Superposed deformations by Mohr construction

The Mohr diagram can provide a simple constructional method for superposing various kinds of deformation. Examples are given for superposed pure shears, and various combinations of pure shear, simple shear and area change. Construction methods are developed on a Mohr diagram for reciprocal stretch vs rotation, which is actually a representation of the ‘backwards deformation’ tensor, d. The superposition of apure shear or a simple shear on an earlier deformation follows elementary principles in Mohr space, enabling the total deformation to be determined simply. More general deformations can be considered as a combination of dilation, pure shear and simple shear (if body rotations arc omitted), which are all amenable to the Mohr construction method. gh confined to problems of two-dimensional superposed deformation, this new method provides a useful alternative to mathematical or computer-based methods to determine the effects of oblique superposition of several deformations The visual appeal of such graphical constructions should aid in the teaching and understanding of deformation processes.