Related papers: Variational principles and finite element Bloch an…
The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals. Considering…
We present a procedure for the systematic estimation of the dispersion properties of linear discrete systems with periodic time-varying coefficients. The approach relies on the analysis of a single unit cell, making use of Bloch theorem…
We evaluated the performance of the classical and spectral finite element method in the simulation of elastodynamic problems. We used as a quality measure their ability to capture the actual dispersive behavior of the material. Four…
This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
In this work, we present a computational analysis of the planar wave propagation behavior of a one-dimensional periodic multi-stable cellular material. Wave propagation in these materials is interesting because they combine the ability of…
We introduce the concept of effective phononic crystals, which combine periodicity with varying isotropic material properties to force periodic coefficients in the elastic equations of motion in a non-Cartesian basis. Periodic coefficients…
The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of…
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
This paper addresses fundamental questions arising in the theory of Bloch-Floquet waves in chiral elastic lattice systems. This area has received a significant attention in the context of "topologically protected" waveforms. Although…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized…
We investigate the band-gap structure of the frequency spectrum for elastic waves in a high-contrast, two-component periodic elastic medium. We consider two-dimensional phononic crystals consisting of a background medium which is perforated…
Elastic wave propagation provides a noninvasive way to probe granular materials. The discrete element method using particle configuration as input, allows a micromechanical interpretation on the acoustic response of a given granular system.…
A new variational technique is developed to investigate the polaronic features of the Holstein Molecular Crystal Model. It is based on a linear superposition of Bloch states that describe large and small polaron wave functions. It is shown…
The dynamic behaviour of periodic thermodiffusive multi-layered media excited by harmonic oscillations is studied. In the framework of linear thermodiffusive elasticity, periodic laminates, whose elementary cell is composed by an arbitrary…
In this paper the relaxed micromorphic continuum model with weighted free and gradient micro-inertia is used to describe the dynamical behavior of a real two-dimensional phononic crystal for a wide range of wavelengths. In particular, a…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…