LEADER 03521nam 2200685 450 001 9910768477503321 005 20240115175216.0 010 $a981-19-8800-5 024 7 $a10.1007/978-981-19-8800-4 035 $a(CKB)5710000000116826 035 $a(DE-He213)978-981-19-8800-4 035 $a(MiAaPQ)EBC7248773 035 $a(Au-PeEL)EBL7248773 035 $a(PPN)269658793 035 $a(EXLCZ)995710000000116826 100 $a20230803d2023 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEnergetic Relaxation to Structured Deformations $eA Multiscale Geometrical Basis for Variational Problems in Continuum Mechanics /$fJose´ Matias, Marco Morandotti, and David R. Owen 205 $aFirst edition. 210 1$aSingapore :$cSpringer Nature Singapore Pte Ltd.,$d[2023] 210 4$dŠ2023 215 $a1 online resource (XII, 152 p. 1 illus.) 225 0 $aSpringerBriefs on PDEs and Data Science Series 311 $a981-19-8799-8 320 $aIncludes bibliographical references. 327 $a1. Introduction -- 2. Mathematical preliminaries -- 3. Energetic relaxation to first-order structured deformations -- 4. Energetic relaxation to second-order structured deformations -- 5. Outlook for future research. 330 $aThis book is the first organized collection of some results that have been obtained by the authors, their collaborators, and other researchers in the variational approach to structured deformations. It sets the basis and makes more accessible the theoretical apparatus for assigning an energy to a structured deformation, thereby providing motivation to researchers in applied mathematics, continuum mechanics, engineering, and materials science to study the deformation of a solid body without committing at the outset to a specific mechanical theory. Researchers will benefit from an approach in which elastic, plastic, and fracture phenomena can be treated in a unified way. The book is intended for an audience acquainted with measure theory, the theory of functions of bounded variation, and continuum mechanics. Any students in their last years of undergraduate studies, graduate students, and researchers with a background in applied mathematics, the calculus of variations, and continuum mechanics will have the prerequisite to read this book. 410 0$aSpringerBriefs on PDEs and Data Science,$x2731-7609 606 $aCalculus of variations 606 $aDeformations (Mechanics) 606 $aMathematical optimization 606 $aMechanics, Applied 606 $aDeformacions (Mecānica)$2thub 606 $aMecānica aplicada$2thub 606 $aOptimitzaciķ matemātica$2thub 606 $aCālcul de variacions$2thub 608 $aLlibres electrōnics$2thub 615 0$aCalculus of variations. 615 0$aDeformations (Mechanics) 615 0$aMathematical optimization. 615 0$aMechanics, Applied. 615 7$aDeformacions (Mecānica) 615 7$aMecānica aplicada 615 7$aOptimitzaciķ matemātica 615 7$aCālcul de variacions 676 $a620.1123 700 $aMatias$b Jose´$01457384 702 $aMorandotti$b Marco 702 $aOwen$b David R. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910768477503321 996 $aEnergetic Relaxation to Structured Deformations$93657920 997 $aUNINA