Wave Propagation in Heterogeneous Media with Local and Nonlocal Material Behavior

Abstract

Wave propagation in heterogeneous solids has been an interest of researchers due to industrial applications. Some of the heterogeneous materials can exhibit power law scaling in material behavior which can be characterized by the fractal dimension of the microstructure. In this study, wave propagation in heterogeneous media with self-similar structure is investigated via fractional calculus along with space-time discontinuous Galerkin method. One and two dimensional problems are studied to demonstrate the capability of the proposed model in modeling heterogeneous media. The results show that the proposed model is a good candidate for modeling the mechanical behavior of disordered materials.

Nonlocal Diffusion in Porous Media: A Spatial Fractional Approach

“…In the present work, the model proposed in (Sen and Ramos, 2012) is revisited and generalized to investigate the diffusion process on finite porous domains. The approach represents somehow an extension of the well-established method proposed in the framework of nonlocal elasticity (Carpinteri et al, 2011(Carpinteri et al, , 2014 (see also (Di Paola and Zingales, 2008;Drapaca and Sivaloganathan, 2012)) and later implemented also to study wave propagation in nonlocal media (Atanackovic and Stankovic, 2009;Sapora et al, 2013;Challamel et al, 2013;Aksoy , 2016).…”