Energetic Relaxation to Structured Deformations
A Multiscale Geometrical Basis for Variational Problems in Continuum Mechanics
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Beschreibung
This book is the first organized collection of some results that have been obtained by the authors, their collaborators, and other researchers in the variational approach to structured deformations. It sets the basis and makes more accessible the theoretical apparatus for assigning an energy to a structured deformation, thereby providing motivation to researchers in applied mathematics, continuum mechanics, engineering, and materials science to study the deformation of a solid body without committing at the outset to a specific mechanical theory. Researchers will benefit from an approach in which elastic, plastic, and fracture phenomena can be treated in a unified way.
The book is intended for an audience acquainted with measure theory, the theory of functions of bounded variation, and continuum mechanics. Any students in their last years of undergraduate studies, graduate students, and researchers with a background in applied mathematics, the calculus of variations, and continuum mechanics will have the prerequisite to read this book.
This book is the first organized collection of some results that have been obtained by the authors, their collaborators, and other researchers in the variational approach to structured deformations. It sets the basis and makes more accessible the theoretical apparatus for assigning an energy to a structured deformation, thereby providing motivation to researchers in applied mathematics, continuum mechanics, engineering, and materials science to study the deformation of a solid body without committing at the outset to a specific mechanical theory. Researchers will benefit from an approach in which elastic, plastic, and fracture phenomena can be treated in a unified way.
The book is intended for an audience acquainted with measure theory, the theory of functions of bounded variation, and continuum mechanics. Any students in their last years of undergraduate studies, graduate students, and researchers with a background in applied mathematics, thecalculus of variations, and continuum mechanics will have the prerequisite to read this book.
Provides state-of-the-art results and techniques in compact presentation style Offers a broad introduction to newcomers Presents in-depth techniques for readers acquainted with the field
Autor*in
José Matias
Themen in »Energetic Relaxation to Structured Deformations«
(First-order) structured deformations (Second-order) structured deformations Multiscale geometry Energy relaxation Integral representation of functionals Energy minimization Bulk and interfacial energy densities Optimal design Dimension reduction Periodic Homogenization Upscaling and spatial localization of non-local energies Hierarchical structured deformations