Abstract
We study the homogenized properties of linear viscoelastic composite materials in three dimensions. The composites are assumed to be constituted by a non-aging, isotropic viscoelastic matrix reinforced by square or hexagonal arrangements of elastic transversely isotropic long and short fibers, the latter being cylindrical inclusions. The effective properties of these kind of materials are obtained by means of a semi-analytical approach combining the Asymptotic Homogenization Method (AHM) with numerical computations performed by Finite Elements (FE) simulations. We consider the elastic-viscoelastic correspondence principle and we derive the associated local and homogenized problems, and the effective coefficients in the Laplace–Carson domain. The effective coefficients are computed from the microscale local problems, which are equipped with appropriate interface loads arising from the discontinuities of the material properties between the constituents, for different fibers’ orientations in the time domain by inverting the Laplace–Carson transform. We compare our results with those given by the Locally Exact Homogenization Theory (LEHT), and with experimental measurements for long fibers. In doing this, we take into consideration Burger’s and power-law viscoelastic models. Additionally, we present our findings for short fiber reinforced composites which demonstrates the potential of our fully three dimensional approach.
Highlights
Materials characterized by both a viscoelastic response and a composite-like geometrical arrangement are found in several biological contexts driven by natural evolution, see, e.g., (Atthapreyangkul et al, 2021; Ojanen et al, 2017; Sherman et al, 2017)
Among the most used techniques addressing the calculation of the effective properties of viscoelastic heterogeneous structures we find the Asymptotic Homogenization Method (AHM)
In the present work, we aim to study the effective properties of viscoelastic composites by means of the combination of the AHM and the Finite Elements (FE) method, the latter allows us to find the numerical solution of the microscale periodic local problem for different three-dimensional arrangements
Summary
Materials characterized by both a viscoelastic response and a composite-like geometrical arrangement are found in several biological contexts driven by natural evolution, see, e.g., (Atthapreyangkul et al, 2021; Ojanen et al, 2017; Sherman et al, 2017). High performance composites are typically made of long continuous fibres embedded in a polymer matrix and exhibit viscoelastic properties (see, e.g., Ornaghi Jr. et al, 2020; Wang et al, 2020). The multiscale modelling of viscoelastic composites has been increasingly addressed in recent contributions. In this respect, micromechanical models are suitable whenever the aim is to determine the effective response of materials on the basis of individual constituents’ properties, such as viscoelastic moduli and fibers properties in terms of geometrical arrangement, volume fraction and orientation. The effective viscoelastic creep behavior of aligned short fiber composites is obtained in Wang and Smith (2019) via a RVE-based Finite Element algorithm.
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