Introduction to unified mechanics theory with applications / Cemal Basaran.

Format:

Book

Author/Creator:

Basaran, Cemal, author.

Language:

English

Subjects (All):

Continuum mechanics.

Physical Description:

1 online resource (xviii, 519 pages) : illustrations (some color)

Edition:

Second edition.

Place of Publication:

Cham : Springer, [2022]

Summary:

This text describes the mathematical formulation and proof of the unified mechanics theory (UMT) which is based on the ab-initio level unification of Newtons laws and the laws of thermodynamics. It also presents formulations and experimental verifications of the theory for thermal, mechanical, electrical, corrosion, chemical, and fatigue loads, and it discusses why the original universal laws of motion proposed by Isaac Newton in 1687 are incomplete. The author provides concrete examples, such as how Newtons second law, F = ma, gives the initial acceleration of a soccer ball kicked by a player but does not tell us how and when the ball would come to a stop. Throughout Introduction to Unified Mechanics Theory, Dr. Basaran illustrates that Newtonian mechanics does not account for the thermodynamic changes happening in a system over its usable lifetime. And in this context, this book explains how to design a system to perform its intended functions safely over its usable lifetime and predicts the expected lifetime of the system without using empirical models, a process is currently done using Newtonian mechanics and empirical degradation/failure/fatigue models which are curve-fit to test data. Written as a textbook suitable for upper-level undergraduate mechanics courses, as well as first-year graduate level courses, this book is the result of over 30 years of scientific activity with the contribution of dozens of scientists from around the world including the USA, Russia, Ukraine, Belarus, Spain, China, India, and the U.K. Presents continuum mechanics through an explanation of the unified mechanics theory with extensive experimental validation and finite element implementation using real-world examples Draws the connections to the thermodynamics of degradation in solids from the mathematical and microstructural perspective Discusses shortcomings and incompleteness of Newtons universal laws of motion Posits why the space-time coordinate system is insufficient to describe organic and inorganic systems and modifies Newtonian space-time with the introduction of an additional axis (Thermodynamic State Index axis).

Contents:

Intro

Foreword

Preface

References

Contents

Abbreviations

Chapter 1: Introduction

1.1 What Is the Mechanics of Continuous Medium?

Chapter 2: Stress and Strain in Continuum

2.1 Newtonś Universal Laws of Motion

2.1.1 First Universal Law of Motion

2.1.1.1 Formulation of the First Law

2.1.2 Second Universal Law of Motion

2.1.2.1 Formulation of Newtonś Second Law

2.1.3 Third Universal Law of Motion

2.1.4 Range of Validity of Newtonś Universal Laws of Motion

2.1.5 Relation to the Thermodynamics and Conservation Laws

2.2 Stress

2.2.1 Definitions of Stress and Traction

2.2.2 Stress Vector on an Arbitrary Plane

2.2.3 Symmetry of Stress Tensor

2.2.4 Couple Stresses

2.2.5 Principal Stresses and Principal Axes

2.2.6 Stress Tensor Invariants

2.2.6.1 Stress Invariants in Principal Axes

2.2.6.2 Representation of Stress Tensor in Spherical and Deviatoric Components

2.2.6.3 Invariants of the Deviatoric Stress Tensor

2.2.7 Octahedral Plane and Octahedral Stresses

2.3 Deformation and Strain

2.3.1 Small Strain Definition

2.3.1.1 Elementary Definition of Pure Uniaxial Strain

2.3.1.2 Pure Shear Strain

2.3.1.3 Pure Rigid Body Motion

2.3.2 Small Strain and Small Rotation Formulation

2.3.2.1 Definition of Material (Local) Coordinates

2.3.2.2 Small Strain in Local Coordinates

2.3.2.3 Shear Strain in Local (Material) Coordinates

2.3.3 Small Strain and Rotation in 3-D

2.4 Kinematics of Continuous Medium

2.4.1 Material (Local) Description

2.4.2 Referential Description (Lagrangian Description)

2.4.3 Spatial Description (Eulerian Description)

2.4.4 Material Time Derivative in Spatial Coordinates (Substantial Derivative)

2.5 Rate of Deformation Tensor and Rate of Spin Tensor

2.5.1 Comparison of Rate of Deformation Tensor, D, and Time Derivative of the Strain Tensor,

2.5.2 True Strain (Natural Strain) (Logarithmic Strain)

2.6 Finite Strain and Deformation

2.6.1 Green Deformation Tensor, C, Cauchy Deformation Tensor, B-1

2.6.2 Relation Between Deformation, Strain, and Deformation-Gradient Tensors

2.6.3 Comparing Small Strain and Large (Finite) Strain

2.6.4 Strain Rate and Rate of Deformation Tensor Relations

2.6.5 Relation Between, the Spatial Gradient of Velocity Tensor, L and the Deformation-Gradient Tensor, F

2.7 Rotation and Stretch Tensors in Finite Strain

2.8 Compatibility Conditions in Continuum Mechanics

2.9 Piola-Kirchhoff Stress Tensors

2.9.1 First Piola-Kirchhoff Stress Tensor σ0

2.9.2 Second Piola-Kirchhoff Stress Tensor

2.10 Direct Relation Between Cauchy Stress Tensor and Piola-Kirchhoff Stress Tensors

2.11 Conservation of Mass Principle

2.12 The Incompressible Materials

2.13 Conservation of Momentum Principle

Notes:

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed January 19, 2023).

ISBN:

9783031186219

3031186214

OCLC:

1356944005

Access Restriction:

Restricted for use by site license.