### Abstract

The mechanical behavior of a three-dimensional cross-linked fiber network embedded in a matrix is studied in this work. The network is composed from linear elastic fibers which store energy only in the axial deformation mode, while the matrix is also isotropic and linear elastic. Such systems are encountered in a broad range of applications, from tissue to consumer products. As the matrix modulus increases, the network is constrained to deform more affinely. This leads to internal forces acting between the network and the matrix, which produce strong stress concentration at the network cross-links. This interaction increases the apparent modulus of the network and decreases the apparent modulus of the matrix. A model is developed to predict the effective modulus of the composite and its predictions are compared with numerical data for a variety of networks.

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

Pages (from-to) | 6398-6405 |

Number of pages | 8 |

Journal | Soft Matter |

Volume | 9 |

Issue number | 28 |

DOIs | |

State | Published - Jul 28 2013 |

### Fingerprint

### Cite this

*Soft Matter*,

*9*(28), 6398-6405. https://doi.org/10.1039/c3sm50838b

**Cross-linked fiber network embedded in an elastic matrix.** / Zhang, L.; Lake, S. P.; Barocas, Victor H; Shephard, M. S.; Picu, R. C.

Research output: Contribution to journal › Article

*Soft Matter*, vol. 9, no. 28, pp. 6398-6405. https://doi.org/10.1039/c3sm50838b

}

TY - JOUR

T1 - Cross-linked fiber network embedded in an elastic matrix

AU - Zhang, L.

AU - Lake, S. P.

AU - Barocas, Victor H

AU - Shephard, M. S.

AU - Picu, R. C.

PY - 2013/7/28

Y1 - 2013/7/28

N2 - The mechanical behavior of a three-dimensional cross-linked fiber network embedded in a matrix is studied in this work. The network is composed from linear elastic fibers which store energy only in the axial deformation mode, while the matrix is also isotropic and linear elastic. Such systems are encountered in a broad range of applications, from tissue to consumer products. As the matrix modulus increases, the network is constrained to deform more affinely. This leads to internal forces acting between the network and the matrix, which produce strong stress concentration at the network cross-links. This interaction increases the apparent modulus of the network and decreases the apparent modulus of the matrix. A model is developed to predict the effective modulus of the composite and its predictions are compared with numerical data for a variety of networks.

AB - The mechanical behavior of a three-dimensional cross-linked fiber network embedded in a matrix is studied in this work. The network is composed from linear elastic fibers which store energy only in the axial deformation mode, while the matrix is also isotropic and linear elastic. Such systems are encountered in a broad range of applications, from tissue to consumer products. As the matrix modulus increases, the network is constrained to deform more affinely. This leads to internal forces acting between the network and the matrix, which produce strong stress concentration at the network cross-links. This interaction increases the apparent modulus of the network and decreases the apparent modulus of the matrix. A model is developed to predict the effective modulus of the composite and its predictions are compared with numerical data for a variety of networks.

UR - http://www.scopus.com/inward/record.url?scp=84879911676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879911676&partnerID=8YFLogxK

U2 - 10.1039/c3sm50838b

DO - 10.1039/c3sm50838b

M3 - Article

VL - 9

SP - 6398

EP - 6405

JO - Soft Matter

JF - Soft Matter

SN - 1744-683X

IS - 28

ER -