Shear Strain vs Deviatoric Strain

Question

Hi All, 
 I am looking to extract shear strains from a model to compare with shear box test data and determine if my ground will be subject to any strain softening. 
 I believe the output cartesian strain (gammaxy) is the shear strain I'm interested in - but given it is a cartesian strain, is there a risk it doesn't capture the maximum shear strain? 
 The only "gamma" strain under the total strain section is deviatoric strain. This is a shear strain, but again does it capture the maximum shear strain? 
 Has anyone done a similar task and have any thoughts on the most appropriate output? 
 Thank you, 
 Rebecca

Vasileios Basas · Answer

Hi Rebecca, 
 In a sense, both strains are shear strains. On the one hand, the cartesian shear strain is defined as the change in dimensions upon original dimensions. On the other hand, we know that the total strain in a body can be decomposed into deviatoric and volumetric (hydrostatic or mean) components. The mean strain (volumetric) is involved in the change in the volume and the deviatoric strain is involved in the change in the shape of a solid. 
 By definition: T otal strain = mean strain + deviatoric strain or &epsilon;ij = &epsilon;&rsquo;ij + &epsilon;m . We could say that the deviatoric strain is what's left after subtracting out the hydrostatic strain. So, the mathematical expression of a deviatoric strain becomes: 
 where &epsilon;m is the mean strain (&epsilon;m = 1/3(&epsilon;x + &epsilon;y + &epsilon;z)). You can find the equation which expresses the deviatoric strain as a function of the cartesian strains in Equation 26 of PLAXIS &ndash; Material Models manual. 
 Therefore, to answer your question, both shear (&gamma;xy) and deviatoric (&gamma;s or &epsilon;q) strains will capture the maximum strain in the shear box test, but their values will not be identical (see equation 26) due to the difference in definition.

Shear Strain vs Deviatoric Strain

Top Replies