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020 _a9783031519208
_9978-3-031-51920-8
024 7 _a10.1007/978-3-031-51920-8
_2doi
050 4 _aQA808.2
072 7 _aPHD
_2bicssc
072 7 _aSCI065000
_2bisacsh
072 7 _aPHD
_2thema
100 1 _aStolz, Claude.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_972103
245 1 0 _aIntroduction to Non-linear Mechanics
_h[electronic resource] :
_bA Unified Energetical Approach /
_cby Claude Stolz.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXV, 334 p. 61 illus., 14 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Solid and Structural Mechanics,
_x2195-352X ;
_v14
505 0 _aChapter 1. Introduction -- Chapter 2. Non-linear and linear elasticity -- Chapter 3. Elasto-plasticity -- Chapter 4. Fracture Mechanics -- Chapter 5. Moving Discontinuities -- Chapter 6. Damage modelling and initiation of defect -- Chapter 7. A thermodynamical approach to contact wear -- Chapter 8. Delamination of laminates -- Chapter 9. Micro-macro relations -- Chapter 10. Homogenization in linear elasticity -- Chapter 11. Optimal control and non linear inverse problems -- Chapter 12. Conclusion.
520 _aThis book presents an introduction to the non-linear mechanics of materials, focusing on a unified energetical approach. It begins by summarizing the framework of a thermodynamic description of continua, including a description of the kinematics of deformation, and a summary of the equations of motion. After a short description of the motion of the system and the mechanical interaction, the book introduces the Lagrangean and Hamiltonian functionals of the system, transitioning to the quasistatic characterization with emphasis on the role of potential energy and pseudo-potential of dissipation. The framework is then extended to fracture and damage mechanics with a similar energetical approach proposed for material damage and wear. The book looks at homogenization in non-linear mechanics for locally plastic or damaged material with an analysis of stability and bifurcation of the equilibrium path. Lastly, inverse problems in non-linear mechanics are introduced using optimal control theory. All the concepts introduced in the book are illustrated using analytical solutions on beams, rods, plates, or using spherical and cylindrical symmetries. Graduate students and researchers working on continuum mechanics and interested in a deeper understanding of materials damage, wear, and fatigue will find this book instructive and informative.
650 0 _aContinuum mechanics.
650 0 _aThermodynamics.
_966400
650 0 _aMaterials
_xFatigue.
_967940
650 0 _aMechanics, Applied.
650 0 _aSolids.
_965936
650 0 _aMathematical physics.
650 0 _aMetals.
650 1 4 _aContinuum Mechanics.
650 2 4 _aThermodynamics.
_966400
650 2 4 _aMaterials Fatigue.
_967941
650 2 4 _aSolid Mechanics.
_965938
650 2 4 _aMathematical Methods in Physics.
_970877
650 2 4 _aMetals and Alloys.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031519192
776 0 8 _iPrinted edition:
_z9783031519215
776 0 8 _iPrinted edition:
_z9783031519222
830 0 _aSpringer Series in Solid and Structural Mechanics,
_x2195-352X ;
_v14
_972104
856 4 0 _uhttps://doi.org/10.1007/978-3-031-51920-8
912 _aZDB-2-PHA
912 _aZDB-2-SXP
999 _c58001
_d58001