  We present a model for the dynamics of elastic or poroelastic bodies with
monopolar repulsive long-range (electrostatic) interactions at large strains.
Our model respects (only) locally the non-self-interpenetration condition but
can cope with possible global self-interpenetration, yielding thus a certain
justification of most of engineering calculations which ignore these effects in
the analysis of elastic structures. These models necessarily combine Lagrangian
(material) description with Eulerian (actual) evolving configuration evolving
in time. Dynamical problems are studied by adopting the concept of nonlocal
nonsimple materials, applying the change of variables formula for
Lipschitz-continuous mappings, and relying on the positivity of the determinant
of the deformation gradient thanks to a result by Healey and Kroemer.
