What might cause Abaqus/Standard to diverge with NUMERICAL SINGULARITY warnings?

QUESTION

My Abaqus/Standard analysis has failed to find equilibrium, and there are NUMERICAL SINGULARITY warnings in the message file; what is causing this?

ANSWER

(The following applies to all releases.)

These warnings indicate that so many digits are lost during linear equation solution that the results are not reliable. Most likely the model is experiencing an unconstrained rigid body motion, which is most commonly caused by a lack of constraints against such motion in a static stress analysis. Unconstrained rigid body motion results in a singular tangent stiffness matrix (i.e. one that cannot be inverted); this is indicated by the presence of NUMERICAL SINGULARITY warnings in the message (.msg) file and very large displacement corrections.

Frequently the reason for the rigid body motions is that contact has not been established and, therefore, cannot prevent rigid body motion.

The corrective action is to constrain the model properly (using boundary conditions or soft springs). In contact problems where contact and friction will prevent rigid body motion once contact is established, use:

• *CONTACT STABILIZATION to apply viscous damping stabilization to the normal and tangential directions in a general contact domain
• *CONTACT CONTROLS, STABILIZE to apply viscous damping stabilization to the normal and tangential directions of a contact pair

The *STATIC, STABILIZE option or discrete dashpots or soft springs can be used as well, but it is better to avoid the problem by defining the correct boundary conditions or by establishing contact using displacement boundary conditions before applying loads. We recommend that this option not be used in combination with contact-specific stabilization as this will overdamp the model.

Care must be taken when using any type of viscous stabilization. Check the viscous forces (output variable VF) and compare them with the expected nodal forces to make sure that the viscous forces do not dominate the solution. If necessary, follow the stabilized step with another step in which stabilization is not used or with a step in which a much smaller amount of damping is used. This will allow the model to re-equilibriate without the viscous forces.

With any of the aforementioned stabilization techniques, the energy dissipated by the artificial viscous forces (output variables ALLSD, ALLVD, ALLCCSD) should remain small compared to the total internal energy (output variable ALLIE) in the problem.