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.

• Introduction.- Preliminaries.- Constitutive relations for neo-Hookean isotropic hyperelastic material models.- Some volumetric functions and their properties.- Constitutive inequalities for neo-Hookean materials.- Testing neo-Hookean materials in homogeneous deformations.- Concluding remarks.

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.

• Introduction.- Preliminaries.- Constitutive relations for neo-Hookean isotropic hyperelastic material models.- Some volumetric functions and their properties.- Constitutive inequalities for neo-Hookean materials.- Testing neo-Hookean materials in homogeneous deformations.- Concluding remarks.

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.

• Introduction.- Preliminaries.- Constitutive relations for neo-Hookean isotropic hyperelastic material models.- Some volumetric functions and their properties.- Constitutive inequalities for neo-Hookean materials.- Testing neo-Hookean materials in homogeneous deformations.- Concluding remarks.