Shear shock formation in incompressible viscoelastic solids

A hyperbolic generalized Zener model for nonlinear viscoelastic waves

“…The components of the Cauchy stress σ (13)-( 35) are the hydrodynamic pressure p (39) and the shear stress S (37)-( 46). We introduce the covectors e β as the columns of F − = (e 1 , e 2 , e 3 ), with 3 ) , then the unimodular Finger tensors in (37)…”

“…In granular media, the physical source of the nonlinearities and attenuation is related to grain-to-grain interactions [41]. In the biomedical context, both nonlinearities and viscoelasticity are needed to model shock waves in soft solids such as the brain [13,39,5,3] or the liver [8]. At a larger scale, nonlinearities and viscous damping arising during the wave propagation are commonly studied in the context of site effect assessment, and related resonance phenomena [12].…”

“…Nevertheless, these theories are often used for applications related to quasi-static configurations (i.e., where inertial effects are neglected, see e.g. [10]), even though wave propagation problems were considered recently [11,3]. As a consequence, they often do not incorporate some particularities of wave phenomena such as a finite propagation speed, with the notable exception of [3].…”

“…[10]), even though wave propagation problems were considered recently [11,3]. As a consequence, they often do not incorporate some particularities of wave phenomena such as a finite propagation speed, with the notable exception of [3]. This property is fundamental to get explicit-in-time numerical schemes.…”

“…An interesting discussion on the acoustic identification of nonlinear parameters in polymers (PMMA) can be found in [37]. Other identification methods are based on the properties of kink waves [11,3].…”