Mathematical Analysis of Continuum Mechanics and Industrial Applications

Masato KimuraKanazawa UniversityHiromichiItouTokyo University of ScienceVladimir ChalupeckýFujitsu Ltd.KohjiOhtsukaHiroshima Kokusai Gakuin UniversityDaisuke TagamiInstitute of Math-for-Industry, Kyushu UniversityAkira Takada Asahi Glass Co., Ltd.

• Part 1: Fracture Mechanics.- Strong but slippery adhesion of mushroom-shaped polysaccharide gels.- Bridging the scales between discrete and continuum dislocation models.- Phase field crack growth model with Hydrogen embrittlement.- On singularities in 2D linearized elasticity.- Part 2: Shape Optimization.- Two-Parameter Topological Expansion of Helmholtz Problems with Inhomogeneity.- Solution of shape optimization problem and its application to product design.- Shape optimization by GJ-integral: Localization method for composite material.- Shape optimization approach by traction method to inverse free boundary problems.- Part 3: Earthquakes and Inverse Problems.- Synthesis of seismic wave envelopes based on the Markov approximation.- Propagation velocity of pulse-like rupture along earthquake faults.- Inverse Source Problem for a Wave Equation with Final Observation Data.- Part 4: Fluid Mechanics and Interface Dynamics.- The contribution of Kawada to the analytical solution for the velocity induced by a helical vortex filament and modern applications of helical vortices.- A new model for fungal hyphae growth using the thin viscous sheet equations.- On Boundary Conditions for Hele-Shaw Problem.- Part 5: Industrial Applications.- Computer Simulation of the Phase Separation of Polymeric Materials for Industrial Applications.- Highly parallel computation of generalized eigenvalue problem in vibration for automatic transmission of vehicles using Sakurai-Sugiura method and supercomputers.- Mathematical analysis of synchronization from the perspective of network science.- Index

“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)