### Abstract

Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work, the mechanics of cross-linked networks with crimped athermal fibers, with and without an embedding elastic matrix, is studied. The dependence of the effective network stiffness on the fraction of nonstraight fibers and the relative crimp amplitude (or tortuosity) is studied using finite element simulations of networks with sinusoidally curved fibers. A semi-analytic model is developed to predict the dependence of network modulus on the crimp amplitude and the bounds of the stiffness reduction associated with the presence of crimp. The transition from the linear to the nonlinear elastic response of the network is rendered more gradual by the presence of crimp, and the effect of crimp on the network tangent stiffness decreases as strain increases. If the network is embedded in an elastic matrix, the effect of crimp becomes negligible even for very small, biologically relevant matrix stiffness values. However, the distribution of the maximum principal stress in the matrix becomes broader in the presence of crimp relative to the similar system with straight fibers, which indicates an increased probability of matrix failure.

Original language | English (US) |
---|---|

Article number | 041008 |

Journal | Journal of Applied Mechanics, Transactions ASME |

Volume | 83 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2016 |

### Fingerprint

### Cite this

*Journal of Applied Mechanics, Transactions ASME*,

*83*(4), [041008]. https://doi.org/10.1115/1.4032465

**Effect of fiber crimp on the elasticity of random fiber networks with and without embedding matrices.** / Ban, Ehsan; Barocas, Victor H.; Shephard, Mark S.; Picu, Catalin R.

Research output: Contribution to journal › Article

*Journal of Applied Mechanics, Transactions ASME*, vol. 83, no. 4, 041008. https://doi.org/10.1115/1.4032465

}

TY - JOUR

T1 - Effect of fiber crimp on the elasticity of random fiber networks with and without embedding matrices

AU - Ban, Ehsan

AU - Barocas, Victor H.

AU - Shephard, Mark S.

AU - Picu, Catalin R.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work, the mechanics of cross-linked networks with crimped athermal fibers, with and without an embedding elastic matrix, is studied. The dependence of the effective network stiffness on the fraction of nonstraight fibers and the relative crimp amplitude (or tortuosity) is studied using finite element simulations of networks with sinusoidally curved fibers. A semi-analytic model is developed to predict the dependence of network modulus on the crimp amplitude and the bounds of the stiffness reduction associated with the presence of crimp. The transition from the linear to the nonlinear elastic response of the network is rendered more gradual by the presence of crimp, and the effect of crimp on the network tangent stiffness decreases as strain increases. If the network is embedded in an elastic matrix, the effect of crimp becomes negligible even for very small, biologically relevant matrix stiffness values. However, the distribution of the maximum principal stress in the matrix becomes broader in the presence of crimp relative to the similar system with straight fibers, which indicates an increased probability of matrix failure.

AB - Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work, the mechanics of cross-linked networks with crimped athermal fibers, with and without an embedding elastic matrix, is studied. The dependence of the effective network stiffness on the fraction of nonstraight fibers and the relative crimp amplitude (or tortuosity) is studied using finite element simulations of networks with sinusoidally curved fibers. A semi-analytic model is developed to predict the dependence of network modulus on the crimp amplitude and the bounds of the stiffness reduction associated with the presence of crimp. The transition from the linear to the nonlinear elastic response of the network is rendered more gradual by the presence of crimp, and the effect of crimp on the network tangent stiffness decreases as strain increases. If the network is embedded in an elastic matrix, the effect of crimp becomes negligible even for very small, biologically relevant matrix stiffness values. However, the distribution of the maximum principal stress in the matrix becomes broader in the presence of crimp relative to the similar system with straight fibers, which indicates an increased probability of matrix failure.

UR - http://www.scopus.com/inward/record.url?scp=84957035988&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957035988&partnerID=8YFLogxK

U2 - 10.1115/1.4032465

DO - 10.1115/1.4032465

M3 - Article

C2 - 27222599

AN - SCOPUS:84957035988

VL - 83

JO - Journal of Applied Mechanics, Transactions ASME

JF - Journal of Applied Mechanics, Transactions ASME

SN - 0021-8936

IS - 4

M1 - 041008

ER -