This article is concerned with the linear theory of chiral Cosserat thermoelas- tic bodies. We investigate the deformation of chiral plates. First, we present the basic equations which govern the deformation of thin plates. Then, we present reciprocity and uniqueness results. In the next section, we establish the instability of solutions whenever the internal energy is negative. We use a semigroup approach to prove the existence of a solution. The deformation of an in nite plate with a circular hole is investigated.
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Africa Review on 17/04/2014, available online:http://www.tandfonline.com/doi/full/10.1080/01495739.2016.1217180
In this article, we use the Nunziato–Cowin theory of materials with voids to derive a theory of thermoelastic solids, which have a double porosity structure. The new theory is not based on Darcy's law. In the case of equilibrium, in contrast with the classical theory of elastic materials with double porosity, the porosity structure of the body is influenced by the displacement field. We prove the uniqueness of solutions by means of the logarithmic convexity arguments as well as the instability of solutions whenever the internal energy is not positive definite. Later, we use semigroup arguments to prove the existence of solutions in the case that the internal energy is positive. The deformation of an elastic space with a spherical cavity is investigated.
Electronic version of an article published as "Journal of thermal stresses", vol. 37, no 9, 2014, p. 1017-1036. DOI: 10.1080/01495739.2014.914776
This article is concerned with the linear theory of thermoelasticity with
microtemperatures. In a recent article we have used the logarithmic convexity method
to investigate uniqueness, instability and structural stability. The results are restricted
to the case when the constitutive coefficients
k1 and k3 have the same signs. Here we
prove that these results also hold when the coefficients k1 and k3 have opposite signs.
Green and Naghdi proposed three theories of thermoelasticity labelled as type I, II and III, respectively. Here we investigate the spatial behaviour of solutions of a problem determined by the type III thermoelasticity. We study the growth/decay alternative in the spatial variable for the linear theory in the case that the thermoelastic deformations and the instant T are constrained to be proportional to the ones at the instant zero. In the case that the solutions decay, an upper bound for the amplitude term by means of the data of the problem can be obtained. We sketch how to obtain it. we finish by noting (through examples) that for several families of cases the solutions can be periodic in the spatial variable and the Phragmen-Lindelof alternative is not satisfied.
In this paper we investigate the thermomechanical theory of thermoelasticity without energy dissipation. We consider the case where the assumptions on the constitutive tensor are different from the usual ones in the current literature. These assumptions are suitable because they correspond to situations where the material is prestressed and has initial entropy flux. When we restrict our attention to the one-dimensional problem, we first establish a condition on the coefficients to guarantee the hyperbolicity of the system. Then we prove that the problem is well posed and stable. When the hyperbolicity condition is not satisfied we prove that the problem is ill-posed. We also prove a similar result when the dimension is greater than one whenever the domain satisfies a certain condition. Though we cannot expect in general the stability of solutions in dimension greater than one, we prove the uniqueness and stability of radial solutions in the general case. To obtain the results, we need the use of a conservation law which has not previously been considered in the literature. Similar results are not known for other thermoelastic theories.
The thermodynamical foundations of generalized thermoelasticity formulated by Lord and Shulman are reviewed and memory effects on the heat flux are generalized. An existence and uniqueness theorem for the evolution integro-differential equations is obtained using semi-group theory.