Journal article
Well-posedness of a random coefficient damage mechanics model
Applicable analysis, v 101(11), pp 1-28
07 Jan 2022
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We study a one-dimensional damage mechanics model in the presence of random materials properties. The model is formulated as a quasilinear partial differential equation of visco-elastic dynamics with a random field coefficient. We prove that in a transformed coordinate system the problem is well-posed as an abstract evolution equation in Banach spaces, and on the probability space it has a strongly measurable and Bochner integrable solution. We also establish the existence of weak solutions in the underlying physical coordinate system. We present numerical examples that demonstrate propagation of uncertainty in the stress-strain relation based on properties of the random damage field.
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Details
- Title
- Well-posedness of a random coefficient damage mechanics model
- Creators
- Petr Plechac - University of DelawareGideon Simpson - Drexel UniversityJerome R. Troy - University of Delaware
- Publication Details
- Applicable analysis, v 101(11), pp 1-28
- Publisher
- Taylor & Francis
- Number of pages
- 28
- Grant note
- W911NF-19-1-0243 / U.S. Army Research Office Award Army Research Laboratory DMS-1818726 / U.S. National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000740112000001
- Scopus ID
- 2-s2.0-85122425280
- Other Identifier
- 991019168759204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied