Pedregal P. Variational Methods in Nonlinear Elasticity

SIAM, 2000. – 112 pp., ISBN: 0898714524, OCR.The underlying mathematical problems in nonlinear elasticity are fascinating. The variational methods developed to tackle them are even more so. The graduate student and the newcomer to the subject may, however, have difficulty appreciating these statements and may feel disappointed to discover that the path leading to a reasonable degree of understanding of the relevant issues, to the point where they feel confident enough to pursue new directions by themselves or under the guidance of a senior researcher, is not well trodden. Filling concisely this gap in the case of the mathematical theory of nonlinear elasticity is the main motivation for this text. It originated in the form of lecture notes for a summer course in materials science and engineering held in Coimbra in 1997 under the auspices of Centro Internacional de Matematica (CIM, Portugal). Later, I completed that material with the idea of producing a reference that might help readers get rapidly and efficiently to the heart of the matter of vector variational methods in the context of nonlinear elasticity, as pointed out above.
My purpose is in reality very modest: to focus on explaining the complexity of vector variational problems from the aspect of existence- nonexistence of equilibrium configurations, with special emphasis on the relevance of structural assumptions.Elastic Materials and Variational Principles
Quasi Convexity and Young Measures
Polyconvexity and Existence Theorems
Rank- one Convexity and Microstructure
Technical Remarks