  We study the evolution of high amplitude stress pulses in periodic
dissipative laminates taking into account the nonlinear constitutive equations
of the components and their dissipative behavior. Aluminum and Tungsten
laminate was taken as an example due to the large difference in acoustic
impedances of aluminum and tungsten, the significant nonlinearity of aluminum
constitutive equation at the investigated range of stresses, and its possible
practical applications. Laminates with different cell size, which controls
internal time scale, impacted by the plates with different thicknesses,
determining the incoming pulse duration, were investigated. It has been
observed that the ratio of the duration of the incoming pulse to the internal
characteristic time determines the nature of the high amplitude dissipative
propagating waves, the oscillatory shock like profile, the train of localized
pulses or a single localized pulse. These localized quasistationary waves
resemble solitary waves even in the presence of dissipation: the similar pulses
emerged from different initial conditions, indicating that they are inherent
properties of the corresponding laminates, their characteristic length scale is
determined by the mesostructural scale and the stress amplitude, and they
mostly recover their shapes after collision with phase shift and a linear
relationship exists between their speed and amplitude. A theoretical
description approximating the shape, length scale and speed of these high
amplitude dissipative pulses was proposed based on the Korteweg de Vries type
equation with a dispersive term dictated by the mesostructure. The nonlinear
term is derived from nonlinear constitutive equations of Aluminum and Tungsten,
which were extracted from their Hugoniot curves.
