Effective Youngs Modulus of Two-Phase Elastic Composites by Repeated Isostrain and Isostress Constructions and Arithmetic-Geometric Mean

A relationship is established between the effective Youngs modulus of a two-phase elastic composite and a known mathematical mean value. Specifically, the effective Youngs modulus of a composite obtained from repeated parallel and serial constructions is equal to the arithmetic-geometric mean of the Youngs moduli of the component materials. This result also applies to electric circuits with resistors in repeated parallel and serial connections.