On the continuum mechanics approach in modeling nanosized structural elements

During the last 50 years the nanotechnology is established as one of the advanced technologies manipulating matter on an atomic and molecular scale. By this approach new materials, devices or other structures possessing at least one dimension sized from 1 to 100 nm are developed. The question arises how structures composed of nanomaterials should be modeled. Two approaches are suggested—theories which take into account quantum mechanical effects since they are important at the quantum-realm scale or theories which are based on the classical continuum mechanics adapted to nanoscale problems. Here the second approach will be discussed in detail. It will be shown that the classical continuum mechanics (kinematics, stress states analysis, balances and constitutive equations) with some improvements is enough for a sufficient description of the mechanical behavior of nanomaterials and -structures in many situations. After a brief recall of the basics of Continuum Mechanics a theory with surface effects will be discussed.