A Unified Energetical Approach Stolz, Claude. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access XV, 334 p. 61 illus., 14 illus. in color. online resource. 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. 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. by Claude Stolz. Continuum mechanics Thermodynamics Materials Fatigue Mechanics, Applied Solids Mathematical physics Metals Continuum Mechanics Thermodynamics Materials Fatigue Solid Mechanics Mathematical Methods in Physics Metals and Alloys QA808.2 9783031519208 https://doi.org/10.1007/978-3-031-51920-8 https://doi.org/10.1007/978-3-031-51920-8 240229 20251030111453.0 978-3-031-51920-8