Snap back happens in cohesive elements due to unstable behavior. Consider a simple model consisting of a spring and a cohesive element. Let their individual force-displacement diagrams be straight lines. The spring will have a positive slope and the cohesive element will have a negative slope. Now, you have to impose a prescribed displacement to the spring-cohesive elemnt system. The cohesive element will remain closed until a certain displacement value is reached. You can now write the total displacement (using the two force-displacement diagrams) and also apply force equilibrium. Then you can observe that for certain values of intitial conditions (constants in the force-displacement diagram), an unstable configuration is achieved. This tends to produce numerical instability and in case of Finite Elments, the analysis does not converge.
I was wondering what a good example of snap-back would be. Thanks, Arun, for a clear explanation.
A good example of snap through can be visualized with a pin-pin supported two-bar truss loaded at the common joint to cause compression. At a high enough load, the truss will displace, for example, from ^ to -- to V. The same load now pertains to a dramatically increased displacement, hence the term "snap through".
Look for work on the "Arc Length Method" by Ramm for a solution to both problems.
Recently, I also try to figure out the "elastic snap-back instability", for I am preparing to simulate the delamination of fiber/metal plate under low-velocity impact with the cohesive zone model.
After reading the above paper, I seemed understand the reason of "elastic snap-back instability" which occurs just after the stress reaches the peak strength of the interface. But when I read other authors' papers[1,2], I get confused.
For example, the delamination of DBC was simulated with cohesive zone model based on the bilinear constitutive model, the load-displacement curve comes up with "spurious oscillation (see bottom figure)" which results from "snap-back instability". And the papers point out that the problem can be alleviated with fine mesh, or by choosing very low interface strength and the initial interface stiffness. I cannot understand why these methods can work and how to explain them with the exposition in your paper.
Thank you for your time and attention!
--Wenqiong
[1] N. Hu,et al. Stable numerical simulations of propagations of complex damages in composite structures under transverse loads. Composites Science and Technology 67 (2007) 752–765.
[2] A.M. Elmarakbi, N. Hu, H. Fukunaga. Finite element simulation of delamination growth in composite materials using LS-DYNA. Composites Science and Technology (2009), in press.
You can consult
You can consult "Crisfield, Non-linear Finite Element Analysis of Solids and Structures, V1:p267. Wiley 1997".
Snap Back
I can answer one part of your question.
Snap back happens in cohesive elements due to unstable behavior. Consider a simple model consisting of a spring and a cohesive element. Let their individual force-displacement diagrams be straight lines. The spring will have a positive slope and the cohesive element will have a negative slope. Now, you have to impose a prescribed displacement to the spring-cohesive elemnt system. The cohesive element will remain closed until a certain displacement value is reached. You can now write the total displacement (using the two force-displacement diagrams) and also apply force equilibrium. Then you can observe that for certain values of intitial conditions (constants in the force-displacement diagram), an unstable configuration is achieved. This tends to produce numerical instability and in case of Finite Elments, the analysis does not converge.
-Arun
snap through
I was wondering what a good example of snap-back would be. Thanks, Arun, for a clear explanation.
A good example of snap through can be visualized with a pin-pin supported two-bar truss loaded at the common joint to cause compression. At a high enough load, the truss will displace, for example, from ^ to -- to V. The same load now pertains to a dramatically increased displacement, hence the term "snap through".
Look for work on the "Arc Length Method" by Ramm for a solution to both problems.
this paper can help
http://web.utk.edu/~ygao7/publication.htm, journal paper #7
In reply to this paper can help by Yanfei Gao
spurious oscillation
Recently, I also try to figure out the "elastic snap-back instability", for I am preparing to simulate the delamination of fiber/metal plate under low-velocity impact with the cohesive zone model.
After reading the above paper, I seemed understand the reason of "elastic snap-back instability" which occurs just after the stress reaches the peak strength of the interface. But when I read other authors' papers[1,2], I get confused.
For example, the delamination of DBC was simulated with cohesive zone model based on the bilinear constitutive model, the load-displacement curve comes up with "spurious oscillation (see bottom figure)" which results from "snap-back instability". And the papers point out that the problem can be alleviated with fine mesh, or by choosing very low interface strength and the initial interface stiffness. I cannot understand why these methods can work and how to explain them with the exposition in your paper.
Thank you for your time and attention!
--Wenqiong
[1] N. Hu,et al. Stable numerical simulations of propagations of complex damages in composite structures under transverse loads. Composites Science and Technology 67 (2007) 752–765.
[2] A.M. Elmarakbi, N. Hu, H. Fukunaga. Finite element simulation of delamination growth in composite materials using LS-DYNA. Composites Science and Technology (2009), in press.