Time Rates of Generalized Strain Tensors. Part 2. Approximate Basis-Free Formulas

Abstract

Utilizing the component formulas derived in Part I, we obtain approximate basis-free formulas for the material time derivative of a generalized Lagrangian strain tensor and for the Jaumann rate of a generalized Eulerian strain tensor. These formulas provide good estimates when the shear strains are small, regardless of the volumetric strain and the strain rate. We also derive explicit bounds for the error in the approximate formulas. By applying our general results to the logarithmic strain tensors, we obtain improved versions of approximate basis-free formulas due to Hill and Gurtin and Spear.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1991
Accession Number
ADA242095

Entities

People

  • Michael J. Scheidler

Organizations

  • Ballistic Research Laboratory

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  • Calculus or Mathematical Analysis
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