Geometric Continuum Mechanics

Reuven Segev · Marcelo Epstein

2020년 5월 · Advances in Mechanics and Mathematics 43권 · Springer Nature

eBook

416

페이지

검증되지 않은 평점과 리뷰입니다. 자세히 알아보기

eBook 정보

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include:

Global stress and hyper-stress theories
Applications of de Rham currents to singular dislocations
Manifolds of mappings for continuum mechanics
Kinematics of defects in solid crystals

Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.