Ensuring Simulation Stability for Convergence and Contact in Non-linear FEA

Non-linear FEA (finite element analysis) presents unique challenges, particularly in achieving stable and convergent solutions. Abaqus provides a range of tools and techniques to address these challenges effectively. This guide explores essential methods to ensure simulation stability using Abaqus.

Essential tools and techniques using Abaqus

Boundary conditions

Boundary conditions are critical in defining how the model interacts with its environment. In Abaqus, proper application of boundary conditions can significantly impact the convergence of a non-linear analysis. Ensure that boundary conditions are applied accurately to reflect the physical constraints of the problem. Misapplied or overly restrictive boundary conditions can lead to non-convergence or unrealistic results. For example, it is possible to create boundary conditions in Abaqus/CAE and control how they take effect through different steps where different load cases are applied.

Managing boundary conditions effectively involves using the boundary conditions manager to activate or deactivate conditions as needed across different steps.

Increment size control

Increment size control is essential in non-linear FEA to manage the load application process. Smaller increments can improve convergence by allowing the solver to handle non-linearities more effectively. Abaqus provides options to adjust increment sizes dynamically based on the convergence behavior, which can help in achieving a stable solution. For highly non-linear problems, setting the initial increment size sufficiently small and adjusting the maximum increment size can prevent sudden stiffness changes from causing convergence issues.

Displacement control

Displacement control involves specifying displacements directly rather than forces. This method can be particularly useful in non-linear problems where force control might lead to instability. By controlling displacements, the solver can better manage the non-linear response of the model, leading to improved convergence. This approach is especially beneficial in contact problems where initial contact needs to be established without causing unconstrained rigid body motions.

Automatic stabilization

Automatic stabilization in Abaqus introduces artificial damping to help control instabilities during the analysis. This technique is particularly useful in cases where the model experiences sudden stiffness changes or contact issues. However, it should be used cautiously, as excessive stabilization can introduce errors into the simulation. The goal is to minimize stabilization energy relative to the total energy of the model. It is crucial to check the ALLSD (stabilization energy) against the ALLIE (internal energy) of the model, ensuring that ALLSD remains a small fraction (no more than 2%) of ALLIE.

General contact formulation

Abaqus’ general contact formulation allows for the automatic detection and management of contact interactions within the model. This feature simplifies the setup of complex contact scenarios and helps in achieving stable convergence by ensuring that contact conditions are handled accurately throughout the analysis.

Simplified modeling approach

Simplified modeling approaches can reduce computational complexity and improve convergence. This might involve using symmetry, reducing model size, or simplifying geometry and material properties. By focusing on the critical aspects of the problem, you can achieve more stable and efficient simulations. Starting with a simplified model and gradually adding details can help identify and resolve sources of convergence difficulties.

Unsymmetric solver

The unsymmetric solver in Abaqus is designed to handle problems where the stiffness matrix is not symmetric, which is common in non-linear analyses involving contact or material non-linearities. Using the unsymmetric solver can improve convergence in these challenging scenarios. For problems with significant friction or relative finite sliding of contacting surfaces, invoking the unsymmetric solver can enhance the convergence rate.

Hybrid elements

Hybrid elements combine the benefits of different element formulations to improve convergence in non-linear analyses. These elements can handle complex deformation patterns and material behaviors more effectively, leading to more stable solutions. Hybrid elements are particularly useful for nearly incompressible materials, where standard elements might struggle to provide accurate results.

Summary

Achieving simulation stability in non-linear FEA requires a combination of carefully considered techniques and tools. Abaqus offers robust solutions for simulating complex real-world scenarios where linear assumptions fall short. These simulations are essential in applications involving material non-linearity, geometric non-linearity, and contact non-linearity. Whether validating new designs, improving existing ones, or analyzing failures, Abaqus provides the necessary tools to ensure stability, convergence, and accuracy in non-linear simulations. Employing the techniques outlined in this guide can help engineering teams accelerate development cycles while enhancing product performance and reliability.