Does stress stiffening occur in the direction of the stress?

[dirnad]

Most descriptions tell us that a tensile stress in one direction stiffens a structure against deflection in other directions.

But does it also stiffen against further deformation in the same direction?

Some testing with FEA software says yes - vibration modes in the direction of the stress have a higher frequency than without stress. But it leads to a strange situation. If you put a bar in compression it softens axially. Enough compression and it becomes unstable, indicating buckling (?) in the axial direction, which seems somewhat unphysical. Although this happens with an axial engineering strain of -1 which itself is unphysical.

Can anyone provide some explanation of how this phenomenon works and if some of it is just an artifact of the software?

 

[Reitzel]

Hi Dirnad

As far as I'm concerned stress stiffening only has an effect on the stiffness in the other directions, i.e. it describes the coupling between the stress in a given direction to the stiffness in the other directions. In ANSYS it's called a stress-stiffness matrix, which is formed and added to the regular stiffness matrix in case stress-stiffening is applied. As far as I'm concerned stress-stiffening is relevant for structures in which one direction is much smaller than the other(s). Examples include the membrane of a drum or a guitar string, in which a membrane stress or an axial stress, respectively, will increase the transverse stiffness of the drum skin or guitar string.

The "stiffening" that occurs in the same direction of the applied stress is called strain hardening. Is that what you think of?
Could you explain to me, how a bar softens axially when subjected to compression? As far as im concerned a shorter bar means a higher stiffness - in all directions!?

 

[dirnad]

Thanks Reitzel

The ANSYS theory manual shows that the stress stiffness matrix for 3-D solid elements is the same in all directions regardless of the direction of the stress. This suggests the stiffening happens equally in all directions. Perhaps it's an approximation because it will always be negligible in the stressed direction?

On the other hand, for LINK8 elements it's the opposite. With no axial stiffening. This is in line with what you said.

I got the axial stiffening from an FEA model. It's not strain hardening (material model is linear). It's caused by stress stiffening. When you turn that off, the effect disappears.

 

[Reitzel]

Hi Dirnad

Makes sort of sense I guess the stress stiffening effect is negligible when each dimension in a 3d element are similar, whereas for an element, e.g. LINK8, in which the transverse stiffness in one direction is small in comparison to the others, stress stiffening plays a greater role.