LEADER 04280nam 22006015 450 001 9910755074103321 005 20240701170152.0 010 $a3-031-35655-1 024 7 $a10.1007/978-3-031-35655-1 035 $a(MiAaPQ)EBC30841388 035 $a(Au-PeEL)EBL30841388 035 $a(DE-He213)978-3-031-35655-1 035 $a(PPN)272914290 035 $a(CKB)28642503100041 035 $a(EXLCZ)9928642503100041 100 $a20231031d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFoundations of Geometric Continuum Mechanics $eGeometry and Duality in Continuum Mechanics /$fby Reuven Segev 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (410 pages) 225 1 $aAdvances in Continuum Mechanics,$x2524-4647 ;$v49 311 08$aPrint version: Segev, Reuven Foundations of Geometric Continuum Mechanics Cham : Springer International Publishing AG,c2023 9783031356544 327 $a1. Introduction -- 2. Prelude: Finite Dimensional Systems -- Part I Algebraic Theory: Uniform Fluxes -- 3. Simplices in Affine Spaces and Their Boundaries -- 4. Uniform Fluxes in Affine Spaces -- 5. From Uniform Fluxes to Exterior Algebra -- Part II: Smooth Theory -- 6. Smooth Analysis on Manifolds: A Short Review -- 7. Interlude: Smooth Distributions of Defects -- 8. Smooth Fluxes -- 9. Frames, Body Points, and Spacetime Structure -- 10. Stresses -- 11. Smooth Electromagnetism on Manifolds -- 12. The Elasticity Problem -- 13. Symmetry and Dynamics -- Part III Non-Smooth, Global Theories -- 14. Banachable Space of Sections of Vector Bundles over Compact Manifolds -- 15. Manifolds of Sections and Embeddings -- 16. The General Framework for Global Analytic Stress Theory -- 17. Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals -- 18. de Rham Currents -- 19. Interlude: Singular Distributions of Defects in Bodies -- 20. Vector-Valued Currents -- 21. The Representation of Forces by Stresses and Hyperstresses -- 22. Simple Forces and Stresses -- 23. Whitney's Geometric Integration Theory and Non-Smooth Bodies -- 24. Optimal Fields and Load Capacity of Bodies -- Index. 330 $aThis monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author?s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics. 410 0$aAdvances in Continuum Mechanics,$x2524-4647 ;$v49 606 $aGeometry, Differential 606 $aContinuum mechanics 606 $aDifferential Geometry 606 $aContinuum Mechanics 606 $aMecānica dels medis continus$2thub 606 $aMatemātica$2thub 608 $aLlibres electrōnics$2thub 615 0$aGeometry, Differential. 615 0$aContinuum mechanics. 615 14$aDifferential Geometry. 615 24$aContinuum Mechanics. 615 7$aMecānica dels medis continus 615 7$aMatemātica 676 $a531.7 676 $a531.7 700 $aSegev$b Reuven$01435890 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910755074103321 996 $aFoundations of Geometric Continuum Mechanics$93593953 997 $aUNINA