Search

In the past, to model fibre stiffness of finite-radius fibres, previous finite-strain (nonlinear) models were mainly based on the theory of non-linear strain-gradient (second-gradient) theory or Kirchhoff rod theory. We note that these models characterize the mechanical behaviour of polar transversely isotropic solids with infinitely many purely flexible fibres with zero radius. To introduce the effect of fibre bending stiffness on purely flexible fibres with zero radius, these models assumed the existence of couple stresses (contact torques) and non-symmetric Cauchy stresses. However, these stresses are not present on deformations of actual non-polar elastic solids reinforced by finite-radius fibres. In addition to this, the implementation of boundary conditions for second gradient models is not straightforward and discussion on the effectiveness of strain gradient elasticity models to mechanically describe continuum solids is still ongoing. In this paper, we develop a constitutive equation for a non-linear non-polar elastic solid, reinforced by embedded fibers, in which elastic resistance of the fibers to bending is modelled via the classical branches of continuum mechanics, where the development of the theory of stresses is based on non-polar materials; that is, without using the second gradient theory, which is associated with couple stresses and non-symmetric Cauchy stresses. In view of this, the proposed model is simple and somewhat more realistic compared to previous second gradient models. [ABSTRACT FROM AUTHOR]

Mechanical models of residually stressed fibre-reinforced solids, which do not resist bending, have been developed in the literature. However, in some residually stressed fibre-reinforced elastic solids, resistance to fibre bending is significant, and the mechanical behavior of such solids should be investigated. Hence, in this paper, we model the mechanical aspect of residually stressed elastic solids with bending stiffness due to fibre curvature, which up to the authors' knowledge has not been mechanically modeled in the past. The proposed constitutive equation involves a nonsymmetric stress and a couple-stress tensor. Spectral invariants are used in the constitutive equation, where each spectral invariant has an intelligible physical meaning, and hence they are useful in experiment and analysis. A prototype strain energy function is proposed. Moreover, we use this prototype to give results for some cylindrical boundary value problems. [ABSTRACT FROM AUTHOR]

A constitutive equation is provided for nonlinear transversely isotropic elastic solids, wherein the linearized strain tensor is assumed to be a function of the Cauchy stress tensor; this elastic constitutive equation belongs to a subclass of a more general set of implicit constitutive relations proposed in the recent years. The proposed constitutive equation is valid for both compressible and incompressible bodies and can be simply modified, to exclude the mechanical influence of compressed fibres and to model inextensible fibres. A crude specific constitutive model is proposed to compare with a uniaxial experimental data on Marcellus shale. Some simple boundary value problems are analyzed. [ABSTRACT FROM AUTHOR]

Electro-sensitive elastomers are materials that can support large elastic deformations under the influence of an electric field. There has been growing interest recently in their applications as so-called ``smart materials''. This paper is devoted to the derivation of universal relations in the context of the nonlinear theory of electroelasticity that underpins such applications. Universal relations are equations relating the components of the stress, the electric variables and the deformation that are independent of the constitutive law for a family of materials. For the general constitutive equations of an isotropic electroelastic material derived from a free energy function and for some special cases of these equations, we obtain universal relations, the word ``universal'' being relative to the considered class or subclass of constitutive laws. These universal relations are then applied to some controllable states (homogeneous and non-homogeneous) in order to highlight some examples that may be useful from the point of view of experimental characterization of the material properties. Additionally, we examine the (non-controllable) problem of helical shear of a circular cylindrical tube in the presence of a radial electric field, and we find that a nonlinear universal relation that has been obtained previously for an elastic material also holds when the electric field is applied. [ABSTRACT FROM AUTHOR]