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We rigorously determine the scale-independent short range elastic parametersin the relaxed micromorphic generalized continuum model for a given periodicmicrostructure. This is done using both classical periodic homogenization and anew procedure involving the concept of apparent material stiffness of aunit-cell under affine Dirichlet boundary conditions and Neumann's principle onthe overall representation of anisotropy. We explain our idea of "maximal"stiffness of the unit-cell and use state of the art first order numericalhomogenization methods to obtain the needed parameters for a given tetragonalunit-cell. These results are used in the accompanying paper [16] to describethe wave propagation including band-gaps in the same tetragonal metamaterial.

Identification of scale-independent material parameters in the relaxed micromorphic model through model-adapted first order homogenization