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 some basic terminology and relationships in continuum mechanics, and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms. To complete the set of equations, we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials. In addition, we discuss some applications for these constitutive equations. Finally, we give a computational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion.

It has been proposed that photosynthetic plankton can be used as a biological carbon pump to absorb and sequester carbon dioxide in the ocean. In this paper, plankton population dynamics are simulated in a single stratified water column to predict carbon dioxide sequestering due to surface iron fertilization in deep ocean. Using a predator-prey model and realistic parameter values, iron fertilization was found to only cause temporary blooms up to 5 months in duration, and relatively small increases in adsorption of atmospheric $\mathrm{CO_{2}}$.

In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices $M$, $D$ and $K$ for the quadratic pencil $Q(\lambda)=\lambda^2M+\lambda D+K$, so that $Q(\lambda)$ has a prescribed subset of eigenvalues and eigenvectors. This method can determine the solvability of the inverse eigenvalue problem automatically. We then consider the least squares model for updating a quadratic pencil $Q(\lambda)$. More precisely, we update the model coefficient matrices $M$, $C$ and $K$ so that (i) the updated model reproduces the measured data, (ii) the symmetry of the original model is preserved, and (iii) the difference between the analytical triplet $(M, D, K)$ and the updated triplet $(M_{\text{new}}, D_{\text{new}}, K_{\text{new}})$ is minimized. In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.

This paper deals with the study of transient waves in a homogeneous isotropic, solid half-space with a permeating substance in the context of the theory of generalized elasto-thermodiffusion. The half-space is assumed to be disturbed due to mechanical loads acting on its boundary. The model comprising of basic governing differential equations and boundary conditions has been solved by employing Laplace transform technique. Noting that the second sound effects are short lived, the small time approximations of solution for various physical quantities have been obtained and the results are discussed on the possible wave fronts. In case of continuous and periodic loads acting at the boundary, the displacement is found to be continuous at each wave front while it is discontinuous in case of impulsive load. The temperature and concentration fields are found to be discontinuous at all the wave fronts. The displacement, temperature change and concentration deviation due to impulsive, continuous and periodic mechanical loads have also been evaluated in the physical domain at all times by employing numerical inversion technique of integral transform. The computer simulated numerical results have been presented graphically in respect of displacement, temperature change and concentration deviation for brass. A significant effect of mass diffusion has been observed on the behaviour of mechanical and thermal waves.

In this work, we present and discuss some modifications, in the form of two-sided estimation (and also for arbitrary source functions instead of usual sign-conditions), of continuous and discrete maximum principles for the reaction-diffusion problems solved by the finite element and finite difference methods.

In this article, natural convection of a temperature-sensitive magnetic fluid in a porous media is studied numerically by using lattice Boltzmann method. Results show that the heat transfer decreases when the ball numbers increase. When the magnetic field is increased, the heat transfer is enhanced; however, the average wall Nusselt number increases at small ball numbers but decreases at large ball numbers due to the induced flow being more likely confined near the bottom walls with a high number of obstacles.