Higher‐Order Terms in the Homogenized Stress‐Strain Relation of Periodic Elastic Media

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Applying the method of two‐scale asymptotic expansions to the displacement field in periodic elastic structures the completed macroscopic stress‐strain relation of such media is derived. This relation contains beside the usually considered local part also weakly nonlocal contributions in the form of strain gradients up to infinite order. Formulae for the determination of the pertaining homogenized material tensors are derived.