Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates

Abstract

We establish that, if a symmetric matrix field defined over a simply-connected open set satisfies the Saint Venant equations in curvilinear coordinates, then its coefficients are the linearized strains associated with a displacement field. Our proof provides an explicit algorithm for recovering such a displacement field, which may be viewed as the linear counterpart of the reconstruction of an immersion from a given flat Riemannian metric. To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).