Space symmetries draw elasticity theory [article]

Chaouqi Misbah, Sofia Biagi, Paolo Politi
2013 arXiv   pre-print
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions are of short range and are therefore localized at the boundary); (ii) the stress tensor must be symmetric in order to prevent spontaneous rotation of the material points. These two requirements are presented to be necessary in classical textbooks on
more » ... y theory. By using only basic spatial symmetries it is shown that elastodynamics equations can be derived, for high symmetry crystals (the typical case considered in most textbooks), without evoking any of the two above physical principles.
arXiv:1304.2119v1 fatcat:2daq773jfzerbjkykwed62aa3y