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homogenization; approximation of material with periodic structure by homogeneous one; terms of displacements; terms of stresses; results compared; multiple-scale method; properties of homogenized coefficients; correctors; convergence of displacement vector; stress tensor; local energy; simplified local energy method
The homogenization problem (i.e. the approximation of the material with periodic structure by a homogeneous one) for linear elasticity equation is studied. Both formulations in terms of displacements and in terms of stresses are considered and the results compared. The homogenized equations are derived by the multiple-scale method. Various formulae, properties of the homogenized coefficients and correctors are introduced. The convergence of displacment vector, stress tensor and local energy is proved by a simplified local energy method.
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