Applicability of hierarchical fiber bundle materials to mechanical environments
Source abstract
Abstract
Biomaterials use a hierarchical structure to optimize their self-healing behavior, for instance. However, the behavior may be constrained under different mechanical environments. In this paper, a system is suggested that the mechanical environment is modeled as a spring connected in series with the fiber bundle material. For the spring, the elastic behavior with stiffness is obeyed while, for the fiber bundle material, the nonlinear elastic constitutive relation is obeyed according to the Weibull distribution and the Daniels’ theory. Relying on the principle of total potential, the applicability condition is proposed for the system and the critical stiffness is thus derived for the spring. The applicability of hierarchical fiber bundle materials is finally investigated. The results show that the hierarchy can significantly change the critical stiffness, and hence demonstrates quite different applicability to a given mechanical environment.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Calcium Carbonate Crystallization and Inhibition · Material Selection and Properties · Bone Tissue Engineering Materials
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (38)
Show source-provided references
1. Amitrano D, Girard L (2016) Fiber bundle model under fluid pressure. Phys Rev E 93:03300310.1103/PhysRevE.93.033003 ↗
2. Banerjee S (2014) On the mechanical properties of hierarchical lattices. Mech Mater 72:19–3210.1016/j.mechmat.2014.01.009 ↗
3. Bosia F, Abdalrahman T, Pugno NM (2012) Investigating the role of hierarchy on the strength of composite materials: evidence of a curial synergy between hierarchy and material mixing. Nanoscale 4:1200–120710.1039/c2nr11664b ↗
4. Bosia F, Croce FD, Pugno NM (2013) Systematic numerical investigation of the role hierarchy in heterogeneous bio-inspired materials. J Mech Behav Biomed Mater 9:34–4210.1016/j.jmbbm.2012.10.020 ↗
5. Carpinteri A, Paggi M (2009) A top-down approach for the predication of hardness and toughness of hierarchical materials. Chaos Solitons Fractals 42:2546–255210.1016/j.chaos.2009.03.150 ↗
6. Cehreli M, Sahin S, Akca K (2004) Role of mechanical environment and implant design on bone tissue differentiation: current knowledge and future context. J Dent 32:123–13210.1016/j.jdent.2003.09.003 ↗
7. Daniels HE (1945) The statistical theory of the strength of bundle of threads I. Proc R Soc A 183:405–43510.1098/rspa.1945.0011 ↗
8. Dunlop JWC, Hartmann MA, Brechet YJ, Fratzl P, Weinkamer R (2009) New suggestions for the mechanical control of bone remodeling. Calcif Tissue Int 85:45–5410.1007/s00223-009-9242-x ↗
9. Fratzl P, Weinkamer R (2007) Nature’s hierarchical materials. Prog Mater Sci 52:1263–133410.1016/j.pmatsci.2007.06.001 ↗
10. Gao HJ (2006) Application of fracture mechanics concepts to hierarchical biomechanics of bone and bone-like materials. Int J Fract 138:101–13710.1007/s10704-006-7156-4 ↗
11. Gautieri A, Vesentini S, Redealli A, Buehler MJ (2011) Hierarchical nanomechanics of collage microfibrils. Nat Preced 11:757–766
12. Guilak F, Mow VC (2000) The mechanical environment of the chondrocyte: a biphasic finite element of cell-matrix interactions in articular cartilage. J Biomech 33:1663–167310.1016/S0021-9290(00)00105-6 ↗
13. Hao SW, Yang H, Liang XZ (2017) Catastrophic failure and critical scaling laws of fiber bundle material. Materials 10:515–61410.3390/ma10050515 ↗
14. Jager I, Fratzl P (2000) Mineralized collagen fibers: a mechanical model with a staggered arrangement of mineral particles. Biol J 79:1737–1746
15. Ji XL, Li LX (2017) Mechanism of self-healing and hierarchy of fiber bundle materials. J Appl Phys (submitted)
16. Ji BH, Gao HJ (2004) Mechanical properties of nanostructure of biological materials. J Mech Phys Solids 52:1963–199010.1016/j.jmps.2004.03.006 ↗
17. Keller A, Hutter K (2014) A viscoelastic damage model for polycrystalline ice, inspired by Weibull-distribution fiber bundle model. Part I: constitutive models. Contin Mech Thermodyn 26:879–89410.1007/s00161-014-0348-7 ↗
18. Kim HJ, Chang SH, Jung HJ (2012) The simulation of tissue differentiation at a fracture gap using a mechano-regulation theory dealing with deviatoric strains in the presence of a composite bone plate. Compos Part B 43:978–98710.1016/j.compositesb.2011.09.011 ↗
19. Liu ZQ, Jiao D, Meyers MA, Zhang ZF (2015) Structure and mechanical properties of naturally occurring lighting weighting foam-filled cylinder—the peacock’s tail coverts shaft and its components. Acta Biomater 17:137–15110.1016/j.actbio.2015.01.035 ↗
20. Manca F, Giordano S, Palla PL, Cleri F (2014) Scaling shift in multicracked fiber bundles. Phys Rev Lett 113:25550110.1103/PhysRevLett.113.255501 ↗
21. McCarteny LN, Smith RL (1983) Statistical theory of the strength of fiber bundles. J Appl Mech 50:601–60810.1115/1.3167097 ↗
22. Mehboob H, Chang SH (2014) Evaluation of healing performance of biodegradable composite bone plate for simulated fractured tibia model by finite element analysis. Compos Struct 111:193–20410.1016/j.compstruct.2013.12.013 ↗
23. Meyers MA, Chen PY, Lin AY-M, Seki Y (2008) Biological materials: structure and mechanical properties. Prog Mater Sci 53:1–20610.1016/j.pmatsci.2007.05.002 ↗
24. Mishnaevsky L (2011) Hierarchical composites: analysis of the damage evolution based on fiber bundle model. Compos Sci Technol 71:450–46010.1016/j.compscitech.2010.12.017 ↗
25. Paramonov Y, Andersons J (2006) A new model family for the strength distribution of fiber in relation to their length. Mech Compos Mater 42:119–12810.1007/s11029-006-0023-6 ↗
26. Porwal PK, Beyerlein IJ, Phoenix SL (2006) Statistical strength of a twisted fiber bundle: an extension of Daniels equal-load-sharing parallel bundle theory. J Mech Mater Struct 8:1425–144710.2140/jomms.2006.1.1425 ↗
27. Pradhan S, Hansen A, Chakrabarti BK (2010) Failure process in elastic fiber bundle. Rev Mod Phys 82:449–55510.1103/RevModPhys.82.499 ↗
28. Pugno NM, Ruoff RS (2006) Nanoscale Weibull statistics. J Appl Phys 99:02430110.1063/1.2158491 ↗
29. Pugno NM, Bosia F, Abdalrahman T (2012) Hierarchical fiber bundle model to investigate the complex architecture of biological materials. Phys Rev E 85:01190310.1103/PhysRevE.85.011903 ↗
30. Qin Z, Cranford S, Ackbarow T, Buehler MJ (2009) Robustness-strength preference of hierarchical alpha-helical protein filaments. Int J Appl Mech 1:85–11210.1142/S1758825109000058 ↗
31. Roy C, Kundu S, Manna SS (2013) Scaling form for relaxation time of fiber bundle model. Phys Rev E 87:062317
32. Sassinek SL, Main IG (2013) Time evolution of damage due to environmentally assisted aging in a fiber bundle model. Phys Rev E 88:03280210.1103/PhysRevE.88.032802 ↗
33. Schulte FA, Ruffoni D, Lambers FM, Christen D, Webster DJ, Kuhn G, Muller R (2013) Local mechanical stimuli regulate bone formation and resorption in mice at the tissue level. PLoS ONE 8:e6217210.1371/journal.pone.0062172 ↗
34. Screen HRC (2009) Hierarchical approaches to understanding tendon mechanics. J Biomech Sci Eng 4:481–49910.1299/jbse.4.481 ↗
35. Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech Trans ASME 51:293–29710.1115/1.4010337 ↗
36. Weiner S, Wagner HD (1998) The material bone: structure-mechanical function relations. Ann Rev Mater Sci 28:271–29810.1146/annurev.matsci.28.1.271 ↗
37. Yao HM, Gao HJ (2006) Mechanics of robust and releasable adhesion in biology: bottom-up designed hierarchical structures of gecko. J Mech Phys Solids 54:1120–114610.1016/j.jmps.2006.01.002 ↗
38. Zienkiewicz OC, Taylor RL (2005) The finite element method: its basis and fundamentals, 6th edn. Elsevier Butterworth-Heinemann, Oxford