The twist-fit problem: Finite torsional and shear eigenstrains in nonlinear elastic solids

Abstract

Eigenstrains in nonlinear elastic solids are created through defects, growth or other anelastic effects. These eigenstrains are known to be important as they can generate residual stresses and alter the overall response of the solid. Here, we study the residual stress fields generated by finite torsional or shear eigenstrains. This problem is addressed by considering a cylindrical bar made of an incompressible isotropic solid with an axisymmetric distribution of shear eigenstrains. As particular examples, we consider a cylindrical inhomogeneity and a double inhomogeneity with finite shear eigenstrains and study the effect of torsional shear eigenstrains on the axial and torsional stiffnesses of the circular cylindrical bar.