Recording: https://disk.pku.edu.cn:443/link/6A99ED6E46A7C530759124CF292BC5D2
Valid Until: 2026-11-30 23:59
Abstract: The homogenization of heterogeneous media has been attracting the attention of scientists for more than a century. The classical homogenization methods are focused on the prediction of the effective or overall properties of heterogeneous media such as the effective elastic tensors or potentials, and conductivity tensors. Recently, the topic becomes a focus of research in mathematics, mechanics, and materials science due to its importance in the modelling of advanced composite materials, in particular, metamaterials. However, the classical methodology produces local forms of governing equations and cannot describe complex dynamic responses of various heterogeneous media such as the dispersion and bandgaps of elastic waves. This lecture will present the recent work of the author’s group on the dynamic homogenization of heterogeneous media. Starting from conventional local linear elastic constituents, we develop a dynamic homogenization framework and derive the macroscopic governing equations for heterogeneous media. The governing equations can reflect spatiotemporal nonlocality and nonuniformity of the field quantities and can correspond to conventional local models and the well-known nonlocal models including the Mindlin equation, Willis formalism, Eringen constitutive relation, and peridynamic formulation. For heat conduction, the governing equation of the average temperature can correspond to the Jeffreys-type equation, Nunziato equation, Gurtin and Pipkin equation, peridynamic formulation, and dual-phase-lag (DPL) equation. All the parameters in the governing equations can be determined from the geometrical and physical parameters of the constituents; thus the framework also sheds light on the physical mechanisms of the relevant formulations.
Bio: Jianxiang Wang is currently a Changjiang Scholar Professor of mechanics in the Department of Mechanics and Engineering Science of Peking University. He received his PhD from The University of Sydney in 1995. He joined Peking University in 1998, after doing post-doctoral research at Imperial College in 1996 and Aalborg University in 1997. Jianxiang Wang’s research interests cover fracture/failure analyses of composite materials, constitutive relations and transport properties of heterogeneous materials and nano-structured materials, surface effects in heterogeneous materials and nanomaterials, and the Eshelby formalism and Eshelby conjecture. He served as secretary-general of the Chinese Society of Theoretical and Applied Mechanics (2006-2010), secretary-general of the 23rd International Congress of Theoretical and Applied Mechanics (ICTAM2012) of the International Union of Theoretical and Applied Mechanics (IUTAM), and member of Congress Committee of the IUTAM (2014-2022). Jianxiang Wang was awarded Excellent Teacher of Beijing (2009), Changjiang Scholar Professor (2008), the Royal Society Visiting Fellowship (1999, 2004), and Honorary Visiting Professor of Cardiff University (2006-2016).
