Details
| Original language | English |
|---|---|
| Pages (from-to) | 192-203 |
| Number of pages | 12 |
| Journal | European journal of mechanics |
| Volume | 73 |
| Publication status | Published - 6 Sept 2018 |
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 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.
Keywords
- Analytical solution, Energy relaxation, Stochastic material behavior, Stochastic series expansion, Stress expectation and variance
ASJC Scopus subject areas
- Materials Science(all)
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
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In: European journal of mechanics, Vol. 73, 06.09.2018, p. 192-203.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A relaxation approach to modeling the stochastic behavior of elastic materials
AU - Junker, Philipp
AU - Nagel, Jan
N1 - Funding information: Jan Nagel thanks for DFG-grant NA 1372/1-1.
PY - 2018/9/6
Y1 - 2018/9/6
N2 - 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.
AB - 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.
KW - Analytical solution
KW - Energy relaxation
KW - Stochastic material behavior
KW - Stochastic series expansion
KW - Stress expectation and variance
UR - http://www.scopus.com/inward/record.url?scp=85052916725&partnerID=8YFLogxK
U2 - 10.1016/j.euromechsol.2018.07.003
DO - 10.1016/j.euromechsol.2018.07.003
M3 - Article
VL - 73
SP - 192
EP - 203
JO - European journal of mechanics
JF - European journal of mechanics
ER -