Necessary and Sufficient Elastic Stability Conditions in Various Crystal   Systems
  While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in non-cubic materials. 
F\'elix Mouhat and Fran\c{c}ois-Xavier Coudert
cond-mat.mtrl-sci cond-mat.stat-mech