04104nam a22006255i 4500 978-3-031-51920-8 DE-He213 20251030111453.0 cr nn 008mamaa 240229s2024 sz | s |||| 0|eng d 9783031519208 978-3-031-51920-8 10.1007/978-3-031-51920-8 doi QA808.2 PHD bicssc SCI065000 bisacsh PHD thema Stolz, Claude. author. aut http://id.loc.gov/vocabulary/relators/aut 72103 Introduction to Non-linear Mechanics [electronic resource] : A Unified Energetical Approach / by Claude Stolz. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XV, 334 p. 61 illus., 14 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Series in Solid and Structural Mechanics, 2195-352X ; 14 Chapter 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. This 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. Continuum mechanics. Thermodynamics. 66400 Materials Fatigue. 67940 Mechanics, Applied. Solids. 65936 Mathematical physics. Metals. Continuum Mechanics. Thermodynamics. 66400 Materials Fatigue. 67941 Solid Mechanics. 65938 Mathematical Methods in Physics. 70877 Metals and Alloys. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031519192 Printed edition: 9783031519215 Printed edition: 9783031519222 Springer Series in Solid and Structural Mechanics, 2195-352X ; 14 72104 https://doi.org/10.1007/978-3-031-51920-8 ZDB-2-PHA ZDB-2-SXP 58001 58001