Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Xiao H. 1998On scalar–, vector– and second–order tensor–valued anisotropic functions of vectors and second–order tensors relative to all kinds of subgroups of the transverse isotropy group CinfinityhPhil. Trans. R. Soc. A.3563087–3122http://doi.org/10.1098/rsta.1998.0308SectionRestricted accessOn scalar–, vector– and second–order tensor–valued anisotropic functions of vectors and second–order tensors relative to all kinds of subgroups of the transverse isotropy group Cinfinityh H. Xiao H. Xiao Institute of Mechanics I, Ruhr-University Bochum, D-44780 Bochum, Germany Google Scholar Find this author on PubMed Search for more papers by this author H. Xiao H. Xiao Institute of Mechanics I, Ruhr-University Bochum, D-44780 Bochum, Germany Google Scholar Find this author on PubMed Search for more papers by this author Published:15 December 1998https://doi.org/10.1098/rsta.1998.0308AbstractScalar–, vector– and second order tensor–valued functions of any finite number of vector and second order tensor variables are considered, which are required to possess invariance or form–invariance under the action of any given subgroup of the transverse isotropy group C∞h. Irreducible functional bases and irreducible generating sets are presented to determine general reduced forms of the anisotropic functions just indicated. The results given are derived in the sense of non–polynomial representation. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Shariff M (2023) On the Smallest Number of Functions Representing Isotropic Functions of Scalars, Vectors and Tensors, The Quarterly Journal of Mechanics and Applied Mathematics, 10.1093/qjmam/hbac022 Xiao H, Bruhns O and Meyers A (2006) On isotropic extension of anisotropic constitutive functions via structural tensors, ZAMM, 10.1002/zamm.200410226, 86:2, (151-161), Online publication date: 16-Feb-2006. Thionnet A and Martin C (2006) A new constructive method using the theory of invariants to obtain material behavior laws, International Journal of Solids and Structures, 10.1016/j.ijsolstr.2005.05.021, 43:2, (325-345), Online publication date: 1-Jan-2006. Bruhns O, Xiao H and Meyers A (2003) Some basic issues in traditional Eulerian formulations of finite elastoplasticity, International Journal of Plasticity, 10.1016/S0749-6419(03)00047-0, 19:11, (2007-2026), Online publication date: 1-Nov-2003. This Issue15 December 1998Volume 356Issue 1749 Article InformationDOI:https://doi.org/10.1098/rsta.1998.0308Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online15/12/1998Published in print15/12/1998 License: Citations and impact Keywordsanisotropic functionsvectors and tensorsirreducible non–polynomial representationsinvariance and form–invariancematerial symmetry groupsconstitutive equations