  In this paper, we present a computational framework based on fully Eulerian
models for fluid-structure interaction for the numerical simulation of
biological capsules. The flexibility of such models, given by the Eulerian
treatment of the interface and deformations, allows us to easily deal with the
large deformations experienced by the capsule. The modeling of the membrane is
based on a full membrane elasticity Eulerian model that is capable of capturing
both area and shear variations thanks to the so-called backward
characteristics. In the validation section several test cases are presented
with the goal of comparing our results to others present in the literature. In
this part, the comparisons are done with different well-known configurations
(capsule in shear flow and square-section channel), and by deepening the effect
of the elastic constitutive law and capillary number on the membrane dynamics.
Finally, to show the potential of this framework we introduce a new test case
that describes the relaxation of a capsule in an opening channel. In order to
increase the challenges of this test we study the influence of an internal
nucleus, modeled as a hyperelastic solid, on the membrane evolution. Several
numerical simulations of a 3D relaxation phenomenon are presented to provide
characteristic shapes and curves related to the capsule deformations, while
also modifying size and stiffness parameter of the nucleus.
