Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1402.4027

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

Patrizio Neff·Bernhard Eidel·Robert Martin
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.HO

Keep this discovery

BibTeXRIS

Patrizio Neff, Bernhard Eidel, Robert Martin. 2014-02-17. The axiomatic deduction of the quadratic Hencky strain energy by Heinrich Hencky. https://arxiv.org/abs/1402.4027

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Perspectives on the unit distance problem

This is a survey on an old open problem in combinatorics called the unit distance problem, and the field of mathematics around it, called incidence geometry. What do we know about the problem? Why is it difficult? How does it connect with other parts of math?

math.HO↗
arXiv2026

A Categorical Approach to Euclidean Ratios and Proportions

A categorial approach to the non-metric geometry in Books V and VI of Euclid's \textit{Elements} is presented. Specifically, we introduce a diagrammatic syntax that can be overlaid immediately on his diagrams, thus bridging intuitive presentation with fidelity to Euclid's arguments. This syntax makes complicated definitions like V.5, and indeed the arguments throughout books V and VI, including arguments about similar figures, intuitively clear. We show in an appendix that this syntax can be used to solve a puzzle regarding ancient mathematics. Finally, we offer evidence that this approach to Euclidean diagrams is rooted in the Aristotelian tradition itself, and that a similar syntax was utilized, in antiquity, for related questions of numeric and proportions. Thus the syntax is plausibly faithful to Euclid's own thought-world, and not an outside-imposition.

math.HO↗
arXiv2026

Some Early Results by Tutte Regarding the Cycle Double Cover Conjecture in 1948

OpenAI recently announced a proof of the Cycle Double Cover (CDC) Conjecture. Most media reports have characterized it as a 50-year-old open problem. In reality, according to a 1987 letter from Tutte to Fleischner, the Cycle Double Cover Problem has been open for at least 80 years. Two early results regarding the CDC conjecture were established in one of Tutte's 1949 publications.

math.HO↗