Elastic and Plastic Deformation of Inhomogeneous Materials such as Polycrystals – an Approach with Models

ABSTRACT Elastic and elastic-plastic deformations of inhomogeneous materials such as polycrystals are analysed adopting plane models of inhomogeneous materials. Constraint ratio is used to represent the deformation behaviour of materials quantitatively. Constraint factor tensor is also defined to represent deformation under multi-axial stress. Numerical calculations of constraint ratio during elastic and elastic-plastic deformations are performed by the finite element method. Discussions are made on the relations among the constraint ratio, the constraint factor tensor, the strain or the stress concentration factor tensor proposed by Hill, and Eshelby's tensor for the ellipsoidal inclusion imbedded in infinite elastic medium. The analogy between elastic deformation of inhomogeneous medium and dislocation distributed in homogeneous medium is suggested.