Eulerian finite cover method for quasi-static equilibrium problems of hyperelastic bodies

We introduce a Eulerian finite cover method that realizes implicit structural analyses for hyperelastic bodies in quasi-static equilibrium by using both the Lagrangian and the Eulerian mathematical meshes simultaneously. The recursive covering of the equilibrated current configuration determined with the Lagrangian mesh by the Eulerian mesh provides the reference configuration in the corresponding time interval, after the physical quantities on the former are mapped onto the latter. Several numerical examples are presented to demonstrate the capability of the method, to assess its validity, and to address a remark on the mapping process of physical quantities.