دانلود کتاب Objective Algorithms for Integrating Hypoelastic Constitutive Relations Based on Corotational Stress Rates

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Preface Acknowledgements Contents Acronyms 1 Introduction 1.1 State of the Art 1.2 Book Writing Goals References 2 Preliminaries 2.1 Local Body Deformations and Basic Kinematics 2.2 Objective Tensor Rates 2.2.1 Objective Rates of Eulerian Tensors 2.2.2 Objective Rates of Lagrangian Tensors 2.2.3 Relationship Between Lagrangian and Eulerian Tensors and Their Rates 2.3 Hooke-Like Isotropic Hypoelasticity Models Based on Corotational Stress Rates References 3 Incremental Tensors and the Incremental Objectivity of Tensors 3.1 Definition of the Incremental Objectivity of Tensors 3.2 Incrementally Objective Kinematic Tensors References 4 Incrementally Objective Algorithms for Integrating CRs for Hooke-Like Hypoelastic Models in the Eulerian Form 4.1 Generalized Midpoint Approximations 4.2 Weak Incrementally Objective Algorithms 4.2.1 Hughes–Winget Algorithm 4.2.2 Rubinstein–Atluri Algorithm and Its Generalization 4.2.3 Simo–Hughes Algorithm and Its Generalization 4.3 Strong Incrementally Objective Algorithms 4.3.1 Necessary Conditions for the Strong Incremental Objectivity of the S–H Algorithm 4.3.2 Expressions for Approximate Incremental Strains for Strong Incrementally Objective Algorithms 4.3.3 Expressions for Approximate Incremental Rotations for Strong Incrementally Objective Algorithms 4.3.4 Expressions for Determining the Kirchhoff Stress Tensors References 5 Absolutely Objective Algorithms for Integrating CRs for Hooke-Like Hypoelastic Models 5.1 Absolutely Lagrangian-Objective Algorithm 5.1.1 Absolutely Lagrangian-Objective Approximate Incremental Strain Tensors 5.1.2 Absolutely Lagrangian-Objective Approximate Incremental Rotation Tensor 5.1.3 Expression for Determining the Absolutely Lagrangian-Objective Rotated Kirchhoff Stress Tensor 5.2 Absolutely Eulerian-Objective Algorithm 5.2.1 Absolutely Eulerian-Objective Approximate Incremental Strain Tensors 5.2.2 Absolutely Eulerian–Lagrangian-Objective Approximate Incremental Rotation Tensor 5.2.3 Expression for Determining the Absolutely Eulerian-Objective Kirchhoff Stress Tensor 5.3 Discussion of Absolutely Objective Algorithms References 6 Comparative Analysis and Verification of Objective Algorithms 6.1 Problems of Uniform Deformation of Hypoelastic Bodies: Exact Solutions and Estimates of the Accuracy of Approximate Incremental Strains 6.2 Background for Computer Simulations 6.3 Simulations Using Weak Incrementally Objective Algorithms 6.3.1 Solutions of Problems without Superimposed Rotations 6.3.2 Solutions of Problems with Superimposed Rotations 6.4 Simulations Using Strong Incrementally Objective Algorithms 6.5 Simulations Using Absolutely Objective Algorithms 6.6 Discussion of the Results of Computer Simulations References 7 Concluding Remarks Reference Appendix A Flowcharts of Objective Algorithms for Integrating Hypoelastic Constitutive Relations Appendix B Algorithms for Determining the Polar Decomposition B.1 Algorithms for Determining the Polar Decomposition in Lagrangian Variables B.2 Algorithms for Determining the Polar Decomposition in Eulerian Variables Appendix C The Rodrigues Formula for Determining an Incremental Rotation Tensor Reference Index