Isotropic Compressible Material Research Articles

Initiation of localized plane deformations at a circular cavity in an infinite compressible nonlinearly elastic medium

This investigation is concerned with the plane strain deformation of an infinite slab, containing a circular cavity, within the theory of finite elastostatics for a particular homogeneous isotropic compressible material, the so-called Blatz-Ko material. The body is subjected to uniform pressure, either internal or external. Exact closed-form solutions for the axisymmetric deformation and stress fields are obtained. In the case of internal pressure, it is found that the applied pressure may not exceed a certain maximum value pmax. At a value of pressure pe (<pmax), the governing equations lose ellipticity at the cavity wall. For greater values of pressure this solution remains smooth, though involving both elliptic and non-elliptic regions. Non-existence of axisymmetric solutions with discontinuous strain fields is established. The possibility of bifurication into a surface mode is considered and it is shown that this occurs at a value of pressure slightly smaller than pe. Such surface wrinkling leads to a periodic distribution of points of stress concentration, from which shear bands may initiate.

A Note on the Finite Elastic Inflation of a Thin Spherical Shell

The finite elastic inflation of a thin spherical shell is considered for compressible isotropic materials. A numerical method is used which allows the inflation problem to be done for any strain energy function. This method reduces to the solution of two nonlinear algebraic equations which can be solved on a desk-type programmable calculator.

Second-order torsion and bending of isotropic elastic cylinders

The problem of the second-order torsion of a cylinder of compressible isotropic material is reduced to the solution of a single boundary-value problem involving two complex potential functions. Without solving this boundary-value problem, a formula for the fractional elongation of the cylinder is obtained in agreement with that found previously by Rivlin (1953). When the region occupied by any cross-section of the cylinder is bounded by a single closed curve the equation satisfied by the complex potentials reduces to that obtained by Green &amp; Shield (1951) for the case of an incompressible cylinder, and a general method of solution was given by these authors. The problem of second-order bending of a cylinder of compressible isotropic material by couples over its plane ends is also reduced to the solution of a single boundary-value problem for two complex potential functions, in addition to the boundary-value problem for classical torsion of a cylinder. A general formula is found for the change in length of the line of centroids and one applicaton of the theory is made to right circular cylinders.