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

This book provides readers with a deep understanding of the use of objective algorithms for integration of constitutive relations (CRs) for Hooke-like hypoelasticity based on the use of corotational stress rates. The purpose of objective algorithms is to perform the step-by-step integration of CRs u...

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Bibliographic Details
Main Authors: Korobeynikov, Sergey (Author), Larichkin, Alexey (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Cham : Springer Nature Switzerland : Imprint: Springer, 2023.
Edition:1st ed. 2023.
Series:SpringerBriefs in Continuum Mechanics,
Subjects:
Continuum mechanics.
Numerical analysis.
Integral equations.
Continuum Mechanics.
Numerical Analysis.
Integral Equations.
Online Access:https://doi.org/10.1007/978-3-031-29632-1
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Table of Contents:
  • 1. Introduction
  • 2. Preliminaries
  • 3. Incremental tensors and the incremental objectivity of tensors
  • 4. Incrementally objective algorithms for integrating CRs for Hooke-like hypoelastic models in the Eulerian form
  • 5. Absolutely objective algorithms for integrating CRs for Hooke-like hypoelastic models
  • 6. Comparative analysis and verification of objective algorithms
  • 7. Concluding remarks. A. Flowcharts of objective algorithms for integrating hypoelastic constitutive relations
  • B. Algorithms for determining the polar decomposition
  • C. The Rodrigues formula for determining an incremental rotation tensor
  • Index.

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