1,721,000 research outputs found
“Inhomogeneous shear of orthotropic incompressible non-linearly elastic solids: singular solutions and biomechanical interpretation”
No full textThe rectilinear shear of fiber-reinforced incompressible non-linearly elastic solids
No full textIn this paper we study the problem of rectilinear shear of a slab of transversely isotropic incompressible non-linearly elastic material. In
particular, the material under consideration is a base neo-Hookean model augmented with a function that accounts for the existence of a
unidirectional reinforcement. The slab is of infinite length in two dimensions and finite thickness in the other one and is clamped to two rigid
plates. Closed form analytic solutions are found for this problem. It is shown that, depending on the reinforcement strength and the fiber
orientation in the undeformed configuration, weak solutions, i.e. solutions for which the smoothness required by the differential equations is
relaxed, are to be expected. These solutions give rise to fiber kinking. It is shown that: (i) both sides of the kink involve fiber contraction; (ii)
a suitable intermediate deformation between the two conjoined kink deformation states is non-elliptic
Proceedings of the WASCOM 2011 conference. Special issue of the journal Acta Applicandae Mathematicae with the contributions of the speakers.
No full textProceedings of the WASCOM 2011 conference. Special issue of the journal Acta Applicandae Mathematicae (ISSN 1572-9036) with the contributions of the speakers. Website of the conference: http://wascom.matematica.unisalento.it
A continuum hyperelastic model for auxetic materials
No full textWe propose a simple mathematical model to describe isotropic auxetic materials in the framework of the classical theory of nonlinear elasticity. The model is derived from the Blatz-Ko constitutive equation for compressible foams and makes use of a non-monotonic Poisson function. An application to the modelling of auxetic foams is considered and it is shown that the material behaviour is adequately described with only three constitutive parameters
Fitting hyperelastic models to experimental data
No full textThis paper is concerned with determining material parameters in incompressible isotropic elastic strain–energy functions on the basis of a non-linear least squares optimization method by fitting data from the classical experiments of Treloar and Jones and Treloar on natural rubber. We consider three separate forms of strain-energy function, based respectively on use of the principal stretches, the usual principal invariants of the Cauchy-Green deformation tensor and a certain set of lsquoorthogonalrsquo invariants of the logarithmic strain tensor. We highlight, in particular, (a) the relative errors generated in the fitting process and (b) the occurrence of multiple sets of optimal material parameters for the same data sets. This multiplicity can lead to very different numerical solutions for a given boundary-value problem, and this is illustrated for a simple example
Proceedings of the WASCOM 2011 conference - Invited SpeakersSpecial issue of the journal Note di Matematica
No full textProceedings of the WASCOM 2011 conference, contributions of the invited speakers. Website of the conference: http://wascom.matematica.unisalento.it/
It is Volume 32 n. 1 of the journal Note di Matematic
Weierstrass's criterion and compact solitary waves
No full textWeierstrass’s theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to identify some differential equations for which compact and even semicompact traveling solitary
waves exist. In the framework of continuum mechanics, these differential equations correspond to bulk shear waves for a special class of constitutive laws
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