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Titlebook: Introduction to Non-linear Mechanics; A Unified Energetica Claude Stolz Book 2024 The Editor(s) (if applicable) and The Author(s), under ex

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书目名称Introduction to Non-linear Mechanics
副标题A Unified Energetica
编辑Claude Stolz
视频video
概述Presents a unified energetical approach to the non-linear continuum mechanics of materials.Detailed analytical solutions on beams, rods, and plates accompany all concepts discussed.Ideal for graduate
丛书名称Springer Series in Solid and Structural Mechanics
图书封面Titlebook: Introduction to Non-linear Mechanics; A Unified Energetica Claude Stolz Book 2024 The Editor(s) (if applicable) and The Author(s), under ex
描述.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 o
出版日期Book 2024
关键词Non linear mechanics; elastoplasticity; standard materials; inverse problem; damage; wear
版次1
doihttps://doi.org/10.1007/978-3-031-51920-8
isbn_softcover978-3-031-51922-2
isbn_ebook978-3-031-51920-8Series ISSN 2195-3511 Series E-ISSN 2195-352X
issn_series 2195-3511
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Moving Discontinuities,ble dissipation make the distinction of phase transformation and irreversible degradation of materials. Finally in the irreversible case, the rate boundary value problem is given in terms of displacement and propagation of the interface in order to description partial damage material.
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,On Relationships Between Micro–Macro Quantities,r proposes some extensions of classical relations to non linear mechanics. To determine the overall behaviour of a body, whose local properties are known, we must solve a complicated boundary value problem. The thermodynamical point of view is used to determine the partition between reversibility and irreversibility of the global response.
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Non-linear and Linear Elasticity,re given. Under hypothesis of small strain, properties of existence and uniqueness of equilibrium solution are presented. Integral formulation is also given, as well as particular solution for specific loadings and geometries.
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Fracture Mechanics,e asymptotic singular stress field and we propose a global approach of rupture. A variational formulation is given to solve the rate boundary value problem. Extensions in finite strain and in dynamics are presented.
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