Strain tensor and displacement field

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The strain tensor can be derived from the displacement field . The calculation is easy in two cases :

Linear deformation:

Deformation lineaire et deplacement.png

Pure shear strain:

Cisaillement et deplacement.png

The relative volume variation is evaluated by the trace of the strain tensor:

The approximation done is described in the picture below:

  • Top : volume before and after deformation;
  • bottom: after deformation, the approximate volume is in green and the neglected part in orange.

Approximation volume deformation.png