1. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 Coordinate system and definitions of θ, φ, and p for a rigid fiber Figure Legend:

2. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 Geometry of two neighboring fibers, showing the gap distance h ij Figure Legend:

3. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 (a) The image of the new parent fiber j intersecting with a pre-existing parent fiber i, and (b) a unit cell containing 272 parent fibers; B = 1.0, r = 100 and ϕ = 2% Figure Legend:

4. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 Maximum packing fractions at the RSA jamming limit in terms of the fiber aspect ratio. Maximum random packing fractions, experimentally found (solid line) ϕ 0 = 5.3/r, and theoretically defined (dotted line) ϕ 0 = 4.0/r by Evans and Gibson [2]. Figure Legend:

5. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 A sketch of the definitions of the shell radius ρ and shell thickness Δρ associated with the reference fiber i and the relative orientation angles η and λ with respect to the fiber j Figure Legend:

6. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 The (a) long-range, and (b) short-range radial pair spatial-distribution function for the RSA and equilibrium configurations Figure Legend:

7. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 The (a) long-range, and (b) short-range center-to-center orientation-distribution function for the RSA and equilibrium configurations Figure Legend:

8. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 A cross section of the spherocylindrical shell surrounding the reference fiber i of length l and a neighboring fiber j. The angle between the two fibers is η. The shell excluded area is obtained by following the center of the fiber j while traveling around fiber i, keeping constant the surface shortest distances between the two fibers. Figure Legend:

9. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 The spatial (top) and orientation (bottom) shortest-distance distribution functions for the RSA and equilibrium configurations Figure Legend:

10. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 Definition of angles λ and η. The spherical shell of the reference fiber j is divided into concentric bins of angular size Δλ = 10 deg. Figure Legend:

11. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 The function H(ρ,λ,η) is plotted in terms of λ and η showing (a) RSA, and (b) equilibrium orientational structures at the most probable separation ρ = 8.25d Figure Legend:

12. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537 The function H(ρ,λ,η) plotted (a) versus η at fixed λ = 0 and π/2, and (b) versus λ at fixed η = 0 and η = π/2. In all cases, ρ is fixed to ρ max = 8.25d. Figure Legend:

13. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537

14. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry J. Appl. Mech. 2013;80(5):051007-051007-10. doi:10.1115/1.4023537