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Introduction to non-linear mechanicsa unified energetical approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to non-linear mechanicsby Claude Stolz.
Reminder of title:	a unified energetical approach /
Author:	Stolz, Claude.
Published:	Cham :Springer International Publishing :2024.
Description:	xv, 334 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Nonlinear mechanics.
Online resource:	https://doi.org/10.1007/978-3-031-51920-8
ISBN:	9783031519208$q(electronic bk.)

Introduction to non-linear mechanicsa unified energetical approach /
Stolz, Claude.

Introduction to non-linear mechanicsa unified energetical approach /[electronic resource] :by Claude Stolz. - Cham :Springer International Publishing :2024. - xv, 334 p. :ill. (some col.), digital ;24 cm. - Springer series in solid and structural mechanics,v. 142195-352X ;. - Springer series in solid and structural mechanics ;v.2..

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.

ISBN: 9783031519208$q(electronic bk.)

Standard No.: 10.1007/978-3-031-51920-8doiSubjects--Topical Terms:

190487
Nonlinear mechanics.

LC Class. No.: QA808

Dewey Class. No.: 531

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505 0 $a 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.
520 $a 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.
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