Chapter 10: Approximations and asymptotic formulas
Graeme Walter Milton · Society for Industrial and Applied Mathematics eBooks · 2022
Countless approximations for estimating effective moduli have been introduced; some are semi-empirical, some are based on ad-hoc assumptions, and some have a reasonable theoretical basis. Here we will only review those well-known approximations that have a reasonable theoretical foundation, and which have withstood the test of time; see also the reviews of Van Beek (1967), Landauer (1978), Willis (1981), Markov (2000), and Buryachenko (2001). In addition, we discuss various asymptotic formulas that are applicable in high-contrast media.