03899nam a22005775i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001200172072001600184072002300200072001500223100008300238245011800321250001800439264007500457300006400532336002600596337002600622338003600648347002400684490007200708505050800780520135401288650002502642650002702667650003102694650002402725650001902749650002602768650001202794650002502806650002702831650003002858650002802888650004402916650002302960710003402983773002603017776003603043776003603079776003603115830007903151856004603230912001403276912001403290999001703304978-3-031-51920-8DE-He21320251030111453.0cr nn 008mamaa240229s2024    sz |    s    |||| 0|eng d  a97830315192089978-3-031-51920-87 a10.1007/978-3-031-51920-82doi 4aQA808.2 7aPHD2bicssc 7aSCI0650002bisacsh 7aPHD2thema1 aStolz, Claude.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97210310aIntroduction to Non-linear Mechanicsh[electronic resource] :bA Unified Energetical Approach /cby Claude Stolz.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXV, 334 p. 61 illus., 14 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Series in Solid and Structural Mechanics,x2195-352X ;v140 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.  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. 0aContinuum mechanics. 0aThermodynamics.966400 0aMaterialsxFatigue.967940 0aMechanics, Applied. 0aSolids.965936 0aMathematical physics. 0aMetals.14aContinuum Mechanics.24aThermodynamics.96640024aMaterials Fatigue.96794124aSolid Mechanics.96593824aMathematical Methods in Physics.97087724aMetals and Alloys.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303151919208iPrinted edition:z978303151921508iPrinted edition:z9783031519222 0aSpringer Series in Solid and Structural Mechanics,x2195-352X ;v1497210440uhttps://doi.org/10.1007/978-3-031-51920-8  aZDB-2-PHA  aZDB-2-SXP  c58001d58001