Finite Deformation Analysis Using Natural Strain

(On Comparison with Other Strain Expressions under Three Different Types of Deformation Paths and the Rationality of Natural Strain)

Abstract

The effectiveness of the Natural Strain theory for describing a large deformation is mentioned in this paper. The Natural Strain is obtained by integrating infinitesimal strain increment on an identical line element over the whole process of the deformation path. Consequently, the shearing strain becomes pure angular strain, which is obtained by removing the rigid body rotation from the rotating angle of a line element. Since the expression of the Natural Strain is different from the strain expression of ordinary rate type, the additive low of strain on an identical line element can be satisfied. In this paper, the finite deformation analyses of a pure elastic body concerning the three different types of deformation paths are discussed on the combined deformation of uni-axial tension and simple shear, and the Natural Strain proposed in this paper is compared with other strain expressions and the rationality of this strain expression is confirmed.