Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section

Abstract

The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic composite materials with fibres of diamond-shaped cross-section. The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne-Keller-Mendelson formula. Matching of limit solutions by two-point Padé approximants gives a formula for the effective properties valid for any volume fraction from the interval [0, 0.5].

Two boundary value problems involving an inhomogeneous viscoelastic solid

“…A detailed exposition on asymptotic homogenization procedure can be found in [18] and further advances can be found in [11,10]. The method has been applied for homogenization of elastic ( [12,2]) and viscoelastic bodies ( [26,5,1]). However, as pointed out in [4,3], while this is a reasonable methodology the existence and uniqueness of the homogeneous parameters is an issue.…”

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

“…Some examples of analytical homogenization of deterministic media can be found in the works of Andrianov et al Interesting results in computational homogenization of deterministic media are presented in the works of Chatzigeorgiou et al, Javili et al, Kästner et al, Legrain et al, Moës et al, and Spieler et al For an overview of existing deterministic homogenization techniques, we refer to the work of Saeb et al…”