Rank 1 perturbations of deformation gradients

ortant role in the nonlinear elasticity and in particular in the theory of solid-to-solid phase transformations. If F, G are rank 1 connected, G is said to be a rank 1 perturbation of F. This paper describes the set of all rank 1 perturbations of F with prescribed singular values. In an n-dimensional space, this set is shown to consist of 2n families of dimension n ÿ 1 and within each family, G and f may be expressed as functions of the unit vector n, given by explicit formulas. These are then specialized to dimensions n ˆ 2 and 3: Some illustrative examples are g