A relaxation approach to modeling the stochastic behavior of elastic materials

Philipp Junker (Corresponding author), Jan Nagel

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


Even in the simple linear elastic range, the material behavior is not deterministic, but fluctuates randomly around some expectation values. The knowledge about this characteristic is obviously trivial from an experimentalist's point of view. However, it is not considered in the vast majority of material models in which “only” deterministic behavior is taken into account. One very promising approach to the inclusion of stochastic effects in modeling of materials is provided by the so-called Chaos Polynomial Expansion. It has been used, for example, to derive the so-called stochastic finite element method. This method yields results that are exactly of the desired kind, but unfortunately at increased numerical costs. This contribution aims to propose a new ansatz that is also based on a stochastic series expansion along with an appropriate relaxation procedure at the Gauβ point level. Energy relaxation provides a synthesized (deterministic) stress measure, while simultaneously offering stochastic properties such as the variance. The total procedure only needs negligibly more computation effort than a simple elastic calculation.

Original languageEnglish
Pages (from-to)192-203
Number of pages12
JournalEuropean Journal of Mechanics. A, Solids
Publication statusPublished - 1 Jan 2019


  • Analytical solution
  • Energy relaxation
  • Stochastic material behavior
  • Stochastic series expansion
  • Stress expectation and variance


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