New advances and applications of the theory of shells modeled as deformable directed surfaces

The subject of the research project is the investigation of the
mechanical properties of elastic shells and plates endowed with a
certain microstructure. In this sense, we employ the model of
deformable directed surfaces, which is effective for the study of thin
bodies with complex internal structure. The objectives of the research
project are the following:
1. to investigate the mathematical aspects of the theory of deformable
directed surfaces: we study the boundary-initial-value problems associated
with the deformation of elastic shells and study the significant
properties of their solutions concerning existence, uniqueness,
reciprocity, variational characterizations, and continuous dependence on
the external loads;
2. to extend this approach for the modeling of shells made of porous
materials or other microstructural materials.