On Stress-Deformation Behavior of Particle Systems


We discuss the continuum notions of effective mechanical quantities
as well as the conditions that give meaningful deformation processes
for homogenization problems with large deformations. A continuum
homogenization framework is presented for the derivation of the
effective constitutive relations of a nonlinear thermoelastic
material via the space-time averaging of the behavior of a purely
hyperelastic material undergoing a motion that includes inertial
effects. This homogenization procedure is recast as a Lagrangian-
based homogenization approach for heterogeneous media that if
formally applicable to both continuum bodies and discrete particle
systems. For particle systems the proposed homogenization procedure
relies on the use of molecular dynamics (MD). A novel constitutive
relation for the effective stress is derived so that the proposed
Lagrangian-based approach can be used for the determination of the
``stress-deformation'' behavior of particle systems. In addition to
the theoretical aspects mentioned above we present some concrete
examples of the use of MD calculations for the derivation equivalent
continuum stress-strain curves. In addition, we will present a
careful comparison between the proposed method and the Parrinello-
Rahman approach to the determination of the ``stress-deformation''
behavior for MD systems. When compared with the Parrinello-Rahman
method, the proposed approach clearly delineates under what
conditions the Parrinello-Rahman scheme is valid.