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The Analysis nonlinear and anisotropy of behavior of a material with microstructure


Author: Viorica Marina
Degree:doctor of physics and mathematics
Speciality: 01.04.27 - Mechanics of deformable solids
Year:2006
Scientific adviser: Vasile Marina
doctor habilitat, professor, Technical University of Moldova
Institution:
Scientific council:

Status

The thesis was presented on the 1 September, 2006
Approved by NCAA on the 26 October, 2006

Abstract

Adobe PDF document – 0.98 Mb / in romanian

Thesis

CZU 539.3

Adobe PDF document 3.97 Mb / in romanian
144 pages

Keywords

stress, strain, structure, property, crystal lattice, anisotropy, deviator, microelasticity, making equations, thermodynamic potentials, symmetry, discrepancy, fluctuations, connection, interactions, conglomerate

Summary

By using the structural model, the dependency of the stress/strain condition at the microlevel on the structure characteristics and the stress/strain condition on the macrolevel is being analyzed. For the polycrystalline materials with cubic lattice, the one-to-one correspondences between the elasticity constants on micro and macro levels have been obtained. The interactions between the structural elements in a conglomerate depend on the elastic characteristics at a microlevel. It is proved that the stress/strain condition at the microlevel depends on the anisotropy factor of the structural elements, the orientation factor of a crystal lattice expressed in Euler angles and the stress/strain condition on the macrolevel. The structure of the material functions that influence the stress/strain condition at the microlevel is obtained.

It is established that in the structural elements with extreme values of the deviation module of the stress/strain tensor, the form of the stress condition coincides with the form of the stress condition at the macrolevel. It is shown that the extreme values of the deviation module of the stress/strain tensor depend only on the value of the deviation module of the stress/strain tensor at the macrolevel and anisotropy factor. The analytic expressions for the material functions are obtained based on which the extreme values have been found. The interval of change of the form of the stress/strain condition at the microlevel as a function of the form of the stress/strain condition at the macrolevel and the anisotropy factor is analyzed. The analysis of the structural model in the case of polycrystallic materials with several phases is given. It is established that the characteristics of the polycrystalline conglomerate change nonlinearly depending on the phase weights. It is proved that the structural elements with below cubic symmetry will generate on the macrolevel nonlinear effects even if each separate structural elements changes linearly.