Wear Simulation
Wear: Theoretical Foundations
What is Wear Simulation?
Professor, can we simulate wear (material loss) using FEM?
Yes. It calculates material removal on contact surfaces based on the Archard wear law and updates the geometry.
$V$ is wear volume, $s$ is sliding distance, $K$ is wear coefficient, $F_n$ is normal force, $H$ is hardness.
Wear is proportional to sliding distance. It's a simple model.
The Archard equation is the simplest, but provides practical accuracy for many wear problems.
Implementation in FEM
Wear simulation procedure (iterative):
1. Contact Analysis — Calculate contact pressure and sliding amount
2. Wear Amount Calculation — Wear depth using Archard's equation
3. Mesh Update — Move nodes by the worn amount
4. Contact Analysis Again — With the updated geometry
5. Iterate until convergence
Updating the mesh each time seems tough.
Can be automated using Abaqus UMESHMOTION (adaptive meshing) or LS-DYNA *MAT_WEAR.
Summary
Key Points:
- Archard Wear Law — $dV/ds = K F_n / H$
- Iteration of Contact → Wear Amount → Mesh Update — Time evolution of wear
- Abaqus UMESHMOTION — Updates wear surface with adaptive mesh
- Bearings, Gears, Brake Pads — Main applications
Archard Wear Law 1953
The Archard wear law, which forms the basis of wear simulation, originates from a paper published by J.F. Archard and W. Hirst in 1953. It is a simple proportional law: wear volume V = k × W × s / H (k: wear coefficient, W: load, s: sliding distance, H: hardness). Even after over 60 years, it continues to be used as the standard model for industrial wear prediction. This paper preceded the launch of the Wear journal (1957) and greatly contributed to the establishment of the academic field of tribology.
Computational Methods for Wear
FEM Implementation of Wear
```
*ADAPTIVE MESH, TYPE=CONTACT SURFACE
wear_surface
*ADAPTIVE MESH CONTROLS, MESHING FREQUENCY=1
*UMESHMOTION $ Calculate wear amount in user subroutine
```
```
*MAT_WEAR
K, H $ Archard coefficient and hardness
```
So LS-DYNA has a dedicated wear material model.
*MAT_WEAR automatically thins contact surface elements to represent wear. Wear progresses without remeshing.
Summary
Numerical Scheme for Geometry Update
The numerical core of wear FEM lies in the iterative process of "wear amount → node movement → mesh update → re-contact". In the Eulerian approach proposed by Podra & Andersson (1997), the wear amount for one cycle is calculated using the Archard law, boundary nodes are retracted in the normal direction, and then element distortion is corrected using a smoothing algorithm. This method is still referenced as a reference implementation for ABAQUS UMESHMOTION user subroutine implementations.
Wear in Practice
Wear in Practice
Practical Checklist
Cutting Tool Wear Prediction
FEM incorporating the Archard wear law for metal cutting tool life prediction has become widespread since the 2000s. In an analysis of carbide end mills published by Sandvik in the 2010s using the DEFORM code, the machining length until tool flank wear width VB=0.3mm was predicted under conditions of cutting speed 200m/min and depth of cut 1mm, with an error of ±18% compared to experimental values. This result is used for design decisions in tool coating optimization.
Wear: Software & Solver Comparison
Wear Tools
Selection Guide
Advanced Wear Models Beyond Archard
While Archard's law remains the industrial standard, several advanced wear models have been proposed since the 1980s. The Kragelsky model incorporates material hardness variation, the Lim-Ashby wear map classifies wear regimes (adhesive, abrasive, surface fatigue, tribochemical), and the Zum Gahr model accounts for grain size effects. However, their computational costs and parameter identification requirements limit their practical adoption. For routine engineering practice, Archard's law remains the first choice due to its simplicity and reasonable predictive accuracy.