Details
| Original language | English |
|---|---|
| Pages (from-to) | 657-670 |
| Number of pages | 14 |
| Journal | Communications in Numerical Methods in Engineering |
| Volume | 16 |
| Issue number | 9 |
| Publication status | Published - 18 Aug 2000 |
Abstract
On a practical level, when computing macroscopic or homogenized mechanical responses of materials possessing heterogeneous irregular microstructure, one can only test finite-sized samples. The macroscopic responses computed from various equal finite-sized samples exhibit deviations from one another. Consequently, any use of such data afterwards contains a degree of uncertainty. For example, certain classes of finite deformation response functions such as compressible Neo-Hookean functions, compressible Mooney-Rivlin functions, and others, employ predetermined linear elastic coefficients in parts of their representations. Therefore, they will contain the mentioned uncertainties. In this work we study the magnitude of deviations between computed homogenized linearly elastic responses among equal finite sized, samples possessing random microstructure. Afterwards, the sensitivity of finite deformation response functions to such deviations is addressed. The primary result is that deviations of the responses in the infinitesimal range bound the resulting perturbed response in the finite deformation range from above.
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- General Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Communications in Numerical Methods in Engineering, Vol. 16, No. 9, 18.08.2000, p. 657-670.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the sensitivity of homogenized material responses at infinitesimal and finite strains
AU - Zohdi, T. I.
AU - Wriggers, Peter
PY - 2000/8/18
Y1 - 2000/8/18
N2 - On a practical level, when computing macroscopic or homogenized mechanical responses of materials possessing heterogeneous irregular microstructure, one can only test finite-sized samples. The macroscopic responses computed from various equal finite-sized samples exhibit deviations from one another. Consequently, any use of such data afterwards contains a degree of uncertainty. For example, certain classes of finite deformation response functions such as compressible Neo-Hookean functions, compressible Mooney-Rivlin functions, and others, employ predetermined linear elastic coefficients in parts of their representations. Therefore, they will contain the mentioned uncertainties. In this work we study the magnitude of deviations between computed homogenized linearly elastic responses among equal finite sized, samples possessing random microstructure. Afterwards, the sensitivity of finite deformation response functions to such deviations is addressed. The primary result is that deviations of the responses in the infinitesimal range bound the resulting perturbed response in the finite deformation range from above.
AB - On a practical level, when computing macroscopic or homogenized mechanical responses of materials possessing heterogeneous irregular microstructure, one can only test finite-sized samples. The macroscopic responses computed from various equal finite-sized samples exhibit deviations from one another. Consequently, any use of such data afterwards contains a degree of uncertainty. For example, certain classes of finite deformation response functions such as compressible Neo-Hookean functions, compressible Mooney-Rivlin functions, and others, employ predetermined linear elastic coefficients in parts of their representations. Therefore, they will contain the mentioned uncertainties. In this work we study the magnitude of deviations between computed homogenized linearly elastic responses among equal finite sized, samples possessing random microstructure. Afterwards, the sensitivity of finite deformation response functions to such deviations is addressed. The primary result is that deviations of the responses in the infinitesimal range bound the resulting perturbed response in the finite deformation range from above.
UR - http://www.scopus.com/inward/record.url?scp=0034273527&partnerID=8YFLogxK
U2 - 10.1002/1099-0887(200009)16:9<657::AID-CNM365>3.0.CO;2-S
DO - 10.1002/1099-0887(200009)16:9<657::AID-CNM365>3.0.CO;2-S
M3 - Article
AN - SCOPUS:0034273527
VL - 16
SP - 657
EP - 670
JO - Communications in Numerical Methods in Engineering
JF - Communications in Numerical Methods in Engineering
SN - 1069-8299
IS - 9
ER -