We formulate a macroscopic particle modeling analysis of metallic
materials (aluminum and copper, etc.) based on theoretical energy and atomic
geometries derivable from their interatomic
potential. In fact, particles in this framework are presenting a large
mass composed of huge collection of atoms and are interacting with each other.
We can start from cohesive energy of metallic atoms and basic crystalline unit
(e.g. face-centered cubic). Then, we can reach to interparticle (macroscopic)
potential function which is presented by the analytical equation with terms of
exponent of inter-particle distance, like a Lennard-Jones potential usually
used in molecular dynamics simulation. Equation of motion for these macroscopic
particles has dissipative term and fluctuation term, as well as the
conservative term above, in order to express finite temperature condition.
First, we determine the parameters needed in macroscopic potential function and
check the reproduction of mechanical behavior in elastic regime. By using the
present framework, we are able to carry out uniaxial loading simulation of
aluminum rod. The method can also reproduce Young’s modulus and Poisson’s ratio
as elastic behavior, though the result shows the dependency on division number
of particles. Then, we proceed to try to include plasticity in this multi-scale
framework. As a result, a realistic curve of stress-strain relation can be
obtained for tensile and compressive loading and this new and simple framework
of materials modeling has been confirmed to have certain effectiveness to be
used in materials simulations. We also assess the effect of the order of
loadings in opposite directions including yield and plastic states and find
that an irreversible behavior depends on different response of the particle
system between tensile and compressive loadings.
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