1. Introduction

Finite element analysis (FEA) is a powerful tool for engineers to simulate the behavior of complex structures and systems under various loading conditions. Abaqus, a leading FEA software, provides a robust set of tools for modeling and analysis. However, like any numerical method, FEA is susceptible to errors, one of the most critical being element distortion.

Distorted elements occur when the underlying mesh, which discretizes your model into small elements, becomes excessively deformed.  This deformation can happen due to large strains, incorrect element choices, or aggressive loads.  Ideal element shapes are essential for accurate calculation of stresses, strains, and displacements within your model. When elements become distorted, these calculations become unreliable.

The consequences of distorted elements in Abaqus simulations can range from subtle inaccuracies to complete analysis failure.  Inaccurate results can lead to poor design decisions, potentially causing structural failures or unexpected system performance.  Convergence issues, where the Abaqus solver struggles to find a solution, hinder efficiency and waste computational time.  In the worst-case scenario, severe distortion can force the analysis to terminate prematurely, leaving you with no results at all.

In this article, we’ll delve into the causes of element distortion in Abaqus,  explain how to identify distorted elements, and provide various strategies to fix and prevent this critical issue. By the end, you’ll have a stronger understanding of how to ensure accurate and reliable Abaqus simulations.

2. Causes of Element Distortion

Several factors can contribute to element distortion in Abaqus. Understanding these causes is crucial for both troubleshooting existing problems and proactively preventing future distortion issues.

2.1. Large Deformations and Strains:

Plastic Deformation: When materials undergo permanent deformation beyond their elastic limit, elements can become significantly distorted.

Buckling & Bending: Slender structures subjected to compressive or bending loads may exhibit large deformations leading to distorted elements.

Dynamic Events: High-speed impacts, vibrations, or sudden changes in loading can cause rapid mesh deformation and potential distortion.

2.2. Incorrect Element Type or Formulation:

Linear vs. Quadratic Elements: Linear elements (simpler shapes) are more prone to distortion under large deformations compared to quadratic elements (more curved shapes).

Reduced Integration: While computationally efficient, reduced integration elements can be more susceptible to distortion, especially under bending loads.

2.3. Poor Mesh Quality or Excessively Coarse Mesh

Irregular Element Shapes: Highly skewed elements or elements with poor aspect ratios are more likely to distort.

Coarse Mesh: A mesh that’s too coarse might not capture the geometry or deformation gradients accurately, leading to distorted elements in critical areas.

2.4. Unrealistic Material Properties:

Excessively Soft Materials: If a material is defined as too soft or has near-zero stiffness, elements may deform uncontrollably under load.

Incompressible Materials: Modeling materials like rubber requires special care, as nearly incompressible materials can cause distortion issues with standard element formulations.

2.5. Aggressive Loading Rates:

Sudden Loads: Applying forces or displacements too quickly may not allow the mesh to deform gradually, leading to distortion.

Dynamic Simulations: High-speed simulations inherently involve larger deformations and are more prone to distortion issues.

2.6. Contact Issues in the Model

Incorrect Contact Definitions: Poorly defined contact surfaces, incorrect friction parameters, or overconstraint can lead to unrealistic forces that distort elements at contact interfaces.

In the table below, we have briefly explained the causes of this phenomenon when solving the problem along with the solutions to solve it. Keep in mind that this valuable table is the result of years of research and analysis of our institution.

No.	Main Reason	Causes of Element Distortion	Solution Methods
1	Large Deformations and Strains	Plastic Deformation	Solution: Utilize element types with better large strain capabilities (e.g., quadratic elements).Consider alternative formulations like hyperelastic material models for materials that undergo significant plastic deformation.
		Buckling & Bending	Solution: Refine the mesh in areas prone to buckling or high bending moments.Consider using more robust element types for slender structures (e.g., shell elements for beams and plates).
		Dynamic Events	Solution: Employ Abaqus/Explicit solver, specifically designed for highly dynamic simulations. Reduce the loading rate or apply the load in smaller increments to allow for a more gradual mesh deformation.
2	Incorrect Element Type or Formulation	Linear vs. Quadratic Elements	Solution: If distortion arises with linear elements, switch to quadratic elements in critical areas for improved accuracy under large deformations.
		Reduced Integration	Solution: Carefully assess the trade-off between computational efficiency and accuracy. Consider switching to full integration elements if distortion becomes a significant issue.
3	Poor Mesh Quality or Excessively Coarse Mesh	Irregular Element Shapes	Solution: Refine the mesh and improve element quality during mesh generation. Ensure a smooth transition between elements of different sizes.
		Coarse Mesh	Solution: Refine the mesh in areas where large deformations or stress concentrations are expected. Conduct mesh convergence studies to determine an appropriate mesh density.
4	Unrealistic Material Properties	Excessively Soft Materials	Solution: Carefully review material properties and ensure they accurately represent the real material behavior.If necessary, define more complex material models that capture the material’s non-linear behavior.
		Incompressible Materials	Solution: Utilize specialized element formulations designed for nearly incompressible materials. Abaqus offers several options for such materials.
5	Aggressive Loading Rates	Sudden Loads	Apply loads gradually in smaller increments. Consider mass scaling (Abaqus/Explicit).
		Dynamic Simulations	Choose appropriate time step size. Smaller time steps help, but increase computational cost.
6	Contact Issues in the Model	Incorrect Contact Definitions	Review contact surfaces and interactions. Adjust friction parameters for realistic contact.
		Overconstraint	Ensure adequate constraints without over-constraining the model.

3. Identifying Distorted Elements

Abaqus offers several mechanisms to help you pinpoint distorted elements in your model. By proactively identifying problematic areas, you can take corrective actions before the distortion jeopardizes the accuracy or stability of your simulation.

3.1. Abaqus Visualization Tools

Element Quality Plots: Within the Visualization module of Abaqus/CAE, you can create plots that color-code elements based on their quality metrics. Common metrics used are the Jacobian, aspect ratio, and others (explained later). Look for areas with heavily distorted elements indicated by a distinct color change within the quality plot.

Deformed Shape Display: Toggling on the deformed shape display, and potentially exaggerating the deformation scale, can visually highlight areas where mesh elements have become severely distorted.

Model Queries: You can query your model in Abaqus/CAE to list elements that fall below a threshold value for a given quality metric. This provides a precise list of problematic elements.

3.2. Warning and Error Messages

Warnings During Analysis: Abaqus often issues warning messages in the message file (.msg) if excessive element distortion is detected during the simulation. Pay close attention to these warnings, as they will indicate the step and potentially the specific elements of concern.

Error Termination: In severe cases, distortion can cause the analysis to terminate prematurely with an error message. These errors often point towards distorted elements as the root cause.

3.3. Interpreting Element Quality Metrics

Jacobian: The Jacobian measures the deviation of an element from its ideal shape in 3D. A perfect hexahedral (brick) element should have a Jacobian of 1 at all points. Values significantly less than 1 indicate distortion and potential for inaccurate results.

Aspect Ratio: This metric measures the ratio of the longest to the shortest edge of an element. Elements with high aspect ratios (very long and thin) are susceptible to distortion and numerical inaccuracies.

Other Metrics: Abaqus provides additional quality metrics like warpage, skew, etc. Refer to the Abaqus documentation for detailed definitions of these metrics.

Important Notes:

• The precise values of quality metrics that indicate “distortion” can be problem-dependent. Experience and some trial and error will help you determine critical thresholds for your models.
• Some element distortion may be unavoidable in simulations with complex geometry or large deformations. In these cases, you’ll need to balance the need for accuracy with the computational cost of excessive mesh refinement.

4. Strategies for Fixing Distorted Elements

This section aims to provide practical solutions for addressing distorted elements that have been identified in your Abaqus model. The goal isn’t merely to get rid of distortion at all costs, but rather to find the best approach for your specific simulation to achieve a balance between accuracy and computational efficiency. Let’s investigate the issue below. Keep in mind the insights gained from the previous table.

4.1. Mesh Refinement:

When: Mesh refinement is a primary strategy for distortion in localized areas of large deformation or complex geometry.

How: Explain the need for targeted refinement (not just everywhere), techniques for localized refinement, and the importance of smooth transitions between coarse and fine regions of the mesh.

4.2. Element Type and Formulation:

Choosing appropriate elements: Discuss when quadratic elements offer advantages over linear, and when to use hybrid formulations for incompressible materials.

Reduced Integration: Offer a brief reminder of the trade-off involved (computational speed vs. potential for “hourglassing” instability).

4.3. Smoothing Algorithms:

Need for Smoothing: Explain that sometimes existing mesh quality is poor, and refinement alone isn’t enough.

Laplacian and Volume Smoothing: Give a very high-level description of the idea behind these algorithms, and when each might be used.

4.4. Material Properties:

Unrealistic Values: Stress that distortion might be due to errors in defining your material model (too soft, etc.), and not always a mesh/solver issue.

4.5. Loading Rate:

Slower Loading/Increments: Recap the idea that sudden loads are problematic, and how smaller increments allow more gradual deformation.

4.6. Contact Adjustments:

Reviewing definitions and parameters: Reiterate that poor contact setup can cause localized distortion, and it’s worth careful review.

4.7. Solution Techniques:

Abaqus/Explicit: Explain the fundamental difference between Explicit and implicit solvers, when Explicit is better for high-deformation problems, and the trade-offs involved.

4.8. Additional Considerations

Iterative Approach: Emphasize that fixing distortion often involves trying several of these techniques in combination.

Prevention: Remind readers that many of these strategies also apply to minimizing distortion in the first place, through good initial modeling practices.

5. Prevention Best Practices

While fixing distorted elements is often necessary, the most effective approach is to minimize the occurrence of distortion in the first place. By following these best practices, you can significantly improve the quality of your Abaqus simulations and reduce the need for troubleshooting later.

5.1. Good Meshing Habits During Model Creation

Element Shape and Quality: Strive to create a mesh composed mostly of elements with regular shapes. Avoid elements with high aspect ratios, small angles, or excessive skewness. Abaqus offers element quality checks to help with this.

Mesh Density in Critical Areas: Identify regions in your model where high stresses, strains, or nonlinear behavior are expected (e.g., contact zones, areas with notches or small geometric details). Refine the mesh in these areas to capture deformations more accurately.

Smooth Mesh Transitions: Ensure that changes in mesh density flow smoothly, avoiding abrupt jumps in element size, which can act as distortion points.

5.2. Conducting Mesh Convergence Studies

The principle: A mesh convergence study involves running your simulation with progressively finer meshes until there’s minimal change in results of interest. This helps determine the optimal mesh density for accuracy without excessive computational cost.

Procedure: Start with a coarse mesh. Refine it systematically, re-running the analysis each time. Plot a relevant result (e.g., peak stress, displacement) vs. mesh density. When the plot becomes relatively flat, you’ve likely reached convergence.

5.3. Applying Loads and Boundary Conditions Gradually

Avoiding Sudden Changes: Applying forces, displacements, or temperatures too suddenly can shock the mesh and lead to distortion.

Smooth Ramping: Use Abaqus’s “amplitude” feature to gradually increase the magnitude of loads or boundary conditions over time or analysis steps. This allows the mesh to adapt more naturally.

5.4. Validating Material Models and Properties

Accurate Representation: Ensure your chosen material models and their corresponding properties closely match the real-world material behavior. Incorrect or unrealistic material models can cause excessive and non-physical deformations.

Sources of Data: Obtain reliable material property data from experimental testing, reputable material databases, or published literature.