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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.

Convex domains. --- Mechanics, Applied -- Mathematical models. --- Mechanics, Applied --- Convex domains --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Mathematical models --- Mathematical models. --- Convex regions --- Convexity --- Engineering. --- Mechanics. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Calculus of variations --- Convex geometry --- Point set theory --- Mechanics, applied. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Rank-one convexity