FEA- Contact Non- Linearity

Hello Everyone,

The types of Non Linearity in FEA are-

1. Geometric Non-Linearity
2. Material Non-Linearity
3. Boundary Conditions/Contact Non-Linearity

Geometric non-linearity - all which involve large deflection fall under this. Here stiffness changes due to deformation. Example: buckling of a fishing rod.

Material non-linearity - here stiffness changes because of material property. Example: plasticity, hyper elasticity, creep etc.

Contact non-linearity - Here a boundary condition may be added or removed during the finite element run like gap analysis. Example: Analyses' having friction contacts.

Today we will discuss about Contacts Non linearity in FEA :- Non-linearity means that the Stiffness matrix (K) changes with the solution, that is, it is K a function of the nodal displacements; as K changes, a new solution must be attained until the thus iterated solution stops changing within tolerances. Contact non linearity occurs when, due to the deformation of one or more parts in contact (pushing or pulling on other) produces a deformation leading to a change in the geometry of the part that translates into a change on K or on the forces (action and reaction) between the parts in contact forcing another iteration on approaching the solution. 

Objective of contact analysis

1. Whether two or more bodies are in contact

2. Where the location or region of contact is

3. How much contact force or pressure occurs in the interface

4. If there is a relative motion after contact in the interface

Contact in Abaqus-

• General Contact: All with Itself approach and high computation cost
• Contact pair- Highly recommenced
• Contact Element- Rarely used

What is Contact Pressure and Force- The force normal to contact area acting between two contact surfaces and contact Pressure= contact force/contact area

Contact stiffness= Contact Force/ penetration ( if penetration equals to zero yhen stiffness become zero. so we it will not easy to solve . need to maintain some amount of penetration like less than 0.05%)

Contact Surface Algorithm :-

Surface-to-surface contact(S2S)- elements are used to model contact between two surfaces. eg. two blocks moving relative to each other, contact between two concentric cylinders, contact between car and road etc.

Node-to-surface contact(N2S)- elements are used to model contact between a surface and a point for eg a sharp object like a pin or bullet impacting a plate, membrane etc .

Contact allows interaction between two defined component surfaces. those interaction surfaces have identifiable orientation is called Contact normal's.

Master Surface and Slave Surfaces

• If you have a combination of Rigid and deformable bodies, the rigid body should be the master and the deformable should be the slave.
• If both surfaces in a contact definition are deformable, then the softer of the two is the slave and the more stronger is the master.
• The densely meshed body should be the slave. This is because, ABAQUS allows master to penetrate into the slave(N2S). To avoid too much penetration, the slave meshing must be denser. If densely meshed, the element size of slave is small which allows the nodes to effectively prevent penetration into their sphere of influence. The coarser mesh is the master.

• The longer of the two surfaces should be the master. This will prevent sliding slave nodes from sliding off from the surface and falling behind. If a slave node falls behind a master, excessive convergence issues occur.
• The more smoother of the two surfaces should be the master. This is because non smooth surfaces can have gaps or peaks in the mesh or cracks in the mesh. A slave node sliding on such non smooth surface can fall through this crack causing convergence issues.

Surface Behavior Techniques & Method : Hard and Soft contact

•  Hard contact (using penalty constraint enforcement)
•  Soft contact (using linear and exponential Pressure-Overclosure relations)

Contact Methodologies - small and finite Sliding schemes allow large rotation and include geometric non linearity and they are being considered for comparison. Similarity and differences between small and finite sliding are given as follows:

? Both formulations allow two bodies to undergo large motions. However limitation in the small sliding is that it assumes that there will be a relatively small amount of sliding of one surface along the other

? The slave node can transfer load to any nodes on the master surface in the finite sliding while it can only transfer load to a limited number of nodes on the master surface for the small sliding.

? In small sliding analysis every slave node interacts with its own tangent plane on the master surface and consequently slave nodes are not monitored for possible contact along the entire master surface. Thus the small sliding is less expensive computationally than the finite sliding contact.

? The finite sliding contact requires that master surfaces to be smooth which it must has a unique surface normal at all points while the small sliding contact does not need master surfaces to be smooth.

Contact Problem to Converge?

1. Fix the Rigid Body Motion:

  a. Start with all parts in the assembly touching. This can be achieved by moving bodies, adding contact offsets, or adding stabilization damping.

  b. Add friction to the contact surfaces

2. Overcome Non-Convergence:

  a. Reduce the stiffness of the contact elements. (Experience has shown that ramping loads slowly and/or lowering contact stiffness will solve 90% of convergence issues).

  b. Refine the mesh in the contact region to reduce the percentage of elements flipping in and out of contact.

Checking Contact convergence issue

1. Check Warning Message
2. Penetration
3. Normals of Surfaces
4. Check Search Distance
5. Reverse Master/Slave
6. Add Contact Stabilization Damping

Please add Your Suggestions in a Comment-Box

Good Evening ...................................................!!!!!!!

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