Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Russian participants

The use of the averaging operator for analyzing macroscopic stress fields near the ensemble of inclusions in infinite matrix

Evlampieva S.E.

Institute of Continuous Media Mechanics,
Urals Branch of Russian Academy of Sciences (Perm)

The integral operator is used to compute the macroscopic parameters of the state of a composite material. Physically, this operator involves the spatial averaging with the weight coefficient which characterizes a contribution of the structural value to its macroscopic value taking into account the remoteness from the considered point of space. The theory of transition from the structural modeling of the composite to its microscopic description is formulated taking into account the finite deformation of the material components.

As an example we have used the integral operator for averaging the calculated fields of macroscopic stresses in the ensemble consisting of 91 rigid inclusions in the Hook infinite matrix (plane problem). The filler concentration is taken to be 50%.

It is shown that the macroscopic fields of mean stresses and stress intensity in the ensemble--elastic matrix system are consistent with the stress fields in the system consisting of one effective inclusion (with macroscopic elastic modulus) and matrix except for the region of smoothing the stress jump at the ensemble-matrix interface. The appearance of these jumps is attributed to the absence of clearly defined boundary at the macroscopic level between the composite region and that of the homogeneous matrix.

The work has been supported by Russian Foundation of Basic Research and Department of Science and Education of Perm Region Administration under Grant 01-01-96492.

Note. Abstracts are published in author's edition

Comments

[Home]
[Conference]