Abstract
The paper gathers and unifies mechanical stability conditions for all symmetry classes of 3D and 2D materials under arbitrary load. The methodology is based on the spectral decomposition of the fourth-order stiffness tensors mapped to secondorder tensors using orthonormal (Mandel) notation, and the verification of the positivity of the so-called Kelvin moduli. An explicit set of stability conditions for 3D and 2D crystals of higher symmetry is also included, as well as a Mathematica notebook that allows mechanical stability analysis for crystals, stress-free and stressed, of arbitrary symmetry under arbitrary loads.Keywords:
mechanical stability, Born’s stability, 2D materials, Kelvin moduli, orthonormal notationSupplementary material
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Mathematica notebook to check mechanical stability
Mathematica notebook that allows mechanical stability analysis for crystals, stress-free and stressed, of arbitrary symmetry under arbitrary loads and its transcript in pdf file
