Artículo de revista
Recovery of a Lamé parameter from displacement fields in nonlinear elasticity models
Fecha
2022Registro en:
J. Inverse Ill-Posed Probl. 2022; 30(4): 521–547
10.1515/jiip-2020-0142
Autor
Carrillo Lincopí, Hugo Patricio Anner
Waters, Alden
Institución
Resumen
We study some inverse problems involving elasticity models by assuming the knowledge of measurements
of a function of the displaced field. In the first case, we have a linear model of elasticity with
a semi-linear type forcing term in the solution. Under the hypothesis the fluid is incompressible, we recover
the displaced field and the second Lamé parameter from power density measurements in two dimensions.
A stability estimate is shown to hold for small displacement fields, under some natural hypotheses on the
direction of the displacement, with the background pressure fixed. On the other hand, we prove in dimensions
two and three a stability result for the second Lamé parameter when the displacement field follows the
(nonlinear) Saint-Venant model when we add the knowledge of displaced field solution measurements. The
Saint-Venant model is the most basic model of a hyperelastic material. The use of over-determined elliptic
systems is new in the analysis of linearization of nonlinear inverse elasticity problems.