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Abstract Fiber networks are the primary structural components of many biological structures, including the cell cytoskeleton and the extracellular matrix. These materials exhibit global nonlinearities, such as stiffening in extension and shear, during which the fibers bend and align with the direction of applied loading. Precise details of deformations at the scale of the fibers during strain stiffening are still lacking, however, as prior work has studied fiber alignment primarily from a qualitative perspective, which leaves incomplete the understanding of how the local microstructural evolution leads to the global mechanical behavior. To fill this gap, we studied how axial forces are transmitted inside the fiber network along paths called force chains, which continuously evolve during the course of deformation. We performed numerical simulations on two-dimensional networks of random fibers under uniaxial extension and shear, modeling the fibers using beam elements in finite element software. To quantify the force chains, we identified all chains of connected fibers for which the axial force was larger than a preset threshold and computed the total length of all such chains. To study the evolution of force chains during loading, we computed the derivative of the total length of all force chains with respect to the applied engineering strain. Results showed that the highest rate of evolution of force chains coincided with the global critical strain for strain stiffening of the fiber network. Therefore, force chains are an important factor connecting understanding of the local kinematics and force transmission to the macroscale stiffness of the fiber network.
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Methodological Aspects and Mesh Convergence in Numerical Analysis of Athermal Fiber Network Material Deformation
A balance between model complexity, accuracy, and computational cost is a central concern in numerical simulations. In particular, for stochastic fiber networks, the non-affine deformation of fibers, related non-linear geometric features due to large global deformation, and size effects can significantly affect the accuracy of the computer experiment outputs and increase the computational cost. In this work, we systematically investigate methodological aspects of fiber network simulations with a focus on the output accuracy and computational cost in models with cellular (Voronoi) and fibrous (Mikado) network architecture. We study both p and h-refinement of the discretizations in finite element solution procedure, with uniform and length-based adaptive h-refinement strategies. The analysis is conducted for linear elastic and viscoelastic constitutive behavior of the fibers, as well as for networks with initially straight and crimped fibers. With relative error as the determining criterion, we provide recommendations for mesh refinement, comment on the necessity of multiple realizations, and give an overview of associated computational cost that will serve as guidance toward minimizing the computational cost while maintaining a desired level of solution accuracy.
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- Award ID(s):
- 2022489
- PAR ID:
- 10509311
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Fibers
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2079-6439
- Page Range / eLocation ID:
- 9
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/fib12010009
