Negative thoughts on negative mass

Abstract: The concept of effective mass is frequently used for simplification of complex models. It i claimed that in the case of wave transmission analysis of some metamaterials the corresponding effective mass can be frequency dependent, negative and it may not even be a scalar quantity. These findings have even led some authors to suggest that Newton's second law needs to be modified within the context of classical continuum mechanics. While there is nothing wrong with the mathematical procedures used to reach these conclusions, the accompanying physical interpretation thereof is absurd. We show that the puzzling concept of negative mass can be easily eliminated provided that we model the corresponding metamaterials using an effective constitutive relation. The effective constitutive relation is a rate-type constitutive relation, and the simple models we study give a clue how to design a non-trivial effective rate-type constitutive relation that is conservative, that is, possessing an associated conserved energy depending on the force/stress and its time derivatives. In short, the rate-type constitutive relations obtained in our study might be seen as a revival of hypoelastic materials.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)