Overall properties of linear viscoelastic composites

Reinaldo Rodríguez-Ramos (University of Havana)

Thursday 15th October, 2020 13:00-14:00 ZOOM (ID: 967 9494 2216)


Several examples of naturally occurring and man-made materials consist of viscoelastic constituents with excellent mechanical performance and widely used in the design of durable and sustainable structural components. The procedure of modeling and characterization of these materials involves significant challenges due to they often present heterogeneous structures with hierarchical disposition. Attractive cases can be found in the human body tissues. For instance, many researches are motivated by the study of the viscoelastic, non-linear hyperelastic and anisotropic behavior of the structural components of the skin. A better understanding of this
biological tissue has a real impact on biomedical applications and also inspires modern technology such as flexible instance electronics, soft robotics and prosthetics.
In the scientific literature, there exist several works focusing on the development of micromechanic techniques to predict the macroscopic properties of composite materials. In particular, the use of multiscale asymptotic homogenization methods takes advantage of the information available at the smaller scales to calculate the effective properties of the medium at its larger scales. This homogenization procedure requires the solution of a cell problem with data corresponding to the homogenized material properties of the previous steps. Also, the use of more general periodic or stratification functions lets to describe the different length scales of the composite materials.
In the present work, the three-scale Asymptotic Homogenization Method (AHM) is applied to model a non-ageing linear viscoelastic composite material with generalized periodicity and two hierarchical levels of organization. As starting point, we consider the elastic-viscoelastic correspondence principle and the Laplace-Carson transform. We present the analytical solution of the local problems associated with each scale and the calculation of the effective coefficients for a hierarchical laminated composites and fibrous heterogeneous materials with anisotropic components and perfect contact at the interfaces. In addition, in order to handle complex microstructures, we apply a semi-analytical technique that combines the theoretical strengths of the AHM with numerical computations based on finite element method (FEM). 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 variety of heterogeneous structures.

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