Nonlinear eigenstrain analysis for compressible Blatz–Ko solids

Abstract

The objective of this research is to present eigenstrain analysis for a certain class of compressible, isotropic nonlinear elastic solids known as Blatz–Ko materials. The deformations and stress fields caused by eigenstrain distributions in (1) a cylindrical wedge with axisymmetric cylindrical eigenstrains, (2) a cylindrical bar with axisymmetric torsional and cylindrical eigenstrains, and (3) a spherical ball with spherically-symmetric eigenstrain distribution, which are supposed to be composed of the special Blatz–Ko material, are studied. In each problem, the form of deformation is first presumed to put the associated material manifold with Riemannian geometry in Euclidean space, and then the governing equilibrium equations are derived. The obtained nonlinear equations are solved and assessed when the structure has an inclusion with uniform eigenstrains. Moreover, this paper investigates the special solutions in which the stress becomes uniform or hydrostatic inside and outside the inclusion, or singular at the sphere center or cylinder axis. To have a better understanding of the analysis, an example is evaluated numerically in each section.