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Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states thanks to energy injection mechanisms that take place throughout the system. These states can be stable even at high…
We present a dynamical theory of a two-dimensional martensitic transition in an elastic solid, connecting a high-temperature phase which is nondegenerate and has triangular symmetry, and a low-temperature phase which is triply degenerate…
Simple strain-rate viscoelasticity models of isotropic soft solid are introduced. The constitutive equations account for finite strain, incompressibility, material frame-indifference, nonlinear elasticity, and viscous dissipation. A…
Understanding the dynamics of instabilities along fluid-solid interfaces is critical for the efficacy of focused ultrasound therapy tools (e.g., histotripsy) and microcavitation rheometry techniques. Non-uniform pressure fields generated by…
In this paper we consider the role of nonmodal instabilities in the dynamics of atmospheric tornadoes. For this purpose we consider the Euler equation, continuity equation and the equation of state and linearise them. As an example we study…
The thermodynamical model of viscoelastic deformable solids at finite strains with Kelvin-Voigt rheology with a higher-order viscosity (using the concept of multipolar materials) is formulated in a fully Eulerian way in rates. Assumptions…
In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode…
We present an analytical and numerical study of a nonlinear diffusion model which describes density relaxation of loosely packed particles under gravity and weak random (thermal) vibration, and compare the results with Monte Carlo…
Incremental stiffness characterizes the variation of a material's force response to a small deformation change. Typically materials have an incremental stiffness that is fixed and positive, but recent technologies, such as super-lenses, low…
We consider vibrations of an inhomogeneous flexible structure modeled by a $1$D viscoelastic equation with Kelvin-Voigt, coupled with an expected dissipative effect : heat conduction governed by Cattaneo's law (second sound). We establish…
A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states $D(\omega)$ of disordered…
A model for harmonic oscillator damping due to the internal friction of solids has been developed, based on considerations of a long period pendulum. The assumption of a complex elastic modulus to describe stress-strain hysteresis in the…
We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to…
The kinematic properties of unsteady highly non-linear 3D wave groups have been investigated using a numerical wave tank. Although carrier wave speeds based on zero-crossing analysis remain within +-7% of linear theory predictions, crests…
Granular materials are ubiquitous in nature and are used extensively in daily life and in industry. The modeling of these materials remains challenging; therefore, finding models with acceptable predictive accuracy that at the same time…
Cracks in soft materials exhibit diverse dynamic patterns, involving straight, oscillation, branching, and supershear fracture. Here, we successfully reproduce these crack morphologies in a two-dimensional pre-strained fracture scenario and…
This is the first of three papers devoted to the nonequilibrium thermodynamics of amorphous materials. Our focus here is on the role of internal degrees of freedom in determining the dynamics of such systems. For illustrative purposes, we…
This paper presents a consistent computational framework for multiscale 1st order finite strain homogenization and stability analyses of rate-independent solids with periodic microstructures. Based on the principle of multiscale virtual…
The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent…
We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically…