Unique Continuation for an Elasticity System with Residual Stress and Its Applications

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 $T+(\nabla u)T$, 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.

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