The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

/pdf/dislocations-in-solids-1gaufoliyg.pdf

Dislocations in solids

Thermomechanics of volumetric growth in uniform bodies

http://fml.t.u-tokyo.ac.jp/~izumi/CMS/report/Multiscale_model_of_plasticity.pdf

A multiscale model of plasticity

An asymptotic procedure based upon a two-scale approach is developed for wave propagation in a doubly periodic inhomogeneous medium with a characteristic length scale of microstructure far less than that of the macrostructure. In periodic media, there are frequencies for which standing waves, periodic with the period or double period of the cell, on the microscale emerge. These frequencies do not belong to the low-frequency range of validity covered by the classical homogenization theory, which motivates our use of the term ‘high-frequency homogenization’ when perturbing about these standing waves. The resulting long-wave equations are deduced only explicitly dependent upon the macroscale, with the microscale represented by integral quantities. These equations accurately reproduce the behaviour of the Bloch mode spectrum near the edges of the Brillouin zone, hence yielding an explicit way for homogenizing periodic media in the vicinity of ‘cell resonances’. The similarity of such model equations to high-frequency long wavelength asymptotics, for homogeneous acoustic and elastic waveguides, valid in the vicinities of thickness resonances is emphasized. Several illustrative examples are considered and show the efficacy of the developed techniques.

/pdf/high-frequency-homogenization-for-periodic-media-45rz5yixos.pdf

High-frequency homogenization for periodic media

Introduction Preliminaries Elastic shells Elastic rods Piezoelectric shells Piezoelectric rods Material constants.

Vibrations of Shells and Rods

A model of elastoplastic bodies with continuously distributed dislocations

Nonlinear continuum theory of dislocations

The paper is concerned with the determination of the anholonomic crystal reference from the given elastic strain (metric) and dislocation density (Cartan torsion). The incompatible inverse elastic deformation is shown to satisfy a system of linear first order differential equations. The integrability condition requires that the curvature of the crystal connection should vanish. The equivalent system of equations and integrability condition for the inverse elastic rotation are also obtained. Formulae for the inverse elastic deformation and the inverse elastic rotation in form of tensor series are derived. The dual problem of determining the plastic deformation and the plastic rotation from the plastic strain and the dislocation density is solved in a similar manner. A linearization procedure is carried out and a comparison with Kroner’s theory is provided.

On the Determination of the Crystal Reference in Nonlinear Continuum Theory of Dislocations

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of high-temperature deformation of aluminum and steel. Using physics-based parameters that we expect theoretically to be independent of strain rate and temperature, we are able to fit experimental stress-strain curves for three different strain rates and three different temperatures for each of these two materials. Our theoretical curves include yielding transitions at zero strain in agreement with experiment. We find that thermal softening effects are important even at the lowest temperatures and smallest strain rates.

Khanh Chau Le

Papers

Vibrations of Shells and Rods

A model of elastoplastic bodies with continuously distributed dislocations

Nonlinear continuum theory of dislocations

On the Determination of the Crystal Reference in Nonlinear Continuum Theory of Dislocations

Thermodynamic dislocation theory of high-temperature deformation in aluminum and steel.