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Deformation gradient tensor and the engineering strain tensor
Wed, 2016-01-20 05:24 - kajalschopra
Hi,
I'm not able to exactly understand the difference between the deformation gradient tensor and the engineering strain tensor.
I understand that the deformation gradient tensor captures the straining and the rigid body motion of the material fibers. But am not physically make out the difference between engineering strain tensor and the deformation gradient tensor.
I shalll be grateful if someone can help
With regards
Kajal
Forums:
I shall be grateful if
I shall be grateful if someone can help with this.
Deformation gradient tensor and the engineering strain tensor
I shall be grateful if someone can help withthe original question (I think the post didn't appear in the first instance). Sorry for re-posting
https://en.wikipedia.org/wiki
https://en.wikipedia.org/wiki/Infinitesimal_strain_theory
https://en.wikipedia.org/wiki/Finite_strain_theory#Deformation_gradient_...
Infinitesimal_strain_theory and Deformation_gradient_tensor
https://en.wikipedia.org/wiki/Infinitesimal_strain_theory
https://en.wikipedia.org/wiki/Finite_strain_theory#Deformation_gradient_...
Deformation gradient tensor and the engineering strain tensor
Yes, I have seen that already.
I'm just trying to understand better.
Can I say:
1) The engineering strain tensor (which is used only in small deformation theeory) measures the displacement of the body relative to the original configuration of the body
2)Deformation gradient tensor measures the position of the body at time 't' relative to the position of the body at time t=0
Please note:
In 1) for engineering strain tensor, I use the term displacement whereas in 2) for deformation gradient tensor, I use the term 'position'
Are my definitions correct?
No, the deformation gradient
No, the deformation gradient contains effect of rotation while the strain not.
You can decompose def grad as F = RU, R is rotation and U is stretch and define strain as E = 1/2(F^TF - I) = 1/2 (UR^TRU - I) = 1/2(U^2 - I), thus the rotation dissapear. The small strain tensor can be seen as a linearized version of E
Deformation gradient tensor and strain tensor
Thanks.
But in the strain tensor matrix, we have the shear strain component. Does that not include the effect of rotation?
Deformation gradient do take
Deformation gradient do take into account the rigid-body rotation of bodies in space.
Think about a piece of material rotates as a rigid body, then the gradient deformation is F = R, R is the rotaion tensor.
You can read a Continuum Mechanics book to have a systematic study.
Deformation gradient..
I understand that deformation gradient tensor take into account effect of rigid body rotation.
My question was the difference bwtween strain tensor (that is used in small deformations) and deformation gradient tensor.
Bafty answered small deformation strain tensor does not take into account rotation. Does he mean rigid body rotation?
I said small deformation tensor has shear comonents in the matrix. The shear component has the effect of rotation, right?
Bafty and Bin_Li
I shall be extremelt grateful to Bafty and Bin_Li if you could reply.
See if this helps
See if this helps
http://www.brown.edu/Departments/Engineering/Courses/En221/Notes/Kinemat...