Linear Isotropic Material Research Articles

The dynamic response of compliant materials to an impulsive pressure field

AbstractThe dynamic interaction between a compliant material and an impulsive pressure field, periodic in space and instantaneous in time, was examined as a first step at modelling the interaction between organized structures in a turbulent boundary layer and a compliant surface. The interaction, modelled two‐dimensionally, was treated dynamically by matching the pressure forces to the surface stresses in the compliant material at each instant of time. A new boundary element method was formulated to model the compliant material which was treated as a linear isotropic material, elastic in dilatation and viscoelastic (Standard) in shear. The inertial forces and viscoelastic creep stresses have been included in this formulation as transient body forces. The elastic interaction was characterized by a non‐dimensional threshold velocity, above which the elastic instabilities grew temporally and spatially in the downstream direction to produce a non‐linear breakdown of the interaction. Freestream velocities as high as 9CT (shear wave speed) were found to produce stable elastic interactions. Thinner materials produced smaller amplitude waves of higher frequencies that grew more rapidly than those in thicker materials. The stability characteristics were independent of the location of the compliant material with respect to the spatial distribution of the pressure pulse. For viscoelastic interactions, the stability curve, which serves as a bound on the types of materials capable of producing drag reduction, shows distinct regions of elastic types of interactions (Class B) and damping dominated interactions (Class A) as a function of the constants of the rheological model describing the compliant material. Class A disturbances in these interactions show slower growth or decay than Class B disturbances.

A generalized variational principle and theoretical model for magnetoelastic interaction of ferromagnetic bodies

The quantitative analysis shows that no theoretical model for 3-d magnetoelastic bodies, in literatures to date, can commonly simulate two kinds of distinct experimental phenomena on magnetoelastic interaction of ferromagnetic structures. This makes it difficult to effectively discribe the magnetoelastic mechanical behavior of structures with complex geometry, such as shells. Therefore, it is a key step for simulating magnetoelastic mechanical characteristics of structures with complex geometry to establish a 3-d model which also can commonly characterize the two distinct experimental phenomena. A theoretical model for three dimension magnetizable elastic bodies, which is commonly suitable for the two kinds of experimental phenomena on magnetoelastic interaction of ferromagnetic plates, is presented by the variational principle for the total energy functional of the coupling system of the 3-d ferromagnetic bodies. It is found that for the case of linear isotropic magnetic materials, the magnetic forces obtained by this model include not only the body magnetic force which is the same as that got from the magnetic dipole model, but also a distribution of the magnetic traction on the surface of the magnetizable body. And the value of the traction is equal to the jumping one of the Faraday electromagnetic stress on the two sides of the surface, which does not appear in any model, such as magnetic dipole model and axiomatic model.

Network representation of electromagnetic fields and forces using generalized bond graphs

We show that it is possible to describe electromagnetic (E-M) fields with a generalized network representation (generalized bond graphs). E-M fields inmoving matter, forces due to E-M fields (Lorentz force, ets.) and field transformations are included in the network description. The relations of these E-M phenomena with respect to each other are clearly represented by the bond graph. We also show that it is not possible to describe E-M phenomena in moving matter with conventional bond graphs, but that a generalized bond graph concept is required. The description of simple E-M devices with conventional bond graphs is based on rather drastic assumptions, i.e. quasi-static conditions (E-M radiation neglected), homogeneous fields, isotropic linear material, etc. These assumptions are not made in this paper.

Inelastic behaviour of rectangular beams subjected to steady axial load and cyclic bending

Analytical and numerical solutions are given for the inelastic behaviour of a rectangular cross-section beam, subjected to a steady axial load and cyclic, fully reversed load-controlled bending. Elastic-perfectly plastic, linear isotropic and kinematic materials are examined and solutions for the strain accumulation and cyclic reverse plastic strains obtained. Also the effect of introducing a creep dwell period into the cycle is considered.

Thermo-acoustical waves in linear thermo-elastic materials

Coupled waves of thermal and mechanical jumps in linear thermo-elastic materials are analysed. General linear anisotropic constitutive equations of thermo-elastic materials are derived from the Clausius-Duhem inequality and Vernotte's heat conduction law is adopted. The waves are defined to have jumps in acceleration and in temperature rate and the four-dimensional thermo-acoustical propagation condition is obtained. The differential equations which govern the variation of the wave amplitudes are obtained. For waves in linear isotropic thermo-elastic materials, there are four principal waves. Two shear waves are purely mechanical and propagate with constant amplitude, while two thermo-longitudinal waves have different propagation velocities: one is larger and other smaller than the purely mechanical longitudinal wave velocity, and their amplitudes decay, in general, exponentially in time.

Effect of random irregularities of the creep of reinforced layered plastics

The authors investigate the creep of inhomogeneous materials consisting of a large number of stiff orthotropic elastic layers alternating with layers of linear isotropic viscoelastic material. The elastic layers are assumed to be almost plane; the functions describing the irregularities (curvature) form a random field. The averaged characteristics of the medium are found together with the variation of the averaged displacements and strains in time. An analogous problem was previously considered in [1, 6] on the assumption that the binder layers are elastic. The present paper is based on the equations of [1] and the elastic-viscoelastic correspondence principle [4]. When the correlation scales of the irregularities are small as compared with the dimensions of the body and the characteristic distances over which the averaged parameters of the stress-strain state vary appreciably is considered in detail. A relation is established between the creep functions for simple cases of the state of stress and the parameters characterizing the properties of the components, the properties of the random field of initial irregularities, etc. The development of perturbations with different wave numbers is investigated. The theory is used to describe the creep of reinforced layered plastics.

Magnetic Shielding Factors of a System of Concentric Spherical Shells

General expressions are developed for the shielding factors of concentric spherical shells of linear isotropic magnetic material. Approximate results are given for shells of highly permeable material which are thin compared to their radii.