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Introduction to Non-linear Mechanics
Authors: ---
ISBN: 9783031519208 9783031519192 9783031519215 9783031519222 Year: 2024 Publisher: Cham Springer International Publishing :Imprint: Springer

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Abstract

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.


Digital
Defect and Material Mechanics : Proceedings of the International Symposium on Defect and Material Mechanics (ISDMM), held in Aussois, France, March 25–29, 2007
Authors: --- ---
ISBN: 9781402069291 Year: 2008 Publisher: Dordrecht Springer Science+Business Media B.V

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