Chinese Journal of Theoretical and Applied Mechani ›› 2006, Vol. 38 ›› Issue (2): 226-235.DOI: 10.6052/0459-1879-2006-2-2004-519
• Research paper •
A spatial and temporal multiscale asymptotic
homogenization method simulating the wave propagation
problem in periodic multiphase materials is systematically studied.
Generalized function field governing equations of wave propagation are expressed
in a unified form with both inertia and velocity items. Amplified spatial
and reduced temporal scales are, respectively, introduced to account for
spatial and temporal fluctuations and nonlocal effect of the homogenized
solution due to material heterogeneity on different time scales. The model is
derived from the higher-order homogenization theory with multiple spatial
and temporal scales. By combining various orders of homogenized function
field equations, the reduced time dependence is eliminated and then the
fourth-order differential equations are derived. To avoid the necessity of
C1-continuity in finite element implementation, the C0-continuous
mixed finite element approximation of the resulting nonlocal equations of
function field is put forward. Non-Fourier heat conduction and thermal
dynamic problem are computed to demonstrate the efficiency and validity of
the theories and models developed and indicate the disadvantages of the
classical spatial homogenization.
thermodynamic,non-Fourier heat conduction,multi-scale method,homogenization,high-order nonlocal model
,,. Thermodynamic analysis of multiphase periodic structures based on a spatial and temporal multiple scale method[J]. Chinese Journal of Theoretical and Applied Mechani, 2006, 38(2): 226-235.
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