Poly-, Quasi- and Rank-One Convexity in Applied Mechanics

Download or read book Poly-, Quasi- and Rank-One Convexity in Applied Mechanics written by Jörg Schröder and published by Springer Science & Business Media. This book was released on 2010-08-04 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models. The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.