Bogdan T. Maruszewski

Thermoelastic damping in an auxetic rectangular plate with thermal relaxation—free vibrations

This work describes an extended thermodynamical model to represent coupled thermomechanical interactions in continuum media having negative Poisson?s ratio. In particular, the Zener thermoelastic damping effect is considered for a plate with auxetic characteristics undergoing free vibrations. The extended thermodynamical model is characterized by a thermal relaxation time to avoid the propagation of thermal waves at infinite velocity. The thermal relaxation time used in this work is not Zener?s characteristic time constant. Strong dependence of the thermoelastic damping is observed for auxetic configurations, various plate thicknesses and ambient temperatures.

Computational Modelling of Auxetics

Modern technologies require new materials of special properties. One of the reasons for interest in materials of unusual mechanical properties comes from the fact that they can be used (either as inclusions or as matrices) to form composites of required properties. There is a number of physical properties that we implicitly assume to be positive. However, one may be surprised to discover that they can also be negative. Negative materials include, amongst other ones, those having negative stiffness (Lakes et al., 2001), negative thermal expansion (Hartwig, 1995), negative refractive index (Sang & Li, 2005), negative permittivity (Ruppin, 2000) and/or negative permeability (Ruppin, 2000). It is worth to add that in presence of some constrains even the compressibility can be negative (Lakes & Wojciechowski, 2008). A new field of challenge are studies of materials exhibiting negative Poisson’s ratio. The latter is a negative ratio of relative transverse dimension change to relative longitudinal dimension change of a body when an infinitesimal change of a stress acting along the longitudinal direction occurs whereas the other stress components remain unchanged. Such materials, first manufactured by Lakes (Lakes, 1987) and coined auxetics by Evans (Evans, 1991), are a subject of intensive studies both in the context of fundamental research and applications (Remillat et al., 2009). The aim of this chapter is to demonstrate recently discovered anomalous deformation of an auxetic plate, constrained by fixing two opposite sides, which is loaded by uniform tension (or compression) applied perpendicularly to two other opposite sides of the plate. The problem was studied both in three dimensions (3D) by Strek et al. (Strek et al., 2008) and in two dimensions (2D) by Pozniak et al. (Pozniak et al., 2010) by finite element methods. In all the cases studied it has been assumed that the material was isotropic. 12

Anomalous Features of the Thermomagnetoelastic Field in a Vortex Array in a Superconductor: Propagation of Love'S Waves

A magnetic field enters a type-II superconductor along an arrangement of Abrikosov vortices. They interact with each other with the help of the Lorentz force creating a new mechanical field different from that coming from the crystal lattice of a superconducting material. That new field presents some anomalous properties as compared to the classical ones of the material. This article deals with a modeling and description of a number of those anomalous features of a vortex field in a superconductor.

Diffusion and dislocation influences on the dynamics of elastic bodies

Abstract A nonconventional model based on the extended irreversible thermodynamics of physical processes in which the diffusion of mass and the dislocation field interact in an elastic body is presented. The theory is applied to a case of diffusion-dislocation interactions with the defective body forced by a periodic subcritical stress which admits the relaxation character of the diffusion and dislocation fields.

Magnetoelastic surface waves in auxetic structure

In modern technologies searching materials of peculiar features is of a fundamental interest for many researchers and engineers. Negative Poissons ratio materials and structures expand transversely when stretching axially. Nowadays, there is an increasing interest in the development of these novel materials called auxetics. We are interested not only in their mechanical properties, but also in their interaction with external physical fields, e.g. electromagnetic field. It is expected that magnetoelastic surface waves propagation has essential meaning in many other physical and biomechanical applications. The paper aims at investigating propagation of magnetoelastic surface waves along an auxetic elastic halfspace in the presence of an external magnetic field of various orientations related to the limiting plane. Dispersion and existence conditions of those waves have been calculated and analyzed in order to present new features of described interactions. It has occurred that the dispersion properties in the case of the Rayleigh-like magnetoelastic surface waves are significantly different for the auxetic material compared to materials of positive Poissons ratio.

Thermoelastic Damping and Thermal Relaxation Time in Auxetics

The paper concerns description of the thermoelastic phenomenon in an auxetic rectangular plate within the extended thermodynamical model. Analyzing vibrations of that plate a dependence of elastic constants on the frequency, particularly of Poissons ratio of auxetic state of the body has been presented. Moreover, considered investigations allow to determine the thermal relaxation time analyzing resonance frequencies of the vibrating plate.

Unconventional Thermodynamical Model of Processes in Material Structures

Fast development of applied sciences, particularly of the technical ones has resulted in the creation of a complex situation in which independently developing scientific branches such as mathematics, mechanics, physics, chemistry, Earth sciences and even biology began to cover each other. So, a new area called the coupled field theory in mono- and multiphase materials of various internal structures has been created. One of the best ways to model real processes and interactions occuring in any continuous material region within the phenomenological manner taking into consideration a reasonably wide range of effects is the so-called thermomechanics. The paper deals with an abbreviated form of this extremely broad area concerning a concise description of physical reality.

Mechanical (acoustic‐like) wave propagation along a vortex array in the superconducting heterostructure

Magnetic flux can penetrate the type ‐ II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes or fluxons) each carrying a quantum of magnetic flux. These tiny vortices of supercurrent tend to arrange themselves in a triangular or quadratic flux‐line lattice. Since the vortices are formed by the applied magnetic field, around of each of them the supercurrent flows. Moreover, there also exist some Lorentz force interactions among them. Those interactions form an origin of an additional mechanical (stress) field occurring in the type‐II superconductor. The paper deals with an analysis of elastic (acoustic‐like) wave propagation solely along vortices in a heterostructure consisted of the superconducting layer put on the superconducting substrate. Dispersion and the amplitude distribution of those waves in the vortex field existing in that structure has been presented.

Amplitude distribution of magnetoelastic waves propagating in a vortex field in a superconducting layer

Magnetic field enters the type ‐ II superconducting body along a discrete arrangement of magnetic vortex lines. In the dynamic case when the magnetic field vary in time, around each such a line a supercurrent flows. So, the vortices interact one to another with the help of the Lorentz force forming this way a new mechanical field of elastic properties. Moreover, those lines arrange themselves in a triangular or quadratic lattice. Such a set is observed if the intensity of the applied to the material magnetic field is close to its lower limiting value. The paper aims at investigating amplitude distributions of magnetoelastic waves propagating solely in the vortex field of the superconducting layer. Our attention have been focused on the applied magnetic field intensity influence on those amplitudes for various wave frequencies.