The theory of finite strain and compressibility of solids

It is noted that the usual theory of finite strain has an ambiguity in the derivation owing to a lack of uniqueness in the definition of finite strain itself. This can be correlated with the fact that the usual theory can be derived without reference to a physical description of the nature of binding forces. This difficulty can be resolved by a generalization of the theory. As an example, it is shown that the theory of finite strain can be made asymptotic to the degenerate Thomas-Fermi atomic model by defining elastic strain as the tensor ∈ik - ½∈ij∈jk, where ∈ij is the quadratic strain of the usual theory.