From the free surface flow of a viscoelastic fluid towards the elastic deformation of a solid

The free surface flow of an Oldroyd-B viscoelastic fluid is considered, following A. Bonito, M. Picasso, and M. Laso (2006)[1]. When removing a term in the extra-stress constitutive relation, the description of an elastic incompressible solid is obtained, in Eulerian coordinates, with the velocity field as the unknown, rather than the usual deformation field. Two simulations are proposed, a bouncing ball and an oscillating beam. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. Allrightsreserved.