LS-Dyna is a general-purpose finite element software that capable of simulating complex real world problems and its very good in term of simulating different contact.

Thanks

Spherical surface to spherical surface is a classical contact problem. I guess it's your modeling/meshing approach that's the cause of issue, and not the contact algorithm of Abaqus. Yes, you can try to use Ls-Dyna; however, I suspect the same issue will arise over there too unless you're planning to use explicit integration scheme :)

Thank you both of you for Ls-Dyna recommendation.

Dear Mr Abhimanyu Kumar Could you tell me more about why the meshing approach results in this issue?

Dear Nhan,

there are multiple reasons to consider when convergency issues arise in a contact simulation. I have been using Abaqus/Standard for geometrically non linear contact simulations between a very soft substrate and either rigid or deformable bodies and could always reach convergence with reasonable efficiency, although I had to struggle on for quite a long time.

I suggest you to read carefully the section of Abaqus Analysis User's Guide dedicated to contact definition in Abaqus/Standard, where you can read about mesh improvement and how to define the interactions correctly. Additionally, but only after you feel confident that your model cannot be improved, you may need to check the convergence criteria for non linear problems in the "Analysis Solution and Control" section of Abaqus Analysis User's Guide.

I cannot say what is the origin of the error you've obtained, but for my experience it might be connected to the severe discontinuity iterations (SDI) which happen in contact problems. The most direct way to ease the convergence is to set ANALYSIS=DISCONTINUOUS with the CONTROLS command. Hope this might help!

Dear Nhan,

In response to your first error, you could increase the number of permissible iterations and check for convergence.

1) This can be done by going to Step->Other->General Solution Controls

2) Choose to edit your step and alter time incrementation constants, I_0, I_R, I_C and I_A to a larger value such as 20.

Hope this helps to an extent!

Dear Nhan,

good methods for the simulation of contact problems, depend on several questions:

1. Are your surfaces smooth enough that you can neglect roughness?

2. Are the contacting bodies large compared to the deformed contact region? If so, they can usually be considered as infinite ("half-space approximation").

3. Are the contacting bodies more or less homogeneous or do they have a complex (for example composite) structure?

4. Do you have constitutive non-linearities like plasticity?

For large, homogeneous bodies with smooth surfaces your problem of spherical contact has a long-known analytical solution, which can be found in any textbook on contact mechanics.

For large, homogeneous bodies with linear material behavior (mostly independent of roughness or contact geometry) there are several numerical methods to simulate contact problems, which work faster and more stable than any FEM software, for example the Boundary Element Method in contact mechanics (accelerated by the FFT) or Green's Function Molecular Dynamics. However, there are recent "tweaks" to improve FEM for contact problems, for example the "FEM with embedded roughness", but I don't know, whether these have already made it into commercial FE code like ABAQUS or LS-DYNA.

In general, FEM is only necessary, if the macroscopic shape of the contacting bodies does matter, or if the bodies have a complex structure for which no fundamental solution (i.e. stresses and strains under point loading) can be found in closed form, or if the material behavior is non-linear, for example due to an elasto-plastic constitutive relation.