Plecháč, PetrSimpson, GideonTroy, Jerome R.2022-03-142022-03-142022-01-07Petr Plecháč, Gideon Simpson & Jerome R. Troy (2022) Well-posedness of a random coefficient damage mechanics model*, Applicable Analysis, DOI: 10.1080/00036811.2021.20211921563-504Xhttps://udspace.udel.edu/handle/19716/30646This 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.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.en-USViscoelasticitydamage mechanicsrandom coefficient differential equationmild solutionsArticle