On 3D Anticrack Problem of Thermoelectroelasticity

A solution is presented for the static problem of thermoelectroelasticity involving a transversely isotropic space with a heat-insulated rigid sheet-like inclusion (anticrack) located in the isotropy plane. It is assumed that far from this defect the body is in a uniform heat flow perpendicular to the inclusion plane. Besides, considered is the case where the electric potential on the anticrack faces is equal to zero. Accurate results are obtained by constructing suitable potential solutions and reducing the thermoelectromechanical problem to its thermomechanical counterpart. The governing boundary integral equation for a planar anticrack of arbitrary shape is obtained in terms of a normal stress discontinuity. As an illustration, a closed-form solution is given and discussed for a circular rigid inclusion.

Analysis of the Nonlinear Elastic Response of Rubber Membrane with Embedded Circular Rigid Inclusion

Rubber membranes exhibit a particular nonlinear elastic behaviour known as hyper elasticity. Analysis has been proposed by utilizing the modified strain energy function from Gao’s constitutive model, in order to reveal the mechanical property of rubber membrane containing circular rigid inclusion. Rubber membrane is taken into incompressible materials under axisymmetric stretch, based on finite deformations theory. Stress distribution of different constitutive parameters has been analyzed by deducing the basic governing equation. The effects on membrane deformation by different parameters and the failure reasons of rubber membrane have been discussed, which provides reasonable reference for the design of rubber membrane.

Boundary Perturbation Solution for Nearly Circular Holes and Rigid Inclusions in an Infinite Elastic Medium

The boundary perturbation method is used to solve the problem of a nearly circular rigid inclusion in a two-dimensional elastic medium subjected to hydrostatic stress at infinity. The solution is taken to the fourth order in the small parameter epsilon that quantifies the magnitude of the variation of the radius of the inclusion. This result is then used to find the effective bulk modulus of a body that contains a dilute concentration of such inclusions. The corresponding results for a cavity are obtained by setting the Muskhelishvili coefficient κ equal to −1, as specified by the Dundurs correspondence principle. The results for nearly circular pores can be expressed in terms of the pore compressibility. The pore compressibilities given by the perturbation solution are tested against numerical values obtained using the boundary element method, and are shown to have good accuracy over a substantial range of roughness values.