Modeling the behavior of elastic materials with stochastic microstructure

J. Nagel, P. Junker

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

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 Karhunen-Loève expansion. It has been used, for example, in the stochastic finite element method, where it yields results of the desired kind, but unfortunately at drastically increased numerical costs. This contribution aims to propose a new ansatz that is based on a stochastic series expansion, but at the Gauß point level. Appropriate energy relaxation allows to derive the distribution of a synthesized stress measure, together with explicit formulas for the expectation and variance. The total procedure only needs negligibly more computation effort than a simple elastic calculation. We also present an outlook on how the original approach in [7] can be applied to inelastic materials.

Original languageEnglish
Title of host publicationProceedings of the 14th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2017
EditorsEugenio Onate, Djordje Peric, D. Roger J. Owen, Michele Chiumenti
Place of PublicationBarcelona
PublisherInternational Center for Numerical Methods in Engineering (CIMNE)
Pages296-307
Number of pages12
ISBN (Electronic)9788494690969
Publication statusPublished - 1 Jan 2017
Event14th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2017 - Barcelona, Spain
Duration: 5 Sep 20177 Sep 2017

Conference

Conference14th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2017
Country/TerritorySpain
CityBarcelona
Period5/09/177/09/17

Keywords

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

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