  Monitoring structures of elastic materials for defect detection by means of
ultrasound waves (Structural Health Monitoring, SHM) demands for an efficient
computation of parameters which characterize their mechanical behavior.
Hyperelasticity describes a nonlinear elastic behavior where the second
Piola-Kirchhoff stress tensor is given as a derivative of a scalar function
representing the stored (strain) energy. Since the stored energy encodes all
mechanical properties of the underlying material, the inverse problem of
computing this energy from measurements of the displacement field is very
important regarding SHM. The mathematical model is represented by a
high-dimensional parameter identification problem for a nonlinear, hyperbolic
system with given initial and boundary values. Iterative methods for solving
this problem, such as the Landweber iteration, are very time-consuming. The
reason is the fact that such methods demand for several numerical solutions of
the hyperbolic system in each iteration step. In this contribution we present
an iterative method based on sequential subspace optimization (SESOP) which in
general uses more than only one search direction per iteration and explicitly
determines the step size. This leads to a significant acceleration compared to
the Landweber method, even with only one search direction and an optimized step
size. This is demonstrated by means of several numerical tests.
