Well-posedness of a random coefficient damage mechanics model

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-pos...

Full description

Saved in:
Bibliographic Details
Published in:Applicable analysis 2022-07, Vol.101 (11), p.3858-3885
Main Authors: Plecháč, Petr, Simpson, Gideon, Troy, Jerome R.
Format: Article
Language:English
Subjects:
Banach spaces
Coordinates
Damage
damage mechanics
Fields (mathematics)
Material properties
Mechanics (physics)
mild solutions
Partial differential equations
random coefficient differential equation
Stress propagation
Stress-strain relationships
Viscoelasticity
Well posed problems
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2021.2021192