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Pure axial shear of isotropic, hyperelastic, incompressible nonlinear elastic materials with limiting chain extensibility
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Simple torsion of isotropic, hyperelas- tic, incompressible materials with limiting chain extensibility
No full text“A Two Point Boundary Value Problem for the Axial Shear of Isotropic Incompressible Nonlinearly Elastic Materials”
No full textThe purpose of this research is to investigate a pure axial shear problem for the annular region between two concentric rigid cylinders occupied by an incompressible isotropic nonlinearly elastic material. Our main concern is with the subclass of these materials that exhibits hardening at large deformations. Such hardening at large strains is observed experimentally but is often not predicted by commonly used strain-energy densities. The particular axial shear problem that we investigate arises when the elastic material is perfectly bonded to an inner rigid circular core and to an outer rigid circular container. The deformation is driven by an axial pressure gradient. The problem is formulated as a two-point boundary-value problem for a second-order nonlinear ODE. For a broad class of incompressible isotropic hyperelastic materials, existence of smooth solutions is established on conversion to an initial value problem. We then specialize the material class to be of generalized neo-Hookean type, that is, where the strain-energy density depends only on the first invariant of the strain tensor. Two classes of such materials that exhibit hardening at large deformations are considered. The first class models limiting chain extensibility at the molecular level, and the second class is of power-law type. An interesting limiting case of the latter leads to an exponential strain-energy function commonly used in modeling biological materials. Some specific strain-energy densities from each class are examined in detail. Numerical boundary-value methods with quasilinearization for nonlinear second-order ODEs are used to illustrate a special feature of the solutions. It was previously shown by other authors that, for softening power-law materials, a boundary layer behavior is exhibited near the bonded surfaces: the axial displacement undergoes a sharp increase from zero at the endpoints and is slowly varying in the interior. We provide further numerical results regarding this phenomenon here. Our main concern is, however, with hardening materials. For such materials, the numerical results exhibit an interior localization at a location which is almost the midpoint between the boundaries. The axial displacement has a sharp change of slope which, in the limit of infinitely large pressure gradients, gives rise to a cusp in the displacement profile. The results highlight the contrasting behavior between softening and hardening rubber-like or biological materials
End effects for anti-plane shear deformations of periodically laminated strips with imperfect bonding
No full textThe axial decay of Saint-Venant end effects is investigated for anti-plane shear deformations of semi-infinite generally laminated anisotropic strips. Imperfect bonding conditions are imposed at the interfaces. The analytical approach, using a displacement field which decays exponentially in the axial direction, gives rise to a transcendental equation for the real eigenvalues. The decay rate for the stresses is given in terms of the smallest positive eigenvalue. Laminated strips with periodic layout ale then considered. In the presence of imperfect bonding, the effective shear elastic moduli, computed through a homogenization method, depend on the total number of slipping interfaces in the laminate. Numerical examples confirm that the decay lengths computed with effective shear moduli represent the asymptotic values (for an increasing number of layers) for those of periodically laminated strips
End effects in multilayered orthotropic strips with imperfect bonding
No full textThe axial decay of Saint-Venant end effects is investigated for plane strain deformations of semi-infinite generally laminated orthotropic strips, subject to self-equilibrated end loading. General imperfect bonding conditions are imposed at the interfaces. The analytical approach, using an Airy stress function which decays exponentially in the axial direction, gives rise to a transcendental equation for the (generally complex) eigenvalues. The decay rate for the stresses is given in terms of the eigenvalue of smallest positive real part. The decay rates are examined analytically and numerically in a number of special cases. These include a bimaterial orthotropic strip and the special subcases of a symmetric single lap joint made of the same material, symmetric orthotropic sandwich strips and the classical symmetric double lap joint. Asymptotic estimates for the decay rates, in the case of large slip, are obtained which predict extremely slow decay of end effects
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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