Poynting effect in simple shear with zero normal stress

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Consider a simple shear x=kY, y=Y, z=Z. How is Poynting effect defined? If the normal stress along y is 0 but that along x isn't 0, is that also a sort of Poynting effect?
 

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Chestermiller said:
You're talking about the effect of pressure on the Gibbs free energy?
No, but about shear and the corresponding normal stresses
 
feynman1 said:
No, but about shear and the corresponding normal stresses
I have no idea what you are referring to. Are you asking about the components of the stress tensor for the shear deformation you defined?
 
Chestermiller said:
I have no idea what you are referring to. Are you asking about the components of the stress tensor for the shear deformation you defined?
Yes, the normal and shear stress components, that is discussion about the normal components when shear is present.
 
feynman1 said:
Yes, the normal and shear stress components, that is discussion about the normal components when shear is present.
OK. Are you familiar with the 3D tensorial version of Hooke's Law? If so, for this particular deformation, what does that predict for the components of the strain and stress tensors?
 
Chestermiller said:
OK. Are you familiar with the 3D tensorial version of Hooke's Law? If so, for this particular deformation, what does that predict for the components of the strain and stress tensors?
Yes and I did the analysis, just wonder the precise definition of the effect
 
feynman1 said:
Yes and I did the analysis, just wonder the precise definition of the effect
Precise definition of what effect?
 
Chestermiller said:
Precise definition of what effect?
poynting
 
In large deformations (even shear), the stress tensor is not just a linear function of the strain tensor, however that is defined (there are many tensorially acceptable definitions for finite strains). It is a non-linear function of the strain tensor, and this non-linearity results in not only shear stresses, but also normal stresses that are functions of the amount of shear (in simple shear).
 
Chestermiller said:
In large deformations (even shear), the stress tensor is not just a linear function of the strain tensor, however that is defined (there are many tensorially acceptable definitions for finite strains). It is a non-linear function of the strain tensor, and this non-linearity results in not only shear stresses, but also normal stresses that are functions of the amount of shear (in simple shear).
right, but that's just a description not a rigorous definition. Does poynting refer to nonzero normal stresses or one specific normal stress component?
 
feynman1 said:
right, but that's just a description not a rigorous definition. Does poynting refer to nonzero normal stresses or one specific normal stress component?
For the deformation described in this thread, the state of stress is not isotropic, and all three normal stresses are non-zero.
 
Chestermiller said:
For the deformation described in this thread, the state of stress is not isotropic, and all three normal stresses are non-zero.
So if only one of sigma_x and sigma_y is 0, will that be called poyning effect?
 
feynman1 said:
So if only one of sigma_x and sigma_y is 0, will that be called poyning effect?
What it is specifically called does not matter (to me). What matters is whether such an effect exists.
 
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Chestermiller said:
What it is specifically called does not matter (to me). What matters is whether such an effect exists.
agree, but that will affect assessment and comparison with the literature when not knowing if the same thing is discussed