Related papers: Variational principles and finite element Bloch an…

The free propagation of acoustic plane waves through cellular periodic materials is generally accompanied by a flow of mechanical energy across the adjacent cells. The paper focuses on the energy transport related to dispersive waves…

In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…

We develop and compare several analytical approximations for the polaron problem in finite-width, non-parabolic conduction bands. The main focus of the work is an extension of the Feynman variational method to a tight-binding lattice, where…

Mitigating low-frequency vibration or noise is of vital importance to both human health and mechanical engineering. Two-dimensional phononic crystal (PC) structures were proposed by attaching rubber and metallic cylinders on one or both…

The paper provides a rigorous analysis of the dispersion spectrum of SH (shear horizontal) elastic waves in periodically stratified solids. The problem consists of an ordinary differential wave equation with periodic coefficients, which…

On the example of the Poynting-Thomson-Zener rheological model for solids, which exhibits both dissipation and wave propagation - with nonlinear dispersion relation -, we introduce and investigate a finite difference numerical scheme. Our…

Partial complementary energy densities are introduced through partial Legendre transforms from the strain energy density of linear elasticity. They have mixed components of the strain and stress tensors. Mixed variational principles based…

We apply the framework of tempered fractional calculus to investigate the spatial dispersion of elastic waves in a one-dimensional elastic bar characterized by range-dependent nonlocal interactions. The measure of the interaction is given…

Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this…

A numerical model based on the finite-difference time-domain method is developed to simulate fluctuations which accompany the dephasing of atomic polarization and the decay of excited state's population. This model is based on the…

This paper is concerned with the problem of a semi-infinite crack steadily propagating in an elastic solid with microstructures subject to antiplane loading applied on the crack surfaces. The loading is moving with the same constant…

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…

This paper aims first to perform robust continuous analysis of a mixed nonlinear formulation for stress-assisted diffusion of a solute that interacts with an elastic material, and second to propose and analyse a virtual element formulation…

We derive a model-independent expression for finite-volume matrix elements. Specifically, we present a relativistic, non-perturbative analysis of the matrix element of an external current between a one-scalar in-state and a two-scalar…

This paper considers stochastic hybrid stress quadrilateral finite element analysis of plane elasticity equations with stochastic Young's modulus and stochastic loads. Firstly, we apply Karhunen-Lo$\grave{e}$ve expansion to stochastic…

We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…

The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…

This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…

A general procedure to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase field crystal (PFC) models, is presented. It is found…

This article investigates the velocity dispersion and the spurious reflection of the viscoelastic wave that occur in the numerical integration of the viscoelastic wave equation. For this purpose, the classic finite element of two nodes,…