Journal of Elasticity

, Volume 21, Issue 3, pp 271-308

First online:

Compatibility conditions for a left Cauchy-Green strain field

  • Janet A. BlumeAffiliated withDivision of Engineering and Applied Science, California Institute of Technology

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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.