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From Homogenization to Generalized Continua

We derive the generalized continua formulation for heterogeneous medium from mathematical homogenization. We then reformulate the generalized continuum description in terms of C 0 continuous formulation without additional degrees of freedom and free of higher order boundary conditions. We introduce the notion of macro-stress function to replace the classical definition of macro-stress being an average of micro-stresses. The coefficients of the macro-stress function are computed in close form to satisfy the equivalence in virtual strain energy density between the fine scale fields and the corresponding coarse scale fields.