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

Abstract

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)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1995
Accession Number
ADA298295

Entities

People

  • Michael J. Scheidler

Organizations

  • United States Army Research Laboratory

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Analytic Functions
  • Boundaries
  • Bulk Modulus
  • Coefficients
  • Commerce
  • Continuity
  • Decomposition
  • Eigenvalues
  • Equations
  • Guarantees
  • Hyperelastic Materials
  • Identities
  • Materials
  • Military Research
  • Shear Modulus
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra

Technology Areas

  • Space