Time Rates of Generalized Strain Tensors. Part 1. Component Formulas

Abstract

Hill derived a simple component formula for the material time derivative of a generalized Lagrangian strain tensor. We examine Hill's derivation in detail and explain why it is generally valid only when the principal stretches are distinct. We then give a proof of Hill's formula which is valid for any C2 motion and any C1 strain measure. Our proof is based on a component form of the chain rule for a tensor valued function of a time- dependent symmetric tensor. This result is also used to derive component formulas for the Jaumann rate of a generalized Eulerian strained tensor. Finally, we apply the general formulas to the logarithmic strain tensors.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1991
Accession Number
ADA232497

Entities

People

  • Michael J. Scheidler

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Analytic Functions
  • Army
  • Availability
  • Commerce
  • Continuum Mechanics
  • Decomposition
  • Eigenvalues
  • Elastic Materials
  • Equations
  • Identities
  • Intervals
  • Literature
  • Materials
  • Numbers
  • Rotation
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mechanical Engineering/Mechanics of Materials.