Related papers: Strongly Nonlinear Wave Propagation in Elasto-plas…
The transformation method is a powerful tool for providing the constitutive parameters of the transformed material in the new coordinates. In transformation elasticity, a general curvilinear change of coordinates transforms conventional…
Recent interest in metamaterials has led to a renewed study of wave mechanics in different branches of physics. Elastodynamics involves a special intricacy, owing to a coupling between the volumetric and shear parts of the elastic waves.…
In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…
We present a mechanism to generate unidirectional pulse-shaped propagating waves, tamed to exponential growth and dispersion, in active systems with nonreciprocal and nonlinear couplings. In particular, when all bulk modes are exponentially…
The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous studies often use discrete systems, composed of rigid elements and nonlinear springs, to model the nonlinear dynamic…
We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
In this paper we review the recent advances which have taken place in the understanding and applications of acoustic/elastic metamaterials. Metamaterials are artificially created composite materials which exhibit unusual properties which…
Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
Designing metamaterials that carry out advanced computations poses a significant challenge. A powerful design strategy splits the problem into two steps: First, encoding the desired functionality in a discrete or tight-binding model, and…
In recent years, there has been considerable interest in the study of wave propagation in nonlinear photonic lattices. The interplay between nonlinearity and periodicity has led researchers to manipulate light and discover new and…
We numerically study a one dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one dimensional mass-spring system, the linear dispersion relation…
We study the interaction of highly nonlinear solitary waves in granular crystals, with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary…
The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
We develop a framework to understand the mechanics of metamaterial sheets on curved surfaces. Here we have constructed a continuum elastic theory of mechanical metamaterials by introducing an auxiliary, scalar gauge-like field that absorbs…
We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…
The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning…
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…