1
|
Yamaguchi T, Onoue Y, Sawae Y. Topology and Toughening of Sparse Elastic Networks. PHYSICAL REVIEW LETTERS 2020; 124:068002. [PMID: 32109093 DOI: 10.1103/physrevlett.124.068002] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Revised: 12/05/2019] [Accepted: 01/16/2020] [Indexed: 06/10/2023]
Abstract
The toughening of sparse elastic networks, such as hydrogels, foams, or meshes against fracture is one of the most important problems in materials science. However, the principles of toughening have not yet been established despite urgent engineering requirements and several efforts made by materials scientists. Here we address the above-mentioned problem by focusing on the topology of a network. We perform fracture experiments for two-dimensional periodic lattices fabricated from rubber strings and connecters with well-defined topological structures. We find that systematic increase in the largest coordination number while maintaining the average coordination number (=4) as constant leads to significant improvement in toughness. We reproduce the observed toughening behavior through numerical simulations and confirm that the stress concentration in the vicinity of a crack tip can be controlled by the topology of the network. This provides a new strategy for creating tough sparse elastic networks, especially hydrogels.
Collapse
Affiliation(s)
- Tetsuo Yamaguchi
- Department of Mechanical Engineering, Kyushu University, Fukuoka 819-0395, Japan
| | - Yudai Onoue
- Department of Mechanical Engineering, Kyushu University, Fukuoka 819-0395, Japan
| | - Yoshinori Sawae
- Department of Mechanical Engineering, Kyushu University, Fukuoka 819-0395, Japan
- International Institute for Carbon-Neutral Energy Research, Kyushu University, Fukuoka 819-0395, Japan
| |
Collapse
|
2
|
Paturej J, Popova H, Milchev A, Vilgis TA. Force-induced breakdown of flexible polymerized membrane. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021805. [PMID: 22463234 DOI: 10.1103/physreve.85.021805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2011] [Indexed: 05/31/2023]
Abstract
We consider the fracture of a free-standing two-dimensional (2D) elastic-brittle network to be used as protective coating subject to constant tensile stress applied on its rim. Using a molecular-dynamics simulation with a Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphenelike hexagonal sheet for different pulling force f and temperature T. We find that bond rupture occurs almost always at the sheet periphery, and the first mean breakage time <τ> of bonds decays with membrane size as <τ> ∝N(-β), where β≈0.50±0.03 and N denotes the number of atoms in the membrane. The probability distribution of bond scission times t is given by a Poisson function W(t)∝t(1/3)exp(-t/<τ>). The mean failure time <τ(r)> necessary to rip off the sheet declines with growing size N as a power law <τ(r)>∝N(-φ(f)). We also find <τ(r)>∝exp(ΔU(0)/k(B)T), where the nucleation barrier for crack formation ΔU(0)∝f(-2), in agreement with Griffith's theory. <τ(r)> displays an Arrhenian dependence of <τ(r)> on temperature T. Our results indicate a rapid increase in crack spreading velocity with growing external tension f.
Collapse
Affiliation(s)
- J Paturej
- Max Planck Institute for Polymer Research, 10 Ackermannweg, D-55128 Mainz, Germany
| | | | | | | |
Collapse
|
3
|
Holtzman R, Juanes R. Crossover from fingering to fracturing in deformable disordered media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:046305. [PMID: 21230388 DOI: 10.1103/physreve.82.046305] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2010] [Revised: 09/13/2010] [Indexed: 05/30/2023]
Abstract
We investigate the displacement of one fluid by another in a deformable medium with pore-scale disorder. We develop a model that captures the dynamic pressure redistribution at the invasion front and the feedback between fluid invasion and microstructure rearrangement. Our results suggest how to collapse the transition between invasion percolation and viscous fingering in the presence of quenched disorder. We predict the emergence of a fracturing pattern for sufficiently deformable media, in agreement with observations of drainage in granular material. We identify a dimensionless number that appears to govern the crossover from fingering to fracturing.
Collapse
Affiliation(s)
- Ran Holtzman
- Massachusetts Institute of Technology, 77 Massachusetts Avenue, Building 48-319, Cambridge, Massachusetts 02139, USA
| | | |
Collapse
|
4
|
|
5
|
Affiliation(s)
- R. Mark Bradley
- a Department of Physics , Colorado State University , Fort Collins, Colorado 80523 , USA
| | - M. Kevin Crosby
- a Department of Physics , Colorado State University , Fort Collins, Colorado 80523 , USA
| |
Collapse
|
6
|
|
7
|
Zhang S, Louis E, Plá O, Guinea F. Growth instabilities in mechanical breakdown under mechanical and thermal stresses. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:6476-6483. [PMID: 9964166 DOI: 10.1103/physreve.52.6476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
8
|
Tzschichholz F. Fracturing of brittle homogeneous solids: Finite-size scalings. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:9270-9274. [PMID: 9979970 DOI: 10.1103/physrevb.52.9270] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
9
|
Wang X, Huang Y. Dielectric-breakdown-type crack-growth models and the fractal distribution of earthquake faults. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:1476-1479. [PMID: 9963566 DOI: 10.1103/physreve.52.1476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
10
|
Tzschichholz F, Herrmann HJ. Simulations of pressure fluctuations and acoustic emission in hydraulic fracturing. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:1961-1970. [PMID: 9962854 DOI: 10.1103/physreve.51.1961] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
11
|
Hayakawa Y. Pattern selection of multicrack propagation in quenched crystals. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:R1748-R1751. [PMID: 9962260 DOI: 10.1103/physreve.50.r1748] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
12
|
Narayan O, Fisher DS. Nonlinear fluid flow in random media: Critical phenomena near threshold. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:9469-9502. [PMID: 10009746 DOI: 10.1103/physrevb.49.9469] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
13
|
Karttunen ME, Niskanen KJ, Kaski K. Fracture in mesoscopic disordered systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:9453-9459. [PMID: 10009744 DOI: 10.1103/physrevb.49.9453] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
14
|
Caldarelli G, Castellano C, Vespignani A. Fractal and topological properties of directed fractures. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:2673-2679. [PMID: 9961530 DOI: 10.1103/physreve.49.2673] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
15
|
Tzschichholz F, Herrmann HJ, Roman HE, Pfuff M. Beam model for hydraulic fracturing. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:7056-7059. [PMID: 10009438 DOI: 10.1103/physrevb.49.7056] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
16
|
Hayakawa Y. Numerical study of oscillatory crack propagation through a two-dimensional crystal. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:R1804-R1807. [PMID: 9961507 DOI: 10.1103/physreve.49.r1804] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
17
|
Oddershede L, Dimon P, Bohr J. Self-organized criticality in fragmenting. PHYSICAL REVIEW LETTERS 1993; 71:3107-3110. [PMID: 10054859 DOI: 10.1103/physrevlett.71.3107] [Citation(s) in RCA: 65] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
18
|
Wang X. Implications of Griffith's condition on crack growth. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:2205-2206. [PMID: 9960246 DOI: 10.1103/physreve.47.2205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
19
|
Wang W, Canessa E. Biharmonic pattern selection. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:1243-1248. [PMID: 9960128 DOI: 10.1103/physreve.47.1243] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
20
|
Abstract
The geometry of spectrin-free regions in the erythrocyte membrane skeleton is modeled using Monte Carlo calculations for an incomplete triangular lattice of entropy springs under tension. Intact springs correspond to normal spectrin molecules, and cut springs correspond to spectrin that is missing or unable to associate normally. As springs are cut and the network is allowed to relax to mechanical equilibrium, gaps in the network appear. Geometrical properties of these gaps are obtained as a function of the fraction of springs cut. The most important property modeled is the area of the largest spectrin-free region; this area increases approximately exponentially as the fraction of normal spectrin decreases from 100% to approximately 50%. The effect of these gaps on lateral diffusion and vesiculation is discussed.
Collapse
Affiliation(s)
- M J Saxton
- Institute of Theoretical Dynamics, University of California, Davis 95616
| |
Collapse
|
21
|
Ball RC, Blumenfeld R. Ball and Blumenfeld reply. PHYSICAL REVIEW LETTERS 1992; 68:2254. [PMID: 10045348 DOI: 10.1103/physrevlett.68.2254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
22
|
|
23
|
Lemaire E, Levitz P, Daccord G. From viscous fingering to viscoelastic fracturing in colloidal fluids. PHYSICAL REVIEW LETTERS 1991; 67:2009-2012. [PMID: 10044312 DOI: 10.1103/physrevlett.67.2009] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
24
|
Abstract
Simple computer models have been used to investigate a variety of pattern formation processes associated with material failure and deformation. These models reproduce surprisingly well the characteristic morphologies observed in a wide range of real systems. They provide a sound basis for the development of more realistic models that can be used to develop a better understanding of the mechanical properties of real materials. The present algorithms are adequate for some purposes, but substantial improvements are needed if simulation results are to make a major contribution to our theoretical understanding of the asymptotic fractal scaling and universality properties of patterns generated by failure and deformation phenomena.
Collapse
|
25
|
Ball RC, Blumenfeld R. Universal scaling of the stress field at the vicinity of a wedge crack in two dimensions and oscillatory self-similar corrections to scaling. PHYSICAL REVIEW LETTERS 1990; 65:1784-1787. [PMID: 10042362 DOI: 10.1103/physrevlett.65.1784] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
26
|
Pla O, Guinea F, Louis E, Li G, Sander LM, Yan H, Meakin P. Crossover between different growth regimes in crack formation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:3670-3673. [PMID: 9904462 DOI: 10.1103/physreva.42.3670] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|