Abstract
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.
Highlights
Multi-scale modeling of materials behavior with hierarchical approach has attracted much interest in research and development of materials science
We propose a computational framework by using macroscopic particles method (MPM)
The proposed macroscopic particle modeling (MPM) method is constructed from microscopic parameters such as cohesive energy and density of metallic materials, it provides high feasibility on implementing a simple framework for multi-scale simulation and in discussing the deformation of metallic materials
Summary
Multi-scale modeling of materials behavior with hierarchical approach has attracted much interest in research and development of materials science. Stress and strain are absolutely macroscopic evaluations that are only defined under continuum hypothesis and relation, but they can be transferred into atomic simulations with the name of “atomic stresses” [11] or “atomic strains” [12] [13] Another approach is that, to the contrary, an atomistic (microscopic) variable is utilized in macroscopic modeling for materials behavior. To the contrary, an atomistic (microscopic) variable is utilized in macroscopic modeling for materials behavior This idea has already been implemented as some new computational theories, such as quasi-continuum (QC) method [14] [15], virtual atomic cluster (VAC) method [16], and so on [17].
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