Elastic metamaterials have been investigated to achieve negative effective properties, which
cannot be found in the conventional elastic medium. In this paper, plane wave propagation
and reflection in semi-infinite elastic metamaterials with doubly or triply negative material
properties are studied analytically and numerically. The unique negative refractions for the
longitudinal (P) wave and transverse (S) wave are captured by the proposed generalized
Snell's law. Attention is paid to quantitative characterization of the effects of different …