Acta Mechanica

, Volume 227, Issue 6, pp 1533–1556 | Cite as

Fitting of the strength hypotheses

  • V. A. KolupaevEmail author
  • M.-H. Yu
  • H. Altenbach
Original Paper


The equivalent stress approach allows the comparison of arbitrary multiaxial stress states with a uniaxial one. Based on the concept of the equivalent stress, several strength hypotheses (limit surfaces) were formulated. These hypotheses take into account not only existing information from the tests. They can also describe a experiences and different expectations concerning the material behavior mathematically. Due to the simplicity and clarity, the equivalent stress concept is widely used.

Collected experimental data, applications, and know-how make this approach an extremely powerful tool for engineering design. The method can also be easily applied in the case of new materials. As an example, polymethacrylimide (PMI) hard foam ROHACELL® 110IG, from manufacturer Evonik Röhm GmbH (Darmstadt), will be in the focus of this study.

Modern strength hypotheses are functions of several parameters. The application of these hypotheses requires in addition to tension, compression, and torsion test data further experimental results. Such data are often not reliable or widely scattered. Hence, the adjustment of the parameters of the chosen hypothesis is not unique. Some extrapolations with respect to the hydrostatic stress states can lead to unacceptable results and, therefore, the parameters must be restricted.

In this work, several restrictions based on the principles of conservative material description are introduced. They adjust a shape of the limit surface in the principal stress space. These restrictions are geometrically justified. The influence of various restrictions on the limit surface is analyzed. The effectiveness is tested with the help of own measured data. Reliable material descriptions for hard foams will be suggested.


Foam Equivalent Stress Stress Relation Gray Cast Iron Syntactic Foam 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Authors and Affiliations

  1. 1.Fraunhofer Institute for Structural Durability and System Reliability LBFDarmstadtGermany
  2. 2.State Key Laboratory for Strength and Vibration of Mechanical StructuresXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  3. 3.Otto-von-Guericke-Universität MagdeburgMagdeburgGermany

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