Invariant finite strain measures in elasticity and lattice dynamics

Abstract

Some vagueness in the literature concerning the proper measures of strain which may be used in finite elastic strain theory and lattice dynamics is discussed. The requirements for straindependent quantities to be invariant under changes of frame of references are brieffy reviewed, and it is pointed out that the common practice of writing strain-dependent quantities explicity in terms of the Lagrangian strain η is sufficient, but not necessary, for them to be invariant. Invariance is assured if any one of a class of invariant strain tensors is used for this purpose. The use of the non-invariant Eulerian strain tensor ε in some applications has not usually led to difficulties because of the restricted situations which have been considered. Applications to more general situations would require the use. of an invariant strain measure. An analogous invariant strain tensor can be defined which reduces to the Eulerian strain tensor in the case of isotropic strain. © 1973.