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Clustering analysis for elastodynamic homogenization
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DOI：10.1007/s00466-023-02315-w.png)
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Abstract
En 中文
We propose a reduced-order method for the elastodynamic homogenization of periodic composites. With the help of Bloch-wave expansion and Green's function, the Lippmann-Schwinger equations relating the dynamic field variable tensors of strain, velocity, stress and linear momentum are obtained. Then the constitutive relation of the averaged dynamic field tensors and the dispersion relation between frequency and wave vector in Willis theory are formulated explicitly. Using the data compression algorithm, k-means clustering, we decompose computational domain into clusters of possibly disjoint cells. The Lippmann-Schwinger equations are then discretized and solved efficiently. Numerical tests for three-dimensional particle-reinforced composites verify the effectiveness and efficiency of the proposed method.
Keywords:
Numerical homogenization
Elastodynamic
Clustering analysis
Lippmann-Schwinger equation
Wave propagation