Abstract
Effective properties of non-aging linear viscoelastic and hierarchical composites are investigated via a three-scale asymptotic homogenization method. In this approach, we consider the assumption of a generalized periodicity in the different structural levels and their characterization through the so-called stratified functions. The expressions for the associated local and homogenized problems, and the effective coefficients are derived at each level of organization by using the correspondence principle and the Laplace-Carson transform. Considering isotropic components and a perfect contact at the interfaces between the constituents, analytical solutions, in the Laplace-Carson space, are found for the local problems and the effective coefficients are computed. An interconversion procedure between the effective relaxation modulus and the effective creep compliance is carried out for obtaining information about both viscoelastic properties. The numerical inversion to the original temporal space is also performed. Finally, we exploit the potential of the approach and study the overall properties of a hierarchical viscoelastic composite structure representing the dermis.
Highlights
In the scientific literature there exist several works focusing on the development of micromechanical techniques to predict the macroscopic properties of composite materials
Effective properties of non-aging linear viscoelastic and hierarchical composites are investigated via a three-scale asymptotic homogenization method
Multiscale asymptotic homogenization methods take advantage of the information available at the smaller scales of a given heterogeneous medium to predict the effective properties at its larger scales
Summary
In the scientific literature there exist several works focusing on the development of micromechanical techniques to predict the macroscopic properties of composite materials. We generalize the results obtained in [5] for linear elasticity by extending them to a non-aging, linear viscoelasticity framework; we deal with the stratified functions in the homogenization procedure; an analytical solution for the local problems associated with each hierarchical level is obtained; the expressions for the effective coefficients for hierarchical laminated composites with generalized periodicity, isotropic components and perfect contact at the interfaces are provided; and the methodology is used to model the overall behavior of the dermis in the skin. The dermis is assumed to behave as a non-aging linear viscoelastic and hierarchical composite material, and the investigation of its effective properties is based on the correspondence principle and the Laplace transform
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