Multiscale homogenization of viscoelastic composite materials. Combined approach based on deep neural networks

Abstract
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, the study of the viscoelastic behavior of structures such as skin or bones.

In the scientific literature, there exist several works focusing on the development of micromechanics techniques to predict the macroscopic properties of composite materials. In particular, the use of multiscale asymptotic homogenization methods (AHM) takes advantage of the information available at the smaller scales to calculate the effective properties of the medium at its larger scales.

The three-scale Asymptotic Homogenization Method (AHM) is applied to model a non-aging linear viscoelastic composite material with generalized periodicity (the use of the so-called stratification functions permits to describe a more generalized periodicity at the different structural levels of the composite materials) 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 with anisotropic components and perfect contact at the interfaces. Besides, 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), and we perform the numerical inversion to the original temporal space. Finally, we exploit the potential of the approach and study the overall properties of a variety of heterogeneous structures. We perform comparison with different homogenization approaches.

Artificial Intelligence (AI) has a great potential to speed up research processes in various engineering fields, but its application in micro-mechanics is still in early stages. In this presentation, we show the use of Deep Neural Networks for the homogenization of composite materials. In particular, we apply Physics-Informed Neural Networks to solve the so-called local problems and thus learn the mapping between the microstructure and the effective properties. Comparisons with analytical and numerical results of benchmark methods are performed.