Well-posedness of a random coefficient damage mechanics model
Date
2022-01-07
Journal Title
Journal ISSN
Volume Title
Publisher
Applicable Analysis
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.
Description
This is an Accepted Manuscript of an article published by Taylor & Francis in
Applicable Analysis on 01/07/2022, available online: http://www.tandfonline.com/10.1080/00036811.2021.2021192. This article will be embargoed until 01/07/2023.
Keywords
Viscoelasticity, damage mechanics, random coefficient differential equation, mild solutions
Citation
Petr Plecháč, Gideon Simpson & Jerome R. Troy (2022) Well-posedness of a random coefficient damage mechanics model*, Applicable Analysis, DOI: 10.1080/00036811.2021.2021192