Waves in microstructured solids and the Boussinesq paradigm

Waves in periodic dissipative laminate metamaterial generated by plate impact

“…For incoming pulses with short duration, experiments and numerical calculations [5][6][7][8][9] demonstrated the anomalous dependence of leading shock amplitude on the cell size (increase of stress amplitude with decrease of cell size) contradicting expectations based on the acoustic approximation [10]. A combination of dispersive properties and nonlinear elastic behavior of nondissipative laminates may result in the generation of solitary like stress waves, numerically investigated in [11][12][13][14][15][16][17].…”

“…The impact of 800 mm Al plate with velocity 2800 m/s generated a shock-like stress wave. The dynamic response of materials is characterized by significant viscoplastic dissipation that was not considered in previous papers related to small strain dynamic deformation [11][12][13][14][15][16][17]. The ratio of the characteristic duration of the incoming pulse to the characteristic time scale of the laminate determines the formation of a single solitary like traveling pulse, a train of pulses or an oscillating shock like stress wave.…”

Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface

“…Following Cosserat theory, a number of higher-order continuum models were developed by Mindlin (1964), Sun et al (1968), Herrmann and Achenbach (1968). More recently, similar approaches were adopted to describe the propagation of nonlinear strain waves in miscrostructured solids (Engelbrecht et al, 2007(Engelbrecht et al, , 2011Porubov et al, 2004Porubov et al, , 2009Randrüüt and Braun, 2010). A recent review of the modelling of heterogeneous media in terms of internal variables was presented by Berezovski et al (2011a, b).…”

Scaling and hierarchies of wave motion in solids

“…In this way, the most interesting cases when both operators are in force, the derivatives like U T T XX and U XXXX appear. If nonlinearity in the macroscale is included like operator (44) then the result is of the Boussinesq type [32,33]. However, for the Maxwell-Rayleigh model in case of anomalous dispersion, the second wave operator is included in the form of its second derivative with respect to T (see Maugin [34]).…”