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

TL;DR

This paper derives a mathematical relationship linking the effective Young's modulus of two-phase elastic composites to the arithmetic-geometric mean, based on repeated isostrain and isostress constructions, with parallels to resistor networks.

Contribution

It establishes a novel connection between composite elasticity and mean value theory using repeated isostrain and isostress models.

Findings

Effective Young's modulus equals the arithmetic-geometric mean of component moduli.

The relationship applies to both elastic composites and resistor networks.

Provides a new analytical tool for composite material design.

Abstract

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.