This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.

Autorentext
Hiromichi Itou is Associate Professor in the Department of Mathematics at the Tokyo University of Science. He is a representative member of The Japan Society for Industrial and Applied Mathematics (JSIAM). His research interests lie in the areas of Fracture Mechanics, Singular integral equations, Analysis of singularities of corner and crack, theory of elasticity, Inverse problems.

Shiro Hirano is Assistant professor in the College of Science and Engineering at the Ritsumeikan University. His research interests lie in the areas of Mathematical modeling of earthquake fault mechanics, Data analysis of seismicity, Laboratory seismology, Earthquake engineering.

Masato Kimura is the Full Professor in the Faculty of Mathematics and Physics at the Kanazawa University. He is a representative member of The Japan Society for Industrial and Applied Mathematics (JSIAM) and a leader of analysis group in Kanazawa Mathematics and mathematical science Research Group (KMRG). His research interests include moving boundary problems (mean curvature flow, Hele-Shaw problem, Stefan problem etc.), numerical analysis for PDE (FDM, FEM, BEM etc.) singular perturbation for elliptic eigenvalue problems with large drift, crack problems in fracture mechanics, shape derivative and its application, bulk-surface system, inverse Cauchy transform of domains, pattern formation in reaction diffusion systems, mathematical analysis of particle methods.

Victor A. Kovtunenko, PhD (1997), Habilitation (2007) is working at the Lavrentyev Institute of Hydrodynamics of the Siberian Division of the Russian Academy of Sciences, and at the Austrian Academy of Sciences (OeAW). He currently serves as a Project Leader of the Austrian Science Foundation (FWF) at the Institute for Mathematics and Scientific Computing at the University of Graz. His research interests include variational inequalities, shape and topology optimization, nonsmooth and numerical optimization, applications to solid mechanics.

Alexandr M. Khludnev is a head of laboratory at the Lavrentyev Institute of Hydrodynamics of the Siberian Division of the Russian Academy of Sciences. Simultaneously he has a part time professor position at Novosibirsk State University. His research interests include variational inequalities, shape and topology optimization, crack problems, contact and free boundary problems in solid mechanics.

Inhalt
Part 1: Fracture mechanics (incl. Frictional and free boundary problems) : 80 pages

• Atusi Tani (Keio University) : 10 pages

• Takahito Kashiwabara (the University of Tokyo) : 10 pages

• Takeshi Takaishi (Hiroshima Kokusai Gakuin University) : 10 pages

• Yoshimi Tanaka (Yokohama National University) : 10 pages

• Hirofumi Wada (Ritsumeikan University) : 10 pages

• Patrick J.P. van Meurs (Kanazawa University) : 10 pages

• Hayk Mikayelyan (University of Nottingham Ningbo China) : 10 pages

• Karel Svadlenka (Kyoto University) : 10 pages

  Part 2: (Visco)elasticity : 50 pages

• Kumbakonam R. Rajagopal (Texas A&M University) : 10 pages -- Rethinking constitutive relations

• Kazumi Tanuma (Gunma University): 10 pages

• Hiroshi Fujiwara (Kyoto University) : 10 pages

• Hirofumi Notsu (Kanazawa University) : 10 pages

• Masato Kimura (Kanazawa University) : 10 pages

  Part 3: Shape optimization and Inverse problems: 60 pages

• Victor A. Kovtunenko (University of Graz, Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences) : 10 pages -- Shape differentiability of Lagrangians and applications
• Kohji Ohtsuka (Hiroshima Kokusai Gakuin University) : 10 pages -- Generalized J-integral under shape differentiability of Lagrangians
• Takashi Nakazawa (Osaka University): 10 pages -- Shape Optimization Problem for Suppressing Time Periodic Flows
• Kentaro Yaji (Osaka University): 10 pages -- Topology optimization for scalar transport with application to flow channel designs

• Frederic Hecht (Lab. Jacques-Louis Lions, University Pierre and Marie CURIE): 10 pages

• Alemdar Hasanov (Kocaeli University) : 10 pages -- Direct and inverse problems for clamped, simply supported and cantilever beams: Theory and numerical methods with engineering applicationsPart 4: Earthquake and Tsunami : 80 pages

• Tatsuo Iguchi (Keio University) : 10 pages

• Takahiro Hatano (the University of Tokyo) : 10 pages -- Friction in granular matter: simulation and experiment

• Hatano's student (the University of Tokyo) : 10 pages

• Taro Kakinuma (Kagoshima University) : 10 pages

• Harsha S. Bhat (École Normale Supérieure) : 10 pages -- Upscaling earthquake damage : Towards homogenised and discrete models of dynamic fracture damage

• Tatsuhiko Saito (National Research Institute for Earth Science and Disaster Prevention (NIED)) : 10 pages -- Tsunami and seismic waves: from generation to inundation

• Ryoichiro Agata (JAMSTEC) : 10 pages -- Numerical simulation of crustal deformation after an M9-class earthquake based on nonlinear viscoelastic finite element modelling Shiro Hirano (Ritsumeikan University) : 10 pages