On the determination of deformation from strain

The problem of finding a deformation corresponding to a given Cauchy–Green strain is approached with a procedure that employs the Gram decomposition of the deformation gradient. It is shown that the rotation occurring in that decomposition can be obtained by solving a system of partial differential equations in the group of rotations or in its Lie algebra. The equivalence between the integrability conditions of these two systems and those of the systems of equations arising in the usual procedures for determining a deformation from the strain is proved. Examples of application of the proposed procedure are given.