A Dispersive Model for Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales

By Wen Chen, Jacob Fish. 2001

205 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a09d29a48172ba746338c57b563152d5afb5c85e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. H. Askes
2. Elias C. Aifantis
3. Zheng Yuan
4. Jacob Fish
5. T. Bennett
6. A. V. Pichugin
7. G. Nagai
8. A. Tyas

In Computational Theory and Mathematics

1. Elias C. Aifantis
2. Jacob Fish
3. H. Askes
4. Zheng Yuan
5. G. Nagai
6. T. Bennett
7. I. Gitman
8. A. V. Pichugin

In Mechanics of Materials

1. Elias C. Aifantis
2. H. Askes
3. Jacob Fish
4. Zheng Yuan
5. T. Bennett
6. I. Gitman
7. G. Nagai
8. A. V. Pichugin

Citations in the corpus

• Higher order asymptotic homogenization and wave propagation in periodic composite materials (2008, unknown): “A (2008) provides a long-wave approach valid in the low-frequency range (Boutin & Auriault 1993; Boutin 1995; Chen & Fish 2001; Fish & Chen 2001, 2004; Bakhvalov & Eglit 2005).”
• Non‐local dispersive model for wave propagation in heterogeneous media: one‐dimensional case (2002, methodology): “In addition to the fast spatial variable, we introduce multiple time scales [8][ 9 ]”
• Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results (2011, methodology): “(23) and (24) and suggested modifications that avoid instabilities, e.g. Collins (1981), Rubin et al. (1995), Chen and Fish (2001), Andrianov et al. (2003), Andrianov and Awrejcewicz (2008), Pichugin et al. (2008), Andrianov et al. (2010b).”
• Multiscale enrichment based on partition of unity (2005, methodology): “Existing methodologies (see for example [ 55 ,56,57]) are based on continuum (or quasi-continuum) enrichment.”
• Asymptotic equivalence of homogenisation procedures and fine-tuning of continuum theories (2008, methodology): “The possibility of substitution (13) is well recognised; for example, it was used in [8] for the linearised Boussinesq equation, in [9] when modelling thin plates, and recently in [10] in a homogenisation problem for long SH waves in a periodic bi-laminate.”
• Elasticity Theories with Higher-order Gradients of Inertia and Stiffness for the Modelling of Wave Dispersion in Laminates (2007, methodology): “Especially formats of gradient elasticity with inertia gradients have been used by many researchers to capture wave dispersion (Rubin et al., 1995; Chen and Fish, 2001; Wang and Sun, 2002).”