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Discretization error when using finite element models: analysis and evaluation of an underestimated problem.

Hendrik Schmidt¹, Tobias Alber, Tim Wehner

¹Institute of Orthopaedic Research and Biomechanics, University of Ulm, Helmholtzstrasse 14, 89081 Ulm, Germany. h.schmidt@uni-ulm.de

Journal of Biomechanics

|June 9, 2009

Summary

Finite element analysis mesh convergence is complex. Parameters like flank radii and contact conditions significantly impact results, showing that standard convergence tests may not always yield reliable solutions.

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Area of Science:

Biomechanics
Computational Mechanics
Finite Element Analysis

Background:

Mesh convergence is crucial for accurate finite element analyses.
Insufficient mesh convergence testing can lead to unreliable simulation results.
Various parameters can influence mesh convergence behavior.

Purpose of the Study:

To investigate the influence of different parameters on mesh convergence in finite element analysis.
To evaluate the impact of flank radii and contact conditions on simulation accuracy.
To compare mesh convergence behavior between implicit and explicit solvers.

Main Methods:

Utilized a simplified axis-symmetrical finite element model of a pedicle screw-bone construct for pull-out tests.
Performed parameter studies varying flank radii and bone-screw interface contact conditions.
Employed both implicit and explicit solvers, considering parameters like convergence criteria, substeps, velocity, and material density.

Main Results:

Mesh convergence was significantly affected by flank radii and contact conditions.
Implicit solver reaction forces converged rapidly, but von-Mises stress exhibited convergence issues.
Explicit solver maximum von-Mises stresses converged quickly, with pull-out velocity being a key factor.

Conclusions:

Mesh convergence testing in finite element analysis requires careful consideration of multiple parameters.
Standard convergence tests may not guarantee satisfactory or acceptable solutions.
Accurate simulations necessitate a thorough understanding of parameter influence on mesh convergence.