@Article{icces.2023.09355,
AUTHOR = {Linjuan Wang, Jianxiang Wang},
TITLE = {A Spatiotemporal Nonlocal Model for Overall Dynamics of Composites  and Its Analytical Solutions},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {27},
YEAR = {2023},
NUMBER = {1},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v27n1/54088},
ISSN = {1933-2815},
ABSTRACT = {The prediction of overall dynamics of composite materials has been an intriguing research topic more than 
a century, and numerous approaches have been developed for this topic. One of the most successful 
representatives is the classical micromechanical models which assume that the behavior of a composite is 
the same as its constituents except for the difference in mechanical properties, e.g., effective moduli. With 
the development of advanced composite materials in recent years, especially metamaterials, it is found that 
the classical micromechanical models cannot describe complex dynamic responses of composites such as 
the dispersion and bandgaps of elastic waves. Thus, some generalized continuum models for composites 
proposed at the end of last century, e.g., the Willis formulation and Mindlin models, have attracted the 
attention of scientists. But in these generalized continuum models, the relations of their coefficients or 
operators to the microstructural information are unclear. The generalized continuum models with 
microstructure-dependent coefficients for overall dynamics of composite materials are still scarce. <br/>
In this work, we develop a spatiotemporal nonlocal model for overall dynamics of composites through a 
bottom-up dynamic homogenization method. All the coefficients of our model can be explicitly determined 
by microstructural parameters. Our model can capture the dispersion and bandgaps of elastic waves in 
composites, and degenerate into the spatiotemporal nonlocal models, temporal nonlocal models, spatial 
nonlocal models and classical micromechanical models available in the literature, so it sheds light on the 
physical mechanisms of these models. The analytical solutions of our spatiotemporal nonlocal models are 
further derived to manifest the overall dynamic responses of composites. We first find that the 
spatiotemporal nonlocal model has two different Green’s functions for the convolutions with respect to the 
initial condition and the body force, which are radically different from those of other continuum models. The 
analytical solutions of our model are validated by comparison with the results obtained by direct numerical 
simulations of a sandwich composite strip through the finite element method. Finally, the analytical 
solutions are used to quantitatively depict the microstructural effects on overall dynamics of composites. 
The framework of this work is also applicable for other physical systems, e.g., heat conduction in composites, 
diffusion in multi-phase systems, and multi-field coupling analysis in piezoelectric composites.},
DOI = {10.32604/icces.2023.09355}
}