Micropolarはりの均質化骨組構造体における巨視的非局所弾性特性

抄録

The micropolar body with an additional microscopic degree of freedom (DOF) can diversely extend the deformability by modeling the rotational material point instead of the classical rigid one. It contains three DOFs at any point in addition to the macroscopic three DOFs. Based on totally 6 DOFs, two kinds of strain tensors, which total number of components reaches 18, are defined and the conjugate stress and couple stress tensors are obtained via the constitutive laws. In order to make clear of the macroscopic nonlocal elastic properties of micropolar body, two-scale homogenization method based on such microcontinuum theories has been formulated in the finite element method. The orthogonal and oblique lattice framework structures consisting of micropolar beams are analyzed to summarize the size dependence of unit cell. The framework structure consisting of beams, which deformation is expressed by the angle of deflection as well as the deflection, is strongly affected by the surrounding deformation state. Therefore, the beam has been recognized as a pseudo model of nonlocality. The results point out some noticeable facts. First, even if the microscopic framework structure doesn’t have any nonlocality, that is, it just contains the conventional local elastic constants, the nonlocal elastic constants of the homogenized macroscopic body exist because the rotation DOF in the microcontinuum is the same dimension as the angle of deflection in beam. Also, the micropolar body clearly illustrates the size effect for the different size of unit cell with providing the micrometer sized characteristic length.