Mathematical Analysis of Continuum Mechanics and Industrial Applications

1. Front Matter

   Pages i-viii

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2. Fracture Mechanics

   1. Front Matter

      Pages 1-1

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   2. Strong but Slippery Adhesion of Mushroom-Shaped Polysaccharide Gels

      • Yoshimi Tanaka, Teppei Nakamichi

      Pages 3-13

   3. Bridging the Scales Between Discrete and Continuum Dislocation Models

      • Patrick van Meurs

      Pages 15-25

   4. Phase Field Crack Growth Model with Hydrogen Embrittlement

      • Takeshi Takaishi

      Pages 27-34

   5. On Singularities in 2D Linearized Elasticity

      • Hiromichi Itou

      Pages 35-47

3. Shape Optimization

   1. Front Matter

      Pages 49-49

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   2. Two-Parameter Topological Expansion of Helmholtz Problems with Inhomogeneity

      • Victor A. Kovtunenko

      Pages 51-81

   3. Solution of Shape Optimization Problem and Its Application to Product Design

      • Hideyuki Azegami

      Pages 83-98

   4. Shape Optimization by GJ-Integral: Localization Method for Composite Material

      • Kohji Ohtsuka

      Pages 99-109

   5. Shape Optimization Approach by Traction Method to Inverse Free Boundary Problems

      • Shogen Shioda, Ahsani Ummi Maharani, Masato Kimura, Hideyuki Azegami, Kohji Ohtsuka

      Pages 111-123

4. Earthquakes and Inverse Problems

   1. Front Matter

      Pages 125-125

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   2. Synthesis of Seismic Wave Envelopes Based on the Markov Approximation

      • Kentaro Emoto

      Pages 127-142

   3. Propagation Velocity of Pulse-Like Rupture Along Earthquake Faults

      • Shiro Hirano

      Pages 143-152

   4. Inverse Source Problem for a Wave Equation with Final Observation Data

      • Daijun Jiang, Yikan Liu, Masahiro Yamamoto

      Pages 153-164

5. Fluid Mechanics and Interface Dynamics

   1. Front Matter

      Pages 165-165

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   2. The Contribution of Kawada to the Analytical Solution for the Velocity Induced by a Helical Vortex Filament and Modern Applications of Helical Vortices

      • Yasuhide Fukumoto, Valery L. Okulov, David H. Wood

      Pages 167-174

   3. A New Model for Fungal Hyphae Growth Using the Thin Viscous Sheet Equations

      • Thomas de Jong, Georg Prokert, Joost Hulshof

      Pages 175-184

   4. On Boundary Conditions for Hele-Shaw Problem

      • Hisasi Tani

      Pages 185-194

6. Industrial Applications

   1. Front Matter

      Pages 195-195

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This book focuses on mathematical theory and numerical simulation related to various aspects of continuum mechanics, such as fracture mechanics, elasticity, plasticity, pattern dynamics, inverse problems, optimal shape design, material design, and disaster estimation related to earthquakes. Because these problems have become more important in engineering and industry, further development of mathematical study of them is required for future applications. Leading researchers with profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry provide the contents of this book. They help readers to understand that mathematical theory can be applied not only to different types of industry, but also to a broad range of industrial problems including materials, processes, and products.

• Singularity analysis and fracture phenomena
• Mathematics for shape and topology optimization
• Mathematical modeling for earthquakes
• Real-world applications of continuum mechanics
• Theoretical and computational treatments of continuum mechanics

“This book gives the reader a representative view of an enormous variety of continuum mechanics topics. It provides an excellent overview of the current state of research on applied continuum mechanics … The book will be also suitable for use in specialized courses for doctoral students.” (Andrzej Icha, Pure and Applied Geophysics, Vol. 175, 2018)

• Tokyo University of Science, Tokyo, Japan

  Hiromichi Itou

• Inst of Science and Engineering, Kanazawa University, Kanazawa, Japan

  Masato Kimura

• Fujitsu Ltd., Tokyo, Japan

  Vladimír Chalupecký

• Hiroshima Kokusai Gakuin University, Hiroshima, Japan

  Kohji Ohtsuka

• Kyushu University, Fukuoka, Japan

  Daisuke Tagami

• Asahi Glass Co., Ltd., Tokyo, Japan

  Akira Takada

Masato Kimura
Kanazawa University


HiromichiItou
Tokyo University of Science


Vladimir Chalupecký
Fujitsu Ltd.


KohjiOhtsuka
Hiroshima Kokusai Gakuin University


Daisuke Tagami
Institute of Math-for-Industry, Kyushu University


Akira Takada 
Asahi Glass Co., Ltd.

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