Toshinobu Shibata

Effect of Constitutive Parameters on Formation of a Spherical Void in a Compressible Nonlinear Elastic Material

Void formation in materials under isotropic tension is considered within the theory of finite elasticity. This phenomenon is described as the bifurcation of the solution containing a spherical cavity from the state of homogeneous deformation of a solid hyperelastic sphere. The equation giving the bifurcation point is derived, and the critical stretch and stress are numerically calculated for a special class of compressible nonlinear elastic materials for which the strain energy function was proposed by Hill. The effects of constitutive parameters on the post-bifurcation behavior as well as on the critical stretch and stress are discussed.

Inversion scattering in finite space domain

The general integral representation of a scattered acoustic field with arbitrary boundary conditions is introduced. Assuming weakness of the scatterer, two linearized methods for the recovery of an object’s shape and position are derived and briefly discussed. The methods are applied to one‐ and two‐dimensional problems in order to compare them with the standard use of the first Born approximation (1BA). By presenting the numerical examples, this paper discusses the influence of the power spectrum of the incident pulse on exactness of the recovered object, the influence of ‘‘weakness’’ of scatterer, and comparison of proposed methods to 1BA.

Effects of Stress on Magnetostriction and Magnetization Curve of Ferromagnetic Materials.

In ferromagnetic materials, magnetic properties such as the magnetotriction and the magnetization curve depend on the applied stress as well as the relative orientation of the stress and the magnetic fields due to the magnetoelastic interactions. The authors have studied stress dependence of the magnetostriction and the magnetization curve from the constitutive equations of the stress and the magnetization process of soft ferromagnetic materials. The material is assumed to be isotropic in the natural state, i.e. in the absence of the magnetic field and the stress, and undergo a thermodynamically reversible process, so that the effects of hysteresis can be neglected. It is shown that the theoretical results calculated from an appropriate choice of the material parameters in the internal energy density are in excellent agreement with the experimental data of low carbon steel (SM490A) and pure Ni.

Optimal Design of Cantilever with Circular Cross Section Made of Gradient Material by Symbolic Manipulation.

In this paper we consider optimal distribution of a gradient material at the circular cross section of a cantilever. The design variables are the parameters which express the distribution of the material density or the elastic constant, and Youngs modulus is assumed to be linear in the material density. Two problems are analyzed : (1) maximization of the bending stiffness with constant weight, and (2) minimization of the maximum stress at the cross section with constant bending stiffness. In a general case, the above problems reduce to generalized eigenvalue problems which are formulated and solved by symbolic manipulation and numerical calculation. The optimal distribution indicates that for (1), the density is concentrated at the circular surface such as of a circular cylinder, and for (2), Youngs modulus decreases with respect to the radius. The obtained results are also applicable to the optimal design of composite materials where the distribution of the material density is not continuous.

Acoustoelastic Coefficients of High Polymer by Spectral Analysis. Acoustoelastic Coefficients of Longitudinal Waves in Acryl.

Acoustoelasticity is expected to be a powerful method for nondestructive evaluation of the internal stress of materials. The technique is based on the speed shift of ultrasonic waves due to nonlinearity of the elastic coefficients. If the viscocity of the material is high, such as in high polymers, the speed of an ultrasonic wave depends on the frequency of the wave. In general, the nonlinearity of elastic coefficients of such materials is also significant, so that the relation between the speed shift and the stress becomes nonlinear. A theoretical foundation is given for the acoustoelastic laws of viscoelastic material with higher-order nonlinearity. This paper also presents a technique for determination of the speed and the nonlinear acoustoelastic coefficients by spectral analysis of the waveforms. For longitudinal waves propagating in acryl under uniaxial stress, the dependence of the speed and the acoustoelastic coefficients on the frequency and the uniaxial stress is discussed.

A Thermo-Electromechanical Model for an Actuator using Shape Memory Alloy driven by Pulse Width Electric Heating

ABSTRACT Dynamic behavior of an actuator using Shape Memory Alloy is analyzed, based on a thermoplastic model. One half of a SMA wire is electrically heated alternatively and the other half plays the roll of a bias spring. The temperature is governed by the heat equation containing the Joule heat, the latent heat and the heat transfer to the air. The response of the actuator to a cyclic change of the electric power is obtained.

Spectrum Variation of Ultrasonic Waves Reflected in Layered Materials.

It is theoretically shown that the reflection coefficient of an elastic wave in layers of plates depends on the frequency of the incident wave, the width and the number of layers. Then the spectral change of ultrasonic waves reflected in layers composed of aluminum and steel is measured and compared with the theoretical results. It is found that both results agree well if the bond between the materials is taken into account as one of the elastic layers.