Identification of microstructural information from macroscopic boundary measurements in steady‐state linear elasticity
- We consider the upscaled linear elasticity problem in the context of periodic homogenization. Based on measurements of the deformation of the (macroscopic) boundary of a body for a given forcing, it is the aim to deduce information on the geometry of the microstructure. For a parametrized microstructure, we are able to prove that there exists at least one solution of the associated minimization problem based on the L2$$ {L}^2 $$‐difference of the measured deformation and the resulting deformation for a given parameter. To facilitate the use of gradient‐based algorithms, we derive the Gâteaux derivatives using the Lagrangian method of Céa, and we present numerical experiments showcasing the functioning of the method.
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| Author: | Tanja LochnerORCiDGND, Malte A. PeterORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-970927 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/97092 |
| ISSN: | 0170-4214OPAC |
| ISSN: | 1099-1476OPAC |
| Parent Title (English): | Mathematical Methods in the Applied Sciences |
| Publisher: | Wiley |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2023 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2022/08/01 |
| Tag: | General Engineering; General Mathematics |
| Volume: | 46 |
| Issue: | 1 |
| First Page: | 1295 |
| Last Page: | 1316 |
| DOI: | https://doi.org/10.1002/mma.8581 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehr- und Forschungseinheit Angewandte Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
