1,721,045 research outputs found
Modeling Helicoid to Spiral-Ribbon Transitions of Twist-Nematic Elastomers
No full textNematic Elastomers (NEs) possess very interesting properties stemming from the interaction between liquid crystal order and rubber elasticity. For such materials, thermally induced phase transition from the isotropic to the nematic phase may induce very large distortions, which in turn can affect the overall configuration of a macroscopic specimen. The behavior of NEs can be well modeled within the theory of finite elasticity with distortions; here, we test a theoretical model against fancy shapes formation; in particular, we deal with the many different shapes that a thin, slender bar, made of NE, may assume as a consequence of its chiral symmetry during solvent evaporation and subsequent heating. Our goal has been to replicate with numerical experiments the phenomena of shape formation in chiral NEs, and our results constitute a noteworthy assessment of the physical model underlying the numerical solutions
About the Directions of Principal Eccentricities in Continuous Shells
No full textWe recently extended the definition of funicularity for continuous shells, introducing the concept of Relaxed Funicularity (R-Funicularity or RF). Funicular shells are defined as shells whose static behavior is given by only local membrane actions. Extension to RF is needed as funicular shells [1] can only attain pure membrane behavior for very specific boundary conditions (bcs). The RF born also for quantifying the quality of the shape of a shell, for given load and bcs, including ’small’ moments effects. Quantification of RF is made by defining a generalized eccentricity (GE) measure and verifying that the GE fall inside some eccentricity limits. Aim of this work is to discuss the nature of the GE and its associated eigenvalue problem, that allows to calculate principal eccentricities (PEs) and their directions. It is also shown how the directions of PEs are related to the relative angle between the principal directions of membrane and bending internal actions
Leo: a Multimedia Tale of Structural Mechanics
No full textThe authors have devised a method for teaching structural mechanics articulated in three phases: observations (the description of mechanical phenomena, increasingly complex, selected with regards to their pertinence of the problem that one wants to affront, and their efficiency); modeling (the construction of a physical-mathematical model that takes into account its formal content and stresses its importance as an instrument and has the potential for other applications); design (suggestion of cues for applications stimulate the student to exercise his creative imitation). What is proposed to the student is not so much a set of notions, as a method and set of instruments for selecting experiences (for example previous design solutions) to the end of evaluating their repeatability in diverse situations, by means of a physical-mechanical reading which comes from phenomena which one finds in daily life. “Leo” was created as a teaching instrument which is presented as a tale in the form of a hypertext
Comparison of Different Parallel Transport Methods for the Study of Deformations in 3D Cardiac Data
No full textComparing the deformations of different beating hearts is a challenging operation. As in clinics the impaired condition is often recognized upon (local and global) deformation parameters, the particular nature of heart deformation during one beat can be compared among different individuals in the same ordination space more effectively if initial inter-individual form (shape + size) differences are filtered out. This is even more true if the shape of cardiac trajectory itself is under consideration. This need is satisfied by applying a geometric machinery named “parallel transport” in the field of differential geometry. In recent years several parallel transport methods have been applied to cardiological data acquired via echocardiography, CT scan or magnetic resonance. Concomitantly, some efforts were made for comparing different parallel transport algorithms applied to a variety of toy examples and real deformational data. Here we face the problem of comparing the heavily used LDDMM parallel transport with the recently proposed Riemannian “TPS space” in the context of the deformation of the right ventricle. Using local tensors diagnostics and global energy-based and shape distance-based parameters, we explored the maintenance of original deformations in transported data in four systo-diastolic deformations belonging to one healthy subject and three individuals affected by tetralogy of Fallot, atrial septal defect and pulmonary hypertension. We also do the same in a larger dataset relative to the left ventricle of 82 heathly subjects and 21 patients affected by hypertrophic cardiomyopathy. We also do the same in a larger dataset relative to the left ventricle of 82 heathly subjects and 21 patients affected by hypertrophic cardiomyopathy. In particular, we contrasted the TPS space with classic LDDMM and a modified LDDMM able to manage spherical differences. Our results point toward a neat superiority of TPS space over classic LDDMM. The modified LDDMM performs similarly as it maintains better the chosen diagnostics
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