa clear change in the failure mechanism and in the corresponding ultimate peak load. A set of simulations is also performed on reinforced arches previously damaged, to investigate the role played by the reinforcement within a proper repairing procedure. Good correlation with experimental work and numerical simulations is achieved.info:eu-repo/semantics/publishedVersio

Numerical and experimental analysis of full scale arches reinforced with GFRP materials

In this contribution, original limit analysis numerical results are presented dealing with some reinforced masonry arches tested at the University of Minho-UMinho, PT. Twelve in-scale circular masonry arches were considered, reinforced in various ways at the intrados or at the extrados. GFRP reinforcements were applied either on undamaged or on previously damaged elements, in order to assess the role of external reinforcements even in repairing interventions. The experimental results were critically discussed at the light of limit analysis predictions, based on a 3D FE heterogeneous upper bound approach. Satisfactory agreement was found between experimental evidences and the numerical results, in terms of failure mechanisms and peak load.(undefined

Echocardiography combined with cardiopulmonary exercise testing for the prediction of outcome in idiopathic pulmonary arterial hypertension

BACKGROUND: Right ventricular (RV) function is a major determinant of exercise intolerance and outcome in idiopathic pulmonary arterial hypertension (IPAH). The aim of the study was to evaluate the incremental prognostic value of echocardiography of the RV and cardiopulmonary exercise testing (CPET) on long-term prognosis in these patients. METHODS: One hundred-thirty treatment-naïve IPAH patients were enrolled and prospectively followed. Clinical worsening (CW) was defined by a reduction in 6-minute walk distance plus an increase in functional class, or non elective hospitalization for PAH, or death. Baseline evaluation included clinical, hemodynamic, echocardiographic and CPET variables. Cox regression modeling with c-statistic and bootstrapping validation methods were done. RESULTS: During a mean period of 528 ± 304 days, 54 patients experienced CW (53%). Among demographic, clinical and hemodynamic variables at catheterization, functional class and cardiac index were independent predictors of CW (Model-1). With addition of echocardiographic and CPET variables (Model-2), peak O2 pulse (peak VO2/heart rate) and RV fractional area change (RVFAC) independently improved the power of the prognostic model (AUC: 0.81 vs 0.66, respectively; p=0.005). Patients with low RVFAC and low O2 pulse (low RVFAC + low O2 pulse) and high RVFAC+low O2 pulse showed 99.8 and 29.4 increase in the hazard ratio, respectively (relative risk -RR- of 41.1 and 25.3, respectively), compared with high RVFAC+high O2 pulse (p=0.0001). CONCLUSIONS: Echocardiography combined with CPET provides relevant clinical and prognostic information. A combination of low RVFAC and low O2 pulse identifies patients at a particularly high risk of clinical deterioration

Therapeutic Strategies in Pulmonary Arterial Hypertension

Pulmonary arterial hypertension (PAH) is a serious and life-threatening condition for which the prognosis remains poor. Treatment options include endothelial receptor antagonists, phosphodiesterase (PDE5) inhibitors and prostanoids. Despite all demonstrating good short-term efficacy, none of the currently available drug therapies are curative. Treatment with prostanoids is complex and requires careful monitoring and management through a specialist centre. Furthermore, clinical efficacy is dependent on adequate up-titration of the drug. Treatment should be individualised and modified according to clinical response, with the addition of other therapies if required. The importance of monitoring and modifying therapeutic regimes is discussed. There appears to be reluctance among patients and physicians to employ prostanoid therapy, though an aggressive first-line therapy may be appropriate in advanced cases

Permeable Asphalt Hydraulic Conductivity and Particulate Matter Separation With XRT

Permeable asphalt (PA) is a composite material with an open graded mix design that provides a pore structure facilitating stormwater infiltration. PA is often constructed as a wearing course for permeable pavements and on impervious pavements to reduce aquaplaning and noise. The pore structure of PA functions as a filter promoting particulate matter (PM) separation. The infiltrating flow characteristics are predominately dependent on pore diameter and pore interconnectivity. X-Ray microTomography (XRT) has successfully estimated these parameters that are otherwise difficult to obtain through conventional gravimetric methods. Pore structure parameters allow modeling of hydraulic conductivity (k) and filtration mechanisms; required to examine the material behavior for infiltration and PM separation. In this study, pore structure parameters were determined through XTR for three PA mixture designs. Additionally, the Kozeny-Kovav model was implemented to estimate k. PM separation was evaluated using a pore-to-PM diameter categorical model. This filtration mechanism model was validated with data from a rainfall simulator. The filtration model provided a good correlation between measured and modeled data. The identification of filtration mechanisms and k facilitate the design and evaluation of permeable pavement systems as a best management practice (BMP) for runoff volume and peak flow as well as PM and PM-partitioned chemical separation