Journal of Elasticity

, Volume 21, Issue 3, pp 271–308

Compatibility conditions for a left Cauchy-Green strain field

  • Janet A. Blume

DOI: 10.1007/BF00045780

Cite this article as:
Blume, J.A. J Elasticity (1989) 21: 271. doi:10.1007/BF00045780


This paper deals chiefly with various issues pertaining to the existence and uniqueness of a finite deformation that gives rise to a prescribed right or left Cauchy-Green strain-tensor field.

Following a review and discussion of available existence and uniqueness theorems appropriate to a pre-assigned right strain field, the extent of uniqueness of a generating deformation is established under minimal smoothness and invertibility assumptions.

The remainder of the paper is devoted to the more involved corresponding existence and uniqueness questions for a given left strain-tensor field. These questions are first discussed in a three-dimensional setting and are then resolved for the special class of plane deformations. The results thus obtained stand in marked contrast to their counterparts for a given right strain field.

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Janet A. Blume
    • 1
  1. 1.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaU.S.A.
  2. 2.Division of EngineeringBrown UniversityProvidenceU.S.A.

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