Two Types of Compressible Isotropic Neo-Hookean Material Models
暫譯: 兩種可壓縮各向同性的尼奎斯特材料模型
Korobeynikov, Sergey, Larichkin, Alexey, Neff, Patrizio
- 出版商: Springer
- 出版日期: 2026-01-28
- 售價: $2,630
- 貴賓價: 9.5 折 $2,498
- 語言: 英文
- 頁數: 101
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3032060494
- ISBN-13: 9783032060495
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相關分類:
工程數學 Engineering-mathematics
海外代購書籍(需單獨結帳)
商品描述
This book provides readers with a deep understanding of the principles for generating formulations of compressible isotropic hyperelastic material models based on formulations of incompressible material models. The reference high-performance incompressible isotropic hyperelastic material model is Ogden's model, for which the elastic energy is generally represented as the sum of elemental energies based on strain tensors from the Doyle-Ericksen family. For the sake of transparency, the study is confined to considering the elastic energy only for one term of this sum based on the Finger strain tensor corresponding to the well-known neo-Hookean material model. The book presents a systematic study of the performance of two known types of compressible generalization of the incompressible neo-Hookean material model. The first type of generalization is based on the development of volumetric-isochoric neo-Hookean models and involves the additive decomposition of the elastic energy into volumetric and isochoric parts. The second, simpler type of generalization, is based on the development of mixed neo-Hookean models that do not use this decomposition. Theoretical studies of model performance and simulations of some homogeneous deformations have shown that when using "good" volumetric functions, mixed and volumetric-isochoric models show similar performance in applications and have physically reasonable responses in extreme states, which is convenient for theoretical studies. However, compared to volumetric-isochoric models, mixed models allow the use of a wider set of volumetric functions with physically reasonable responses in extreme states. Another feature of mixed models is that they allow for simpler expressions for stresses and tangent stiffness tensors. This book is useful both for novice researchers in developing hyperelastic equations for compressible materials and for experienced researchers by providing a brief overview of methods for generating compressible hyperelastic formulations based on available incompressible hyperelastic formulations.
商品描述(中文翻譯)
本書提供讀者對於基於不可壓縮材料模型的公式生成可壓縮各向同性超彈性材料模型原則的深入理解。參考的高性能不可壓縮各向同性超彈性材料模型為Ogden模型，其彈性能量通常表示為基於Doyle-Ericksen家族的應變張量的元素能量之和。為了透明性，本研究僅考慮基於與著名的neo-Hookean材料模型相對應的Finger應變張量的這個和中的一項的彈性能量。本書系統性地研究了兩種已知的可壓縮一般化的不可壓縮neo-Hookean材料模型的性能。第一種一般化基於體積-等容neo-Hookean模型的發展，涉及將彈性能量加性分解為體積部分和等容部分。第二種較簡單的一般化基於混合neo-Hookean模型的發展，該模型不使用這種分解。對模型性能的理論研究和一些均勻變形的模擬顯示，當使用「良好」的體積函數時，混合模型和體積-等容模型在應用中表現相似，並在極端狀態下具有物理上合理的響應，這對於理論研究是方便的。然而，與體積-等容模型相比，混合模型允許使用更廣泛的體積函數，並在極端狀態下具有物理上合理的響應。混合模型的另一個特點是它們允許對應力和切線剛度張量進行更簡單的表達。本書對於開發可壓縮材料的超彈性方程的新手研究人員以及對於經驗豐富的研究人員提供了基於現有不可壓縮超彈性公式生成可壓縮超彈性公式的方法的簡要概述，均具有實用價值。
作者簡介
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.
作者簡介(中文翻譯)
Dr. Sci. Sergey Korobeynikov 在計算非線性固體力學和納米力學領域擁有超過 50 年的經驗，曾在新西伯利亞國立大學擔任教授。目前，他在俄羅斯科學院西伯利亞分院的 Lavrentiev 水動力學研究所擔任首席研究員。他已出版 2 本俄文教科書和一本專著（2000 年），並且是一本 Springer 簡報書（2023 年）的共同作者。他在不同的國際期刊和著名會議上發表了 51 篇研究論文，成功指導了三位博士生，並獲得了俄羅斯科學院的多項獎項。他是歐洲結構完整性學會（ESIS）的成員，任期從 2006 年至 2019 年，並且是俄羅斯理論與應用力學國家委員會（RNCTAM）的成員。
Dr. Aleksey Larichkin 在實驗固體力學和計算非線性固體力學領域擁有超過 15 年的經驗，目前在新西伯利亞國立大學擔任高級講師。目前，他在俄羅斯科學院西伯利亞分院的 Lavrentiev 水動力學研究所擔任高級研究員。他是一本 Springer 簡報書（2023 年）和一本俄文教科書（2022 年）的共同作者。他在不同的國際期刊和著名會議上發表了 15 篇研究論文。此外，他成功指導了一位博士生。
Patrizio Neff 教授於 1995 年在達姆施塔特工業大學獲得數學學位，並於 2000 年完成有關乘法性塑性的博士學位。在與 Jörg Schröder 教授的合作下，他將 Ball 的多凸性要求擴展到各向異性材料。2001 年至 2002 年，他在美國加州理工學院擔任訪問副教授。2004 年，他在達姆施塔特工業大學成功完成有關有限變形 Cosserat 理論和 Cosserat 殼體的資格論文。自 2009 年以來，他一直擔任杜伊斯堡-埃森大學的非線性分析與建模全職教授。他是超過 240 篇在各種著名國際期刊和會議上發表的研究論文的作者。在他的學術生涯中，他指導了許多博士生，其中五位目前擔任教授。他的研究領域包括應用數學和偏微分方程，特別是廣義 Korn 不等式和廣義連續體（微觀形態、Cosserat）以及非線性彈性。最近，他的研究重點主要集中在各向同性非線性彈性理論上。
