Thermal effects on nonlinear acceleration waves in the Biot theory of porous media

We generalize a theory of Biot for a porous solid based on nonlinear elasticity theory to incorporate temperature effects. Acceleration waves are studied in detail in the fully nonlinear theory. The wavespeeds are found explicitly and the amplitudes are then determined. The possibility of shock formation is discussed

Christov-Morro theory for non-isothermal diffusion

We propose a theory for diffusion of a substance in a body allowing for changes in temperature. The key aspect is that the body is allowed to deform although we restrict our attention to the case where the velocity field is known. In accordance with recent developments in the literature, we concentrate on a situation where diffusion and temperature diffusion are governed by equations which have more of a hyperbolic nature than parabolic. Since this involves relaxation time equations for both the heat flux and the solute flux the fact that the body can deform necessitates the use of appropriate objective time derivatives. In this regard our work is based on recent work of Christov and Morro on heat transport in a moving body. An analysis of well posedness of the theory is commenced in that we establish the uniqueness of a solution to the boundary-initial value problem, and continuous dependence on the initial data for the same. (C) 2011 Elsevier Ltd. All rights reserved

Discontinuity waves in temperature and diffusion models

We analyse shock wave behaviour in a hyperbolic diffusion system with a general forcing term which is qualitatively not dissimilar to a logistic growth term. The amplitude behaviour is interesting and depends critically on a parameter in the forcing term. We also develop a fully nonlinear acceleration wave analysis for a hyperbolic theory of diffusion coupled to temperature evolution. We consider a rigid body and we show that for three-dimensional waves there is a fast wave and a slow wave. The amplitude equation is derived exactly for a one-dimensional (plane) wave and the amplitude is found for a wave moving into a region of constant temperature and solute concentration. This analysis is generalized to allow for forcing terms of Selkov–Schnakenberg, or Al Ghoul-Eu cubic reaction type. We briefly consider a nonlinear acceleration wave in a heat conduction theory with two solutes present, resulting in a model with equations for temperature and each of two solute concentrations. Here it is shown that three waves may propagate

On microstretch thermoviscoelastic composite materials

In this paper we derive a continuum theory for a thermoviscoelastic composite using an entropy production inequality proposed by Green and Laws, presented in Lagrangian description. The composite is modeled as a mixture of a microstretch viscoelastic material of KelvineVoigt type and a microstretch elastic solid. The strain measures and the basic laws are shown and the thermodynamic restrictions are established. Then the linear theory is considered and the constitutive equations are given in both anisotropic and isotropic cases. Finally, a uniqueness result is established within the framework of the linear theory

Nonlinear acceleration wave propagation in the DKM theory

We study the evolutionary development of an acceleration wave propagating in a saturated porous material according to a Biot theory proposed by Donskoy, Khashanah and McKee. The theory is fully nonlinear, includes dissipation, and the analysis presented is exact. We derive sufficient conditions to show that two distinct waves propagate, a fast wave and a slower wave. A solution for the wave amplitude is presented for a wave moving into an equilibrium region

Reconstruction of round voids in the elastic half-space: Antiplane problem

We study the reconstruction of geometry (position and size) of round voids located in the elastic half-space, in frames of antiplane two-dimensional problem. We assume that a known point force is applied to the boundary surface of the half-space, and we can measure the shape of the surface over a certain finite-length interval. Then, if the geometry of the defect is unknown, we construct an algorithm to restore its position and size. Some numerical examples demonstrate a good stability of the proposed algorithm