Smoothness of the Scalar Coefficients in Representations of Isotropic Tensor-Valued Functions

Autor:	Michael J. Scheidler
Rok vydání:	1996
Předmět:	Smoothness Mechanics of Materials General Mathematics Mathematical analysis Isotropy Scalar (mathematics) Symmetric tensor Differential topology General Materials Science Omega Eigenvalues and eigenvectors Isotropic tensor Mathematics
Zdroj:	Mathematics and Mechanics of Solids. 1:73-93
ISSN:	1741-3028 1081-2865
DOI:	10.1177/108128659600100106
Popis:	For a three-dimensional space, an isotropic tensor-valued function omega of a symmetric tensor A has the representation omega(A) = alpha(A)I + beta(A)A + gamma(A)A2, in which the coefficients alpha, beta, and gamma are isotropic scalar-valued functions. It is known that these coefficients may fail to be as smooth as omega at those tensors A that do not have three distinct eigenvalues. Serrin (1959) and Man (1994) determined conditions on the smoothness of P that guarantee the existence of continuous coefficients. We give a different proof of their results and also determine conditions on P that guarantee the existence of continuously differentiable coefficients. (AN)
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ba4f90e2411371795df22fa699ad96e3 https://doi.org/10.1177/108128659600100106 Zobrazit plný text záznamu