Comparative assessments of strain measures for nonlinear analysis of truss structures at large deformations

PurposeIn this paper the use of classical strain measures in analysis of trusses at finite deformations will be discussed. The results will be compared to the ones acquired using a novel strain measure based on the Hyperbolic Sine function. Through the evaluation of results, algebraic development and graph analysis, the properties of the Hyperbolic Sine strain measure will be examined.Design/methodology/approachThrough graph plotting, comparisons between the novel strain measure and the classic ones will be made. The formulae for the implementation of the Hyperbolic Sine strain measure into a positional finite element method are developed. Four engineering applications are presented and comparisons between results obtained using all strain measures studied are made.FindingsThe proposed strain measure, Hyperbolic Sine, has objectivity and symmetry. The linear constitutive model formed by the Hyperbolic Sine strain and its conjugated stress presents an increasing stiffness, both in compression and tension, a behavior that can be useful in the modeling of several materials.Research limitations/implicationsThe structural analysis performed on the four examples of trusses in this article did not consider the variation of the cross-sectional area of the elements or the buckling phenomenon, moreover, only elastic behavior is considered.Originality/valueThe present article proposes the use of a novel strain measure family, based on the Hyperbolic Sine function and suitable for structural applications. Mathematical expressions for the use of the Hyperbolic Sine strain measure are established following the energetic concepts of the positional formulation of the finite element method.

AB0169 INTEREST OF THE ECHOCARDIOGRAPHY IN SCREENING OF CARDIAC INVOLVEMENT IN RHEUMATOID ARTHRITIS PATIENTS

Background:Rheumatoid arthritis (RA) is the most common chronic inflammatory disease which usually affects peripheral joints.Extra-articular manifestations can occur during the course of this disease and even before the onset of arthritis, such as cardiac impairment that is a common cause of mortality in RA.Objectives:The aim of our study is to identify the prevalence of cardiac manifestations in RA using the echocardiography exam and to elaborate its associated factors.Methods:This is a cross-sectional study including consecutive RA’s patients which consulted the rheumatology department in Taher Sfar hospital. The diagnosis of RA was elaborate according to ACR/EULAR 2010 criteria. The epidemiological, clinical and biological data were collected from patients’ records. Echocardiography was performed by a trained cardiologist in the same hospital, using the transthoracic approach.Results:Our study included 67 patients: 63 women (94%) and 4 men (6%), with an average age of 52.55 years [21-75 years] and mean disease duration of 11.85 years [10-40]. Joints deformities were present in 37 cases (55.2%) and radiographic joint damage in 49 cases (73.1%). 34 (50.7%) of the patients had an ESR greater than 30 mm/hour and 24 (35.8%) had a CRP greater than 6mg/L. The mean DAS28-CRP was 3.35 [1.24-6.7] and the mean DAS28-ESR was 4 [1.4-7.35]. Cardiac symptomatology was present in 22 cases (32.8%), dominated by dyspnea on effort in 22 cases (32.8%), dyspnea at rest in 4 cases (6%), chest pain in 8 cases (11.9%)and palpitation in 2 cases (3%). The echocardiography abnormalities were found in 44 cases. Valve damage was detected in 35 patients (52.2%), of which only 2 were significant. Valvular abnormalities were dominated by mitral valve regurgitation and mitral valve thickening in 11 cases (16.4%) each, aortic valve regurgitation in 6 cases (9%),aortic valve thickening in 2 cases (3%), aortic valve stenosis in 3 cases (4.5%),aortic valve calcification in 12 cases (17. 9%) aortic valve nodule in 1 case (1.5%), pulmonary insufficiency in 10 cases (14.9%) and tricuspid insufficiency in 25 cases (37.3%).Pericarditis was found in 2 cases (3%), pulmonary arterial hypertension (PAH) in 5 cases (7,5%) and Left ventricular hypertrophy in 14 cases (20,9%). The study of E/A and E/E’ ratios revealed diastolic dysfunction in 23 cases (34.3%).The mean of longitudinal global strain measure was -17,83 [-21,9 to -10] and it revealed systolic dysfunction in 18 cases (26.86%). Cardiac impairment detected by echocardiography did not appear to be associated with the age (p=0.39) or the disease duration (p=0.62) nor the importance of biological inflammation(p=0.1). However, joints deformities and RA activity (DAS28) were significant predictors of cardiac involvement (p=0.01; p=0.03).Conclusion:Our study shows that cardiac impairment in RA was often asymptomatic and was correlated with the disease activity. The echocardiography with the strain measure represents an excellent tool for its detection in early stages.References:[1]Guedes C, Bianchi-Fior P, Cormier B, Barthelemy B, Rat AC, Boissier MC. Cardiac manifestations of rheumatoid arthritis: A case-control transesophageal echocardiography study in 30 patients. Arthritis Care Res. 2001;45(2):129–35.Disclosure of Interests:None declared

Mapping and classifying large deformation from digital imagery: application to analogue models of lithosphere deformation

Summary Particle Image Velocimetry (PIV), a method based on image cross-correlation, is widely used for obtaining velocity fields from time series of images of deforming objects. Rather than instantaneous velocities, we are interested in reconstructing cumulative deformation, and use PIV-derived incremental displacements for this purpose. Our focus is on analogue models of tectonic processes, which can accumulate large deformation. Importantly, PIV provides incremental displacements during analogue model evolution in a spatial reference (Eulerian) frame, without the need for explicit markers in a model. We integrate the displacements in a material reference (Lagrangian) frame, such that displacements can be integrated to track the spatial accumulative deformation field as a function of time. To describe cumulative, finite deformation, various strain tensors have been developed, and we discuss what strain measure best describes large shape changes, as standard infinitesimal strain tensors no longer apply for large deformation. PIV or comparable techniques have become a common method to determine strain in analogue models. However, the qualitative interpretation of observed strain has remained problematic for complex settings. Hence, PIV-derived displacements have not been fully exploited before, as methods to qualitatively characterize cumulative, large strain have been lacking. Notably, in tectonic settings, different types of deformation - extension, shortening, strike-slip - can be superimposed. We demonstrate that when shape changes are described in terms of Hencky strains, a logarithmic strain measure, finite deformation can be qualitatively described based on the relative magnitude of the two principal Hencky strains. Thereby, our method introduces a physically meaningful classification of large 2D strains. We show that our strain type classification method allows for accurate mapping of tectonic structures in analogue models of lithospheric deformation, and complements visual inspection of fault geometries. Our method can easily discern complex strike-slip shear zones, thrust faults and extensional structures and its evolution in time. Our newly developed software to compute deformation is freely available and can be used to post-process incremental displacements from PIV or similar autocorrelation methods.

A new approach to curvature measures in linear shell theories

The paper presents a coordinate-free analysis of deformation measures for shells modeled as 2D surfaces. These measures are represented by second-order tensors. As is well-known, two types are needed in general: the surface strain measure (deformations in tangential directions), and the bending strain measure (warping). Our approach first determines the 3D strain tensor E of a shear deformation of a 3D shell-like body and then linearizes E in two smallness parameters: the displacement and the distance of a point from the middle surface. The linearized expression is an affine function of the signed distance from the middle surface: the absolute term is the surface strain measure and the coefficient of the linear term is the bending strain measure. The main result of the paper determines these two tensors explicitly for general shear deformations and for the subcase of Kirchhoff-Love deformations. The derived surface strain measures are the classical ones: Naghdi’s surface strain measure generally and its well-known particular case for the Kirchhoff-Love deformations. With the bending strain measures comes a surprise: they are different from the traditional ones. For shear deformations our analysis provides a new tensor [Formula: see text], which is different from the widely used Naghdi’s bending strain tensor [Formula: see text]. In the particular case of Kirchhoff–Love deformations, the tensor [Formula: see text] reduces to a tensor [Formula: see text] introduced earlier by Anicic and Léger (Formulation bidimensionnelle exacte du modéle de coque 3D de Kirchhoff–Love. C R Acad Sci Paris I 1999; 329: 741–746). Again, [Formula: see text] is different from Koiter’s bending strain tensor [Formula: see text] (frequently used in this context). AMS 2010 classification: 74B99

Elastoplastic analysis in functionally graded thick-walled rotating transversely isotropic cylinder under a radial temperature gradient and uniform pressure

In this research paper, an analytical solution with numerical illustration is presented for elastoplastic analysis in a functionally graded thick-walled rotating transversely isotropic cylinder under a radial temperature gradient and uniform pressure using the transition theory of Seth and generalized strain measure theory. The theory of Seth requires no assumptions, such as infinitesimally small deformation or material incompressibility, or a yield criterion, and is important in determining elastoplastic transitional stresses and fully plastic stresses on the basis of Lebesgue strain measure. The combined impacts of an inhomogeneity parameter, uniform pressure, temperature, and angular speed are discussed numerically and shown graphically. It is concluded that a functionally graded thick-walled rotating cylinder made of steel subjected to a radial temperature gradient and uniform pressure is on safer than a cylinder made of titanium, owing to the percentage increase in pressure. This, in turn, brings to the concept of “stress saving,” which reduces the potential for thick-walled cylinder failure. The fully plastic circumferential stress with the application of thermal effects in a functionally graded cylinder is greater than that at room temperature on the inner surface, whereas fully plastic circumferential and radial stresses for a homogeneous cylinder are independent of thermal effects.

Variation of second-order piezoelectric coefficients with respect to a finite strain measure

In this article the consequence of a change of finite strain measure is theoretically considered for nonlinear piezoelectric crystals. Analytical predictions show that second-order piezoelectric coefficients are finite strain measure dependent. Therefore, the use of any finite strain measure in constitutive modelling of piezoelectric materials requires an adequate choice of higher-order piezoelectric coefficients. This allows one to avoid unwanted corrections to the elastic and electric fields in the case of nonlinear modelling of piezoelectric materials, e.g. for piezoelectric heterostructures such as quantum wells or dots. A general transformation formula for second-order piezoelectric coefficients (elastostriction) is derived. As an example, specific transformation formulae for two common crystallographic classes, namely {\bar 4}3m and 6mm, are presented. The piezoelectric coefficients for GaN and GaAs crystals, as representative cases of these crystal classes, are recalculated and their dependence on the strain measure is demonstrated. A further implication of that effect is that a complete set of second-order piezoelectric coefficients should contain additional information about the strain measure applied during calculations or measurements.

Multifractal signatures of gravitational waves detected by LIGO

We analyze the data from the 6 gravitational waves signals detected by LIGO through the lens of multifractal formalism using the MFDMA method, as well as shuffled and surrogate procedures. We identified two regimes of multifractality in the strain measure of the time series by examining long memory and the presence of nonlinearities. The moment used to divide the series into two parts separates these two regimes and can be interpreted as the moment of collision between the black holes. An empirical relationship between the variation in left side diversity and the chirp mass of each event was also determined.