This work presents a lossy partial differential acoustic wave equation including fractional derivative terms. It is derived from first principles of physics (mass and momentum conservation) and an equation of state given by the fractional Zener stress-strain constitutive relation. For a derivative order α in the fractional Zener relation, the resulting absorption α(k) obeys frequency power-laws...

A defect-correction mixed finite element method for solving the time-dependent JohnsonSegalman viscoelastic equations in two dimensions is given. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the resulting residual is corrected in the correction step on the same grid. A streamline upwind PetrovGalerkin SUPG appro...

This article considers transient, planar Poiseuille flows for viscoelastic fluids. We propose a novel time-dependent hybrid finite volume (fv)/finite element (fe) algorithm. This approach combines a Taylor-Galerkin fe-treatment for mass and momentum conservation equations, with a cell-vertex fv-discretisation of the hyperbolic stress constitutive equation. A consistent formulation for the const...

Dislocation models with considering the mismatch of elastic modulus between matrix and reinforcing particles are used to determine the effective strain gradient h for particle reinforced metal matrix composites (MMCp) in the present research. Based on Taylor relation and the kinetics of dislocation multiplication, glide and annihilation, a strain gradient dependent constitutive equation is deve...

A new elastic-viscoplastic (EVP) constitutive model is proposed for the analysis of time-dependent behavior of clay. The proposed model is based on the bounding surface plasticity and the concept of viscoplastic consistency framework to establish continuous transition from plasticity to rate dependent viscoplasticity. Unlike the overstress based models, this model will meet the consistency cond...

in this paper, the transient inertial viscoelastic flow around a circular cylinder is investigated numerically. a second order finite-volume method is used to increase the numerical accuracy. here, the giesekus model is used as the constitutive equation. this nonlinear model has prominent ability in describing normal stress differences and viscosity in power-law regions. the impacts of the elas...

The strong-property-fluctuation theory is developed for the homogenization of the linear dielectric, magnetic, and magnetoelectric properties of a two-constituent bianisotropic composite. The notion of a bianisotropic comparison medium (BCM) is introduced to serve as a springboard for the Dyson equation satisfied by the ensemble-averaged electromagnetic field. With the constitutive properties o...

The methodology of direct finite element (FE) simulation was used to predict the semi-solid constitutive behavior of an industrially important aluminummagnesium alloy, AA5182. Model microstructures were generated that detail key features of the as-cast semi-solid: equiaxed-globular grains of random size and shape, interconnected liquid films, and pores at the triple-junctions. Based on the resu...

We report results concerning the treatment of elastic bodies described by implicit constitutive relations which are not solvable, in the sense of expressing the stresses as functions of the strains or vice versa. Motivated by the theory of generalized hyperelastic materials, which applies also to polyatomic crystals, the field equations to be solved for a body described by a non-solvable implic...

There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging. Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials. We begin with a brief introduction of ...