Introduction to Non-linear Mechanics

A Unified Energetical Approach

Claude Stolz

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Hardback

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English

Springer International Publishing AG
01 March 2024

Classical mechanics; Thermodynamics & heat; Mathematical physics; Mechanics of solids

Series: Springer Series in Solid and Structural Mechanics

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.

By: Claude Stolz
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2024
Volume: 14
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031519192
ISBN 10: 3031519191
Series: Springer Series in Solid and Structural Mechanics
Pages: 334
Publication Date: 01 March 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Claude Stolz's research focuses on the evolution of non-linear mechanical systems (plasticity, fracture, damage). Claude Stolz has taught in France at several high schools of engineering and Universities. He has also worked as a consultant for major French companies. He is currently Director of Research at the CNRS.