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rotation tensor

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2 - Analysis of Strain
from Part I - Fundamentals of Solid Mechanics
Marko V. Lubarda, Vlado A. Lubarda, University of California, San Diego
Book:

Intermediate Solid Mechanics

Published online:

16 December 2019

Print publication:

09 January 2020, pp 31-50
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Summary

The components of the infinitesimal strain tensor are defined, which represent measures of the relative length changes (longitudinal strains or dilatations) and the angle changes (shear strains) at a considered material point with respect to the chosen coordinate axes. The principal strains (maximum and minimum dilatations) and the maximum shear strains are determined, as well as the areal and volumetric strains. The expressions for the strain components are derived in terms of the spatial gradients of the displacement components. The Saint-Venant compatibility equations are introduced which assure the existence of single-valued displacements associated with a given strain field. The matrix of local material rotations, which accompany the strain components in producing the displacement gradient matrix, is defined. The determination of the displacement components by integration of the strain components is discussed.

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2 - Analysis of Strain

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