The axiomatic deduction of the quadratic Hencky strain energy by Heinrich Hencky

TL;DR

This paper revisits Heinrich Hencky's original deductive approach to deriving the quadratic Hencky strain energy, emphasizing its historical significance and providing an accessible English translation of key original works.

Contribution

It rediscoveres and clarifies Hencky's original deductive derivation of the quadratic Hencky strain energy, making it accessible to modern researchers.

Findings

Historical derivation of quadratic Hencky strain energy clarified

Provides first faithful English translation of original works

Highlights the importance of the deductive approach in nonlinear elasticity

Abstract

The introduction of the quadratic Hencky strain energy based on the logarithmic strain tensor log V is a milestone in the development of nonlinear elasticity theory in the first half of the 20th century. Since the original manuscripts are written in German, they are not easily accessible today. However, we believe that the deductive approach taken by Hencky deserves to be rediscovered today. In this work we have gathered parts of the original contributions "\"Uber die Form des Elastizit\"atsgesetzes bei ideal elastischen Stoffen", "Welche Umst\"ande bedingen die Verfestigung bei der bildsamen Verformung von festen isotropen K\"orpern?" and "Das Superpositionsgesetz eines endlich deformierten relaxationsf\"ahigen elastischen Kontinuums und seine Bedeutung f\"ur eine exakte Ableitung der Gleichungen f\"ur die z\"ahe Fl\"ussigkeit in der Eulerschen Form" which center around this deductive approach. We tried to provide, for the first time, a faithful translation into English. All footnotes are our addition.