A brief history of logarithmic strain measures in nonlinear elasticity

Abstract

We demonstrate that the notion of logarithmic strain tensors in nonlinear elasticity theory, which is commonly attributed to Heinrich Hencky, is actually due to the geologist G. F. Becker, who was the first to consider a fully three‐dimensional logarithmic stress response in an 1893 article.

Souriau’s general covariant formulation of Relativistic Hyperelasticity revisited

“…H 0 := 𝛾 −1 0 ∘ Ψ. The first one generalizes the Green-Lagrange strain, whereas the second one generalizes the logarithmic strain introduced by Becker [3] and Hencky [40] (see [56]). They both vanish when H −1 = H −1 0 = 𝛾 0 ∘ Ψ.…”

Objective rates as covariant derivatives on the manifold of Riemannian metrics

“…Remark 4.9. The logarithm of the metric C = ϕ * q on a reference configuration Ω 0 (right Cauchy-Green tensor) has been initially introduced by Becker [2] and Hencky [31] (see also [49]) to define the true strain tensor,…”