The exploration of two-phase composite materials through the lens of asymptotichomogenization presents a fascinating intersection of materials science and mathematicalmodeling. The study in question proposes a novel hybrid method that avoids the traditional
use of the Laplace-Carson transform, a complex mathematical tool often employed in the analysis of systems with linear viscoelastic properties. By utilizing lambda functions, which are a staple in functional programming languages due to their flexibility and conciseness,
the proposed method aims to streamline the calculation of local functions and effective coefficients. Lambda functions, by their very nature, allow for a more succinct expression of mathematical operations, which can be particularly advantageous in the context of
computational materials science. The hybrid method's reliance on these anonymous functions suggests a potential reduction in computational complexity, which could lead to
faster processing times and more efficient simulations. This is crucial in a field where the modeling of materials often requires extensive computational resources, especially when
dealing with two-scale periodicity where the behavior at two distinct scales must be accurately captured.
The study focuses on the analysis of two-phase composite materials with two scale periodicity and linear viscoelastic properties. A hybrid method based on asymptoticexpansion is proposed alternative to calculate the local functions and the effective
coefficients derived from asymptotic homogenization approach without having to employ the Laplace-Carson transform. For this, lambda functions are used, also known as anonymous functions, typical of functional programming languages. The comparison
between both approaches is made considering criteria of computational complexity and precision.