Deformation Waves in Microstructured Materials: Theory and Numerics

Juri Engelbrecht; Arkadi Berezovski; Mihhail Berezovski

doi:10.1007/978-90-481-9893-1_2

Deformation Waves in Microstructured Materials: Theory and Numerics

Juri Engelbrecht, Arkadi Berezovski, Mihhail Berezovski

Mathematics

Tallinn University of Technology

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

A linear model of the microstructured continuum based on Mindlin theory is adopted which can be represented in the framework of the internal variable theory. Fully coupled systems of equations for macro-motion and microstructure evolution are represented in the form of conservation laws. A modification of wave propagation algorithm is used for numerical calculations. Results of direct numerical simulations of wave propagation in periodic medium are compared with similar results for the continuous media with the modelled microstructure. It is shown that the proper choice of material constants should be made to match the results obtained by both approaches

Original language	American English
Title of host publication	Deformation Waves in Microstructured Materials: Theory and Numerics
Place of Publication	Taipei, Taiwan
DOIs	https://doi.org/10.1007/978-90-481-9893-1_2
State	Published - Sep 17 2010

Keywords

Solitary Wave
Direct Numerical Simulation
Internal Variable
Elastic Wave Propagation
Dissipation Inequality

Disciplines

Mechanics of Materials
Numerical Analysis and Computation
Partial Differential Equations

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10.1007/978-90-481-9893-1_2License: CC BY

Deformation Waves in Microstructured Materials: Theory and NumeriFinal published version, 259 KBLicense: CC BY

Cite this

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abstract = " A linear model of the microstructured continuum based on Mindlin theory is adopted which can be represented in the framework of the internal variable theory. Fully coupled systems of equations for macro-motion and microstructure evolution are represented in the form of conservation laws. A modification of wave propagation algorithm is used for numerical calculations. Results of direct numerical simulations of wave propagation in periodic medium are compared with similar results for the continuous media with the modelled microstructure. It is shown that the proper choice of material constants should be made to match the results obtained by both approaches",

keywords = "Solitary Wave, Direct Numerical Simulation, Internal Variable, Elastic Wave Propagation, Dissipation Inequality",

author = "Juri Engelbrecht and Arkadi Berezovski and Mihhail Berezovski",

note = "Engelbrecht J., Berezovski A., Berezovski M. (2010) Deformation Waves in Microstructured Materials: Theory and Numerics. In: Wu TT., Ma CC. (eds) IUTAM Symposium on Recent Advances of Acoustic Waves in Solids. IUTAM Bookseries, vol 26. Springer, Dordrecht",

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T1 - Deformation Waves in Microstructured Materials: Theory and Numerics

AU - Engelbrecht, Juri

AU - Berezovski, Arkadi

AU - Berezovski, Mihhail

N1 - Engelbrecht J., Berezovski A., Berezovski M. (2010) Deformation Waves in Microstructured Materials: Theory and Numerics. In: Wu TT., Ma CC. (eds) IUTAM Symposium on Recent Advances of Acoustic Waves in Solids. IUTAM Bookseries, vol 26. Springer, Dordrecht

PY - 2010/9/17

Y1 - 2010/9/17

N2 - A linear model of the microstructured continuum based on Mindlin theory is adopted which can be represented in the framework of the internal variable theory. Fully coupled systems of equations for macro-motion and microstructure evolution are represented in the form of conservation laws. A modification of wave propagation algorithm is used for numerical calculations. Results of direct numerical simulations of wave propagation in periodic medium are compared with similar results for the continuous media with the modelled microstructure. It is shown that the proper choice of material constants should be made to match the results obtained by both approaches

AB - A linear model of the microstructured continuum based on Mindlin theory is adopted which can be represented in the framework of the internal variable theory. Fully coupled systems of equations for macro-motion and microstructure evolution are represented in the form of conservation laws. A modification of wave propagation algorithm is used for numerical calculations. Results of direct numerical simulations of wave propagation in periodic medium are compared with similar results for the continuous media with the modelled microstructure. It is shown that the proper choice of material constants should be made to match the results obtained by both approaches

KW - Solitary Wave

KW - Direct Numerical Simulation

KW - Internal Variable

KW - Elastic Wave Propagation

KW - Dissipation Inequality

UR - https://commons.erau.edu/publication/926

U2 - 10.1007/978-90-481-9893-1_2

DO - 10.1007/978-90-481-9893-1_2

M3 - Chapter

BT - Deformation Waves in Microstructured Materials: Theory and Numerics

CY - Taipei, Taiwan

ER -

Deformation Waves in Microstructured Materials: Theory and Numerics

Abstract

Keywords

Disciplines

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