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Accurate Prediction of Stress in Fibers with Distributed Orientations Using Generalized High-Order Structure Tensors
Daniel H Cortes1, Dawn M Elliott1
1Department of Biomedical Engineering, University of Delaware, Newark, DE.
Mechanics of Materials : an International Journal
|June 14, 2014
Summary
A new Generalized High-Order Structure Tensors (GHOST) formulation accurately predicts collagen fiber stress in connective tissues. This method is computationally efficient, reducing the effort needed for analyzing fibrous tissue mechanics.
Area of Science:
- Biomechanics
- Materials Science
- Computational Mechanics
Background:
- Collagen fiber orientation significantly influences connective tissue mechanics.
- Existing angular integration methods for distributed fiber orientations are accurate but computationally intensive for finite element analysis.
Purpose of the Study:
- To introduce and validate a pre-integrated Generalized High-Order Structure Tensors (GHOST) formulation.
- To improve the accuracy and computational efficiency of modeling fibrous connective tissue mechanics.
Main Methods:
- Developed a GHOST formulation for modeling distributed fiber orientations.
- Presented simplified GHOST versions for transversely-isotropic and planar fiber distributions.
- Compared GHOST with angular integration under various loading, fiber, and material non-linearity conditions.
Main Results:
- The GHOST formulation achieved stress prediction errors below 10% for uniaxial and biaxial tension.
- Higher-order structure tensors in GHOST minimized errors caused by fiber non-linearity.
- Optimal GHOST performance was observed with elliptical fiber density and binomial strain energy functions.
Conclusions:
- The GHOST formulation accurately predicts stress in fibers with distributed orientations.
- GHOST significantly reduces computational demands for analyzing fibrous tissue mechanics.
- This method offers a more efficient approach to biomechanical modeling of connective tissues.
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