Elastic Modulus Tensor Research Articles

Ein bewegter Stempel auf einem anisotropen elastischen Halbraum

The problem is considered of a semi-infinite homogeneous anisotropic elastic solid deformed in plane strain by an indenter moving steadily over its surface. General expressions are derived for the components of stress throughout the medium for arbitrary anisotropy of the elastic modulus tensor. It is shown that the distribution of normal traction under the indenter and the normal displacement of the free surface outside the region of contact depend on the elastic modulus components and the velocity of the indenter through a single constant, denoted by Ω. A simple, practical method of calculating Ω is presented. The solutions are examined in detail for the case of orthotropic materials and analytical expressions are given for Ω and for the complete stress distribution throughout the medium in this case. Representative numerical results are presented graphically to illustrate the angular variations of the scaled radial shear and tangential stress components near the edge of the punch.

On the Dynamic Response of Disordered Composites

A formulation is obtained that is to be satisfied by the mean (i.e., statistical averaged) field quantities in a statistical sample of heterogeneous, linearly elastic solids. Inertia effects are included in the analysis. A low frequency-long wavelength theory is extracted from the general formulation as an approximation to be used when spatial variations of the mean field quantities are slow relative to spatial variations of the material properties of the inhomogeneous solids. The temporal variations are restricted to slow variations on a time scale defined by the spatial variations of material properties and a characteristic wave speed. The predictions of the low frequency-long wavelength theory can be given a purely deterministic interpretation. Some aspects of the latter formulation are investigated. In particular, it is shown that the infinite wavelength limit reduces to an effective modulus theory. The effective elastic moduli tensor is identical to one that is obtained on ignoring inertia effects from the outset; the mass density to be used is the “averaged” mass density. By retaining correction terms it is then shown that elastic wave propagation will always exhibit both dispersion and decay over large enough propagation distances.

Statistical theory of the microdeformation of polycrystals. II

Starting from an isotropic random distribution of the elastic moduli tensor components of a polycrystal caused by grain disorientation, an attempt is made to find the density distribution function of grain yield points in the direction of expansion at the first and second phases of microdeformation. This permits the solution of the problem of the change in the relative number of plastically deformed grains with increase in the external stress. The nature of the involvement of the grains in plastic deformation is analyzed in materials with various grains sizes.