Aa. Berlin et al., COMPUTER-SIMULATION OF ASSEMBLIES OF RIGID ELASTIC ELLIPTIC PARTICLES, Polymer-plastics technology and engineering, 35(4), 1996, pp. 605-648
Results of computer simulation of static mechanical behavior of a body
consisting of similar to 1000 hard elastic particles have been invoke
d to discuss some problems of mechanics of disordered (amorphous) and
ordered (crystal) bodies: the glass-liquid transition, irreversible de
formation (plasticity in a solid and flow in a liquid states), and int
ermediate (like liquid crystal) state. It has been shown that the exis
tence of two states, solid and liquid; the condition of transition bet
ween them; and the fundamental mechanical properties of a solid body,
viz., plasticity, strain softening, and localization of deformation wi
thin the shear bands, are controlled by the number of physical contact
s between the particles, spatial distribution of contacts, and their d
isintegration under shear deformation. Systems of rigid particles are
in a solid or a liquid state depending on the number of interparticle
contacts. Solid (glass or crystal) and liquid states were determined f
rom the ability of a system to resist shape change under external forc
e. As a criterion of the liquid-to-glass transition the equality of th
e number (translational and relational) of degrees of freedom, F, and
the number of constraints of these motions, C, was used (F = C). A sys
tem is solid if F < C and is liquid if F > C. In systems of rigid part
icles, constraints are due to mechanical contacts (C-1) and/or chemica
l bonds between the particles (C-2). Classes were classified as mechan
ical (granular systems and metallic glasses) if C-1 much greater than
C-2, chemical (nonorganic glasses) if C-1 much less than C-2, and comb
ined (polymer glasses) if C-1 approximate to C-2. Some results of comp
uter imitation confirming the transition criterion are presented. Irre
versible deformation of the particle assemblies in the liquid state, u
nlike in the solid one, showed the following features: extremely low y
ield stress, absence of change in the number of interparticle contacts
and the volume of the system during flow, and random distribution of
local strains. Shear strain of the liquid assemblies is governed by pa
rticle rotation and consists in the changes of particle orientation, w
hile shear strain of a glassy solid is due to the disintegration of in
terparticle contacts. A relationship between distribution function of
particle orientation and shear strain of the body is found. Crystals o
f rigid elliptic particles are anisotropic and demonstrate solidlike,
liquidlike, or intermediate behavior in different directions depending
on the arrangement and ellipse eccentricity. Validity of the geometri
cal concepts for developing the theory of a condensed state is based o
n the assumption that any interaction potential can be decomposed into
two components: hard repulsion and soft attraction, which are respons
ible for various properties of the materials.