Unique continuation for an elasticity system with residual stress and its applications
Journal
SIAM Journal on Mathematical Analysis
Journal Volume
35
Journal Issue
2
Pages
304-317
Date Issued
2004
Author(s)
Nakamura, G.
Abstract
In this paper we prove the unique continuation property for an elasticity system with small residual stress. The constitutive equation of this elasticity system differs from that of the isotropic elasticity system by T + (∇u)T, where T is the residual stress tensor. It turns out this elasticity system becomes anisotropic due to the existence of residual stress T. The main technique in the proof is Carleman estimates. Having proved the unique continuation property, we study the inverse problem of identifying the inclusion or cavity.
Subjects
Probe method; Residual stress; Unique continuation property
Type
journal article