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Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations…
This paper presents a study of nonlinear superpositions of Riemann wave solutions admitted by quasilinear hyperbolic first-order systems of partial differential equations. In particular, we focus on the Euler system and non-elastic wave…
Discrete nonlinear systems support a rich variety of localized and extended wave phenomena, with their dynamics sensitively dependent on the symmetries of the underlying interaction forces within the lattice. Odd elasticity, emerging in…
We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the…
Speed of sound waves in gases and liquids is governed by medium compressibility. There exists another type of non-dispersive waves which speed depends on stress instead of medium elasticity. A well-known example is the Alfven wave…
This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy…
Transformation methods have stimulated many interesting applications of manipulating electromagnetic and acoustic waves by using metamaterials, such as super-lens imaging and cloaking. These successes are mainly due to the form-invariant…
Nonreciprocal wave propagation allows for directional energy transport. In this work, we systematically investigate wave dynamics in an elastic lattice that combines nonreciprocal stiffness with viscous damping. After establishing how…
In classical mechanics, the motion of an object is described with Newton's three laws of motion, which means that the motion of the material elements composing a continuum can be described with the particle model. However, this viewpoint is…
Elastic wave speeds are fundamental in geomechanics and have historically been described by an analytic formula that assumes linearly elastic solid medium. Empirical relations stemming from this assumption were used to determine nonlinearly…
Extending investigations of Antman & Malek-Madani, Schecter & Shearer, Slemrod, Barker & Lewicka & Zumbrun, and others, we investigate phase-transitional elasticity models of strain-gradient effect. We prove the existence of non-constant…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
In this Letter we study the form of the energy spectrum of Riemann waves in weakly nonlinear non-dispersive media. For quadratic and cubic nonlinearity we demonstrate that the deformation of an Riemann wave over time yields an exponential…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid-crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time $\tau_C$. To explore the resulting interplay between…
This paper presents a computational framework for modeling wave propagation in geometrically linear elastic materials characterized by algebraically nonlinear constitutive relations. We derive a specific form of the nonlinear wave equation…
Passive transformation of waves via nonlinear systems is ubiquitous in settings ranging from acoustics to optics and electromagnetics. Passivity is of particular importance for responding rapidly to stimuli and nonlinearity enormously…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
This paper aims to quantitatively relate the energy dissipated at a shock wave in a nonlinearly elastic bar to the energy in the oscillations in two related dissipationless, dispersive systems. In contrast to a phase boundary, there is no…
Identifying a universal material constitutive law, that describes the mechanical response of rubber-like solids for all deformation fields and achievable extensions, is an outstanding challenge. Here, we propose to exploit the propagation…