Identification of boundary conditions by solving Cauchy problem in linear elasticity with material uncertainties

This work is a contribution to non-destructive testing in the context of uncertainties. It consists in identifying boundary conditions on an inaccessible part of a solid body boundary, from the knowledge of over-specified data given on an accessible part of this boundary. This problem is well known as Cauchy problem. The material properties are considered uncertain. Polynomial chaos expansion is used in order to solve this Cauchy problem in the random context. A stochastic constrained optimization problem is formulated and solved. Numerical experiments are presented.