| Summary: | 碩士 === 國立成功大學 === 土木工程學系 === 102 === Cosserat elasticity is a refined elasticity theory used to describe the deformation of elastic media with oriented particles. In addition to three displacements, a micropolar particle has an additional three micro-rotations, allowing it to link the couple moments as well as the stresses. The framework has an intrinsic length scale and is capable to characterize various materials with sufficient insight information, such as foams, materials with helical or twisted fibers. A more recent implication can be directed to the simulation of metametrials. Motivated by the latter progress, in this work, we aim to provide some theoretical studies on Cosserat elasticity. Specifically, we will derive the Green's function and its spatial derivatives. Inclusion problem in an infinite Cosserat medium is also examined. The method of Fourier transform is employed in the formulation. Centro- and non-centrosymmetry Cosserat elasticity are studied. We show that, under a certain restriction on the constitutive material parameters, Green's function can be expressed as a line integral along a unit circle. This form permits us to evaluate the results accurately by Gaussian quadrature. In addition, we find that, for the inclusion problems, even when the eigenstrain or the eigen-curvature is constant, the resulting strain and curvature tensor are not spatially uniform, in distinct with the famous constant Eshelby tensor in classical elasticity. In contrast it is a polynomial of position of second orders. We show that the resulting expressions can be expressed as a surface integral on a unit sphere and can be evaluated by numerical integration procedure. All these results permit us to make further explorations in metamaterials or in composites made of two or more different constituents.
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