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

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Sergey Korobeynikov Alexey Larichkin

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

Sergey Korobeynikov, Alexey Larichkin

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English

Springer International Publishing AG
20 April 2023

Integral calculus & equations; Numerical analysis; Classical mechanics; Algorithms & data structures

Series: SpringerBriefs in Applied Sciences and Technology

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 using fairly large time steps that provide high accuracy of this integration in combination with the exact reproduction of superimposed rigid body motions. Since Hooke-like hypoelasticity is included as a component in CRs for elastic-inelastic materials (e.g., in CRs for elastic-plastic materials), the scope of these algorithms is not limited to hypoelastic materials, but extends to many other materials subjected to large deformations. The authors performed a comparative analysis of the performance of most currently available objective algorithms, provided some recommendations for improving the existing formulations of these algorithms, and presented new formulations of the so-called absolutely objective algorithms. The proposed book will be useful for beginner researchers in the development of economical methods for integrating elastic-inelastic CRs, as well as for experienced researchers, by providing a compact overview of existing objective algorithms and new formulations of these algorithms. The book will also be useful for developers of computer codes for implementing objective algorithms in FE systems. In addition, this book will also be useful for users of commercial FE codes, since often these codes are so-called black boxes and this book shows how to test accuracy of the algorithms of these codes for integrating elastic-inelastic CRs in modeling large rotations superimposed on the uniform deformation of any sample.

By: Sergey Korobeynikov, Alexey Larichkin
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2023
Dimensions: Height: 235mm, Width: 155mm,
Weight: 203g
ISBN: 9783031296314
ISBN 10: 3031296311
Series: SpringerBriefs in Applied Sciences and Technology
Pages: 107
Publication Date: 20 April 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.