Homogenization approaches for the effective characteristics of fractional visco-piezoelastic fibrous composites

Effective properties of fractional viscoelastic composites via two‐scale asymptotic homogenization

“…On the other hand, in Ostoja‐Starzewski and Zhang [19], the Hill–Mandel condition is used to determine the overall response of a random viscoelastic micro‐structure. In the context of asymptotic homogenization, we mention, for instance, the works [20] and [21] where closed formulas for the effective coefficients of fiber‐reinforced viscoelastic and visco‐piezoelastic composites are obtained based on the Rabotnov's fractional exponential kernel. Finally, we mention the paper by Wang and Pindera [15], in which, even though the notion of fractional viscoelasticity is not considered, the authors employ the locally exact homogenization theory to investigate the effective properties of a unidirectional composite with the viscoelastic matrix exhibiting a power‐law constitutive behavior.…”

“…In particular, we conduct our calculations in the general setting of linear viscoelastic materials and specialize them for the case in which the local constitutive response of each constituent is described by a fractional viscoelastic model. Although the approach has common points with that followed in Rodríguez‐Ramos et al [20] and Otero et al [21], we set the problem differently such that it is possible to explicitly split the elastic and the memory contributions of the composite. This is one of the novelties of this work.…”

“…Here, motivated by previous works (see, e.g., [17,20,21,[25][26][27]), we use the asymptotic homogenization method [28][29][30] to compute the effective properties of a composite with viscoelastic constitutive response. In particular, we conduct our calculations in the general setting of linear viscoelastic materials and specialize them for the case in which the local constitutive response of each constituent is described by a fractional viscoelastic model.…”