Representation Theorems for Hemitropic and Tranversely Isotropic Tensor Functions Export

@article{citeulike:6110003, abstract = {Abstract\ \ A representation theorem for transversely isotropic tensor-valued functions of a symmetric tensor variable is proved. The theorem holds in any finite dimension. The proof is based on the decomposition of a symmetric tensor of dimension N into a scalar, a vector, and a symmetric tensor of dimension N-1, and on the fact that the transverse isotropy of the original function is equivalent to the hemitropy of three functions, one scalar-valued, one vector-valued, and one tensor-valued, of the last two terms in the decomposition. Representation theorems for the three functions are obtained as generalizations of two theorems of W. Noll on isotropic functions. The proofs make use of an appropriate algebraic structure based on alternating forms. The three-dimensional case, as well as those of linear and of hyperelastic functions, are treated as special cases.}, author = {Del Piero, Gianpietro}, citeulike-article-id = {6110003}, citeulike-linkout-0 = {http://dx.doi.org/10.1023/A:1007485908989}, citeulike-linkout-1 = {http://www.springerlink.com/content/g46541660h61rm77}, day = {1}, doi = {10.1023/A:1007485908989}, journal = {Journal of Elasticity}, keywords = {tensor}, month = {April}, number = {1}, pages = {43--71}, posted-at = {2009-11-13 16:41:02}, priority = {2}, title = {Representation Theorems for Hemitropic and Tranversely Isotropic Tensor Functions}, url = {http://dx.doi.org/10.1023/A:1007485908989}, volume = {51}, year = {1998} }

TY - JOUR ID - citeulike:6110003 L3 - citeulike-article-id:6110003 N2 - Abstract  A representation theorem for transversely isotropic tensor-valued functions of a symmetric tensor variable is proved. The theorem holds in any finite dimension. The proof is based on the decomposition of a symmetric tensor of dimension N into a scalar, a vector, and a symmetric tensor of dimension N-1, and on the fact that the transverse isotropy of the original function is equivalent to the hemitropy of three functions, one scalar-valued, one vector-valued, and one tensor-valued, of the last two terms in the decomposition. Representation theorems for the three functions are obtained as generalizations of two theorems of W. Noll on isotropic functions. The proofs make use of an appropriate algebraic structure based on alternating forms. The three-dimensional case, as well as those of linear and of hyperelastic functions, are treated as special cases. IS - 1 JF - Journal of Elasticity EP - 71 TI - Representation Theorems for Hemitropic and Tranversely Isotropic Tensor Functions VL - 51 SP - 43 KW - tensor AU - Del Piero, Gianpietro PY - 1998/04/01/ UR - http://dx.doi.org/10.1023/A:1007485908989 ER -