On Eshelby’s inclusion problem in nonlinear anisotropic elasticity

In this paper, the recent literature of finite eignestrains in nonlinear elastic solids is reviewed, and Eshelby’s inclusion problem at finite strains is revisited. The subtleties of the analysis of combinations of finite eigenstrains for the example of combined finite radial, azimuthal, axial and twist eigenstrains in a finite circular cylindrical bar are discussed. The stress field of a spherical inclusion with uniform pure dilatational eigenstrain in a radially-inhomogeneous spherical ball made of arbitrary incompressible isotropic solids is analyzed. The same problem for a finite circular cylindrical bar is revisited. The stress and deformation fields of an orthotropic incompressible solid circular cylinder with distributed eigentwists are analyzed.

A boundary value problem of orthotropic electroelastic circular cylinder

A boundary value problem of orthotropic piezoelectric solid circular cylinder which is in the state of antiplane shear deformation is studied. The whole boundary surface is loaded by an equilibrium axial traction. This paper gives an analytical solution of the considered antiplane shear deformation.

Saint-Venant torsion of non-homogeneous orthotropic circular cylinder

The object of this paper is the Saint-Venant torsion of a radially non-homogeneous, hollow and solid circular cylinder made of orthotropic piezoelectric material. The elastic stiffness coefficients, piezoelectric constants and dielectric constants have only radial dependence. This paper gives the solution of the Saint-Venant torsion problem for torsion function, electric potential function, Prandtl’s stress function and electric displacement potential function.

Hygrothermoelastic response of a finite solid circular cylinder

Purpose In this paper, a solid circular cylinder of finite length occupying the space 0⩽r⩽1, 0⩽z⩽h is considered. The purpose of this paper is to adopt a linear hygrothermal effect to analyze the unsteady state responses in a finite long solid cylinder subjected to axisymmetric hygrothermal loading T=TR and C=CR at the surface. The analytical solution of temperature, moisture and thermal stresses is obtained by using the integral transform technique. The coupling and uncoupling effects of temperature, moisture and thermal stresses are discussed for a graphite fiber-reinforced epoxy matrix composite material (T300/5208). The numerical results of transient response hygrothermoelastic field are presented graphically. Design/methodology/approach In the present problem, hygrothermoelastic response of a finite solid circular cylinder has been investigated by integral transform technique consisting of Laplace transform, Hankel transform and Fourier-cosine transform. The problem is investigated subjected to prescribed sources. Numerical algorithm has been developed for numerical computation. Findings The analytical solution of temperature, moisture and thermal stresses is obtained by using the integral transform technique. The coupling and uncoupling effects of temperature, moisture and thermal stresses are discussed for a graphite fiber-reinforced epoxy matrix composite material (T300/5208). The numerical results of transient response hygrothermoelastic field are presented graphically. Research limitations/implications The work presented here is mostly hypothetical in nature and totally mathematical. Practical implications It may be useful for composite materials, composite laminated plates in hygrothermal environment. Also it is having the applications in hygrothermal field where porous media exposed to heat and moisture. The problem investigated will be beneficial for the researcher working in the field thermoelastic diffusion and hygrothermoelastic materials. Originality/value Till date, the other authors did the research work on hygrothermal effect of an infinitely long cylinder without thickness. In this paper, the authors consider finite solid cylinder with finite length and discuss the hygrothermal effect within a small range. Second, the material properties are both homogenous and isotropic and are independent of both temperature and moisture.

Axisymmetric equilibrium of an isotropic elastic solid circular finite cylinder

Axisymmetric equilibrium of an elastic solid circular finite cylinder is one of the oldest problems in the theory of linear elasticity. Crosswise superposition is a well-known method that is used to solve this boundary value problem (BVP); however, technical realization of its underlying ideas still seems to be vague and the solution obtained by this method suffers from some convergence issues. In this study, we follow two main objectives via analyzing a benchmark problem where an isotropic elastic solid circular cylinder of finite length is subjected to normal lateral loading. The first goal is to add more insight into the method of crosswise superposition by extending the ideas that are used for solving classical BVPs via the superposition principle. For this purpose, a new unified approach that naturally gives rise to the subtle concept of corner conditions (CCs) in the context of crosswise superposition method is introduced. Another goal is to demonstrate the influence of CCs on the convergence of the solution obtained by the method of crosswise superposition. In this avenue, the Love function approach is used to convert the Navier equations for an isotropic elastic material to a single axisymmetric biharmonic equation. Next, a general solution for the axisymmetric biharmonic equation consisting of separable and non-separable solutions is presented in cylindrical coordinates. These two classes of solutions are used to construct the Love function and associated elastic fields through the unified approach. Numerical results reveal that considering the CCs can significantly affect the convergence rate of the solution on the boundaries of the cylinder. Furthermore, it is observed that the solution does not converge to the boundary data at the rims without considering the CCs. Far enough from the boundaries of the cylinder, the solution does not seem to be much different with or without taking the CCs into account.