Mathematical Analysis of Continuum Mechanics and Industrial Applications IIIDynamic Unilateral Contact Problem with Averaged Friction for a Viscoelastic Body with Cracks

Mathematical Analysis of Continuum Mechanics and Industrial Applications III: Dynamic Unilateral... [In order to study the mechanism of earthquake through fracture mechanics, as a first step we discuss a dynamic unilateral contact problem with friction for a cracked viscoelastic body. Here we adopt the viscoelastic model proposed by Landau and Lifshitz [24] and a non-local friction law. The existence of a solution to the problem is obtained by using a penalty method. Several estimates are obtained on the solution to the penalized problem, which enable us to pass to the limit by using compactness results [30].] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Mathematical Analysis of Continuum Mechanics and Industrial Applications IIIDynamic Unilateral Contact Problem with Averaged Friction for a Viscoelastic Body with Cracks

Part of the Mathematics for Industry Book Series (volume 34)
Editors: Itou, Hiromichi; Hirano, Shiro; Kimura, Masato; Kovtunenko, Victor A.; Khludnev, Alexandr M.
18 pages

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Publisher
Springer Singapore
© Springer Nature Singapore Pte Ltd. 2020
ISBN
978-981-15-6061-3
Pages
3 –21
DOI
10.1007/978-981-15-6062-0_1
Publisher site
See Chapter on Publisher Site

Abstract

[In order to study the mechanism of earthquake through fracture mechanics, as a first step we discuss a dynamic unilateral contact problem with friction for a cracked viscoelastic body. Here we adopt the viscoelastic model proposed by Landau and Lifshitz [24] and a non-local friction law. The existence of a solution to the problem is obtained by using a penalty method. Several estimates are obtained on the solution to the penalized problem, which enable us to pass to the limit by using compactness results [30].]

Published: Aug 30, 2020