  A one-dimensional wave propagation through elastically asymmetric media is
investigated. A class of metamaterials possessing an arbitrary elastic
asymmetry is proposed. This asymmetry results in different wave speeds of
tensile and compressive components of elastic waves. The faster component can
overtake the slower one resulting in their dissipative annihilation through
energy cascades. Efficient absorbing assemblies are presented and analysed
numerically. The length of the asymmetric part needed to damp a harmonic signal
is determined analytically and validated numerically. Transmission properties
for random self-affine wave-packets are studied: a universal scaling for the
transmission factor variation with the length of the asymmetric part was
established.
