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.

Explains the step-by-step integration of constitutive relations of objective algorithms Provides a thorough understanding oof objective algorithms for integrating Hooke-like hypoelasticity Offers a comparative survey of the performance of most currently available objective algorithms

Autorentext

Dr. Sci. Sergey Korobeynikov has more than 50 years of experience in the field of Computational Nonlinear Solid Mechanics and Nano-mechanics and has worked in Novosibirsk State University as Professor. Currently he is working as Principal investigator in Lavrentiev Institute of Hydrodynamics of Siberian Branch of Russian Academy of Science. He has published 2 textbooks and one monograph (2000) in Russian, also he is the coauthor of one Springer brief book (2023). He has published 51 research papers in different International Journals and Proceedings of repute. He successfully supervised three PhD students and received numerous awards from Russian Academy of Science. He was the member of European Structural Integrity Society (ESIS) from 2006 up to 2019, and he is the member of Russian National Committee on Theoretical and Applied Mechanics (RNCTAM). Dr. Aleksey Larichkin has more than 15 years of experience in the fields of Experimental Solid Mechanics and Computational Nonlinear Solid Mechanics and is working in Novosibirsk State University as Senior Lecturer. Currently, he is working as Senior researcher in Lavrentiev Institute of Hydrodynamics of Siberian Branch of Russian Academy of Science. He is the coauthor of one Springer brief book (2023) and textbook in Russian (2022). He has published 15 research papers in different International Journals and Proceedings of repute. Furthermore, he successfully supervised one PhD student. Professor Patrizio Neff graduated with a degree in mathematics from the TU Darmstadt in 1995, where he subsequently completed his Ph.D in 2000 concerning multiplicative plasticity. In collaboration with Professor Jörg Schröder he extended the Ball’s polyconvexity requirement to anisotropic materials. From 2001-2002 he served as a Visiting Associate Professor at the California Institute of Technology in Pasadena, USA. In 2004, he successfully completed his habilitation on the subject of finite strain Cosserat theory and Cosserat shells at the TU Darmstadt. Since 2009, he has been a full professor of Nonlinear Analysis and Modelling at the University of Duisburg-Essen. He is the author of over 240 research papers published in various prestigious international journals and proceedings. Throughout his academic career, he has supervised numerous doctoral students, five of whom now hold professorships. His research is in the field of applied mathematics and partial differential equations, including notably generalized Korn’s inequalities and generalized continua (micromorphic, Cosserat) as well as nonlinear elasticity. The primary focus of his research endeavours has recently been directed towards isotropic nonlinear elasticity theory.

Inhalt

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 verication 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.