均質化Microcontinuumを用いたマルチスケールモデリングの提案

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  • Proposal on Multiscale Modeling by Homogenized Microcontinuum Field Theory

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<p>The microcontinuous body with an additional microscopic degree of freedom (DOF) can diversely extend the deformability by modeling the deformable material point instead of the classical rigid one. It contains nine DOFs for the micromorphic body at any point in addition to the macroscopic three DOFs. Based on 12 DOFs totally, three kinds of strain tensors, which total number of components reaches 42, are defined and the conjugate stresses and couple stress tensors are identified via the constitutive laws. In order to introduce the characteristic nonlocal properties, which is essential in the atomic system, two-scale homogenization method based on such microcontinuum theories has been formulated in the finite element method. The orthogonal, oblique and face body-centered (FBC) lattice framework structures consisting of microcontinuous beams were analyzed to produce the unique deformation pattern. The results point out some noticeable facts. First, as increasing the number of additional DOFs the body has, its rigidity becomes decreasing, which fact shows the typical trade-off relationship. Changing Young modulus of beam consisting of FBC lattice, Poisson ratio changes from the positive value to negative and the corresponding homogenized elastic constants were obtained. As one example of the scale transition equivalent to homogenization and localization, these properties were implemented into the macroscopic cantilever with the geometric nonlinearity.</p>

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