二维随机蜂巢网格熔断动力学过程和熔断面标度性质的数值模拟
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摘要
石墨烯等材料具有典型的二维蜂巢结构,而随机电阻丝模型则是研究非均匀材料断裂十分有效的统计物理学模型.本文尝试对二维蜂巢结构随机电阻丝网络熔断的动力学过程及熔断面性质进行数值模拟分析,以此来研究二维非均质蜂窝材料熔断的动力学性质和熔断面的动力学标度性质.模拟研究表明,二维随机蜂窝网格的熔断动力学过程和熔断面具有明显的标度性质,得到的熔断面整体和局域粗糙度指数分别为α=0.911±0.005和α_(loc)=0.808 ± 0.003,这两者之间的明显差异表明熔断面具有奇异标度性.通过对熔断面极值高度的分析发现,熔断面高度的极值统计分布能很好地满足Asym2sig型分布,而不是最常见的三种极值统计分布.本文的研究表明,随机电阻丝模型在模拟非均匀材料的电流熔断过程和熔断表面标度性的分析中同样适用和有效.
Graphene and other materials have a typical two-dimensional(2D)honeycomb structure.The random fuse model is a statistical physics model that is very effective in studying the fracture dynamics of heterogeneous materials.In order to study the current fusing process and the properties of the fractured surface of 2D honeycomb structure materials such as graphene,in this paper we attempt to numerically simulate and analyze the fusing process and melting profile properties of the 2D honeycomb structure random fuse network.The results indicate that the surface width exhibits a good scaling behavior and has a linear relationship with the system size,and that the out-of-plane roughness exponent displays a global value of α=0.911±0.005 and a local value of α_(loc)=0.808±0.003,approximate to those of the materials studied.The global and local roughness and their difference indicate that the fusing process and the fracture profile exhibit significant scale properties and have a strange scale.On the other hand,by analyzing the extreme values of the fused surface with different system sizes,the extreme heights can be collapsed very well,after a lot of trials and analysis,it is found that the extreme statistical distribution of the height of the fused surface can well satisfy the Asym 2 sig type distribution.The extreme height distributions of fracture surfaces can be fitted by Asym 2 Sig distribution,rather than the three kinds of usual extreme statistical distributions,i.e.Weibull,Gumbel,and Frechet distributions.The relative maximal and minimum height distribution of the fused surface at the same substrate size have a good symmetry.In the simulation calculation process of this paper,the coefficient matrix is constructed by using the node analysis method,and the Cholesky decomposition is performed on the coefficient matrix,and then the ShermanMorrison-Woodbury algorithm is used to quickly invert the coefficient matrix,which greatly optimizes the calculation process and calculation.The efficiency makes the numerical simulation calculation and analysis performed smoothly.The research in this paper indicates that the random fuse model is a very effective theoretical model in the numerical analysis of the scaling properties of rough fracture surfaces,and it is also applicable to the current fusing process of the inhomogeneous material and the scaling surface analysis of the fusing surface.In this paper,it is found that materials with anisotropic structure can also find their fracture mode by energization,and the properties of fracture surface can provide reference for the study of mechanical properties of honeycomb structural materials.It is a very effective statistical physical model,and this will expand the field of applications of random fuse models.
Graphene and other materials have a typical two-dimensional(2D)honeycomb structure.The random fuse model is a statistical physics model that is very effective in studying the fracture dynamics of heterogeneous materials.In order to study the current fusing process and the properties of the fractured surface of 2D honeycomb structure materials such as graphene,in this paper we attempt to numerically simulate and analyze the fusing process and melting profile properties of the 2D honeycomb structure random fuse network.The results indicate that the surface width exhibits a good scaling behavior and has a linear relationship with the system size,and that the out-of-plane roughness exponent displays a global value of α=0.911±0.005 and a local value of α_(loc)=0.808±0.003,approximate to those of the materials studied.The global and local roughness and their difference indicate that the fusing process and the fracture profile exhibit significant scale properties and have a strange scale.On the other hand,by analyzing the extreme values of the fused surface with different system sizes,the extreme heights can be collapsed very well,after a lot of trials and analysis,it is found that the extreme statistical distribution of the height of the fused surface can well satisfy the Asym 2 sig type distribution.The extreme height distributions of fracture surfaces can be fitted by Asym 2 Sig distribution,rather than the three kinds of usual extreme statistical distributions,i.e.Weibull,Gumbel,and Frechet distributions.The relative maximal and minimum height distribution of the fused surface at the same substrate size have a good symmetry.In the simulation calculation process of this paper,the coefficient matrix is constructed by using the node analysis method,and the Cholesky decomposition is performed on the coefficient matrix,and then the ShermanMorrison-Woodbury algorithm is used to quickly invert the coefficient matrix,which greatly optimizes the calculation process and calculation.The efficiency makes the numerical simulation calculation and analysis performed smoothly.The research in this paper indicates that the random fuse model is a very effective theoretical model in the numerical analysis of the scaling properties of rough fracture surfaces,and it is also applicable to the current fusing process of the inhomogeneous material and the scaling surface analysis of the fusing surface.In this paper,it is found that materials with anisotropic structure can also find their fracture mode by energization,and the properties of fracture surface can provide reference for the study of mechanical properties of honeycomb structural materials.It is a very effective statistical physical model,and this will expand the field of applications of random fuse models.
引文
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[35]Yang Y,Tang G,Song L J,Xun Z P,Xia H,Hao D P 2014Acta Phys.Sin.63 150501(in Chinese)[杨毅,唐刚,宋丽建,寻之朋,夏辉,郝大鹏2014物理学报63 150501]
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[38]Wu H H,Xiao L N,Wang J,Wang Y D 2018 Laser Opt.Prog.55 011417(in Chinese)[吴海华,肖林楠,王俊,王亚迪2018激光与光电子学进展55 011417]
[39]McGregor D J,Sameh T,William P K 2019 Addit.Manuf.25 10
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[41]Soriano J,Ramasco J J,Rodriguez M A,Hernandez-Machado A 2002 Phys.Rev.Lett.89 026102
[2]Shin Y J,Gopinadhan K,Narayanapillai K 2013 Appl.Phys.Lett.102 666
[3]Lu Y H,Shi L,Zhang C,Feng Y P 2009 Phys.Rev.B 80233410
[4]Moura M J B,Marder M 2013 Phys.Rev.E 88 032405
[5]Ghorbanfekr-Kalashami H,Neek-Amal M,Peeters F M 2016Phys.Rev.B 93 174112
[6]Alava M J,Nukala P K V V,Zapperi S 2006 Adv.Phys.55351
[7]Garcimart'?n A,Guarino A,Bellon L,Ciliberto S 1997 Phys.Rev.Lett.79 3202
[8]Maes C,van Moffaert A,Frederix H,Strauven H 1998 Phys.Rev.B 57 4987
[9]Petri A,Paparo G,Vespignani A,Alippi A,Costantini M1994 Phys.Rev.Lett.73 3423
[10]Salminen L I,Tolvanen A I,Alava M J 2002 Phys.Rev.Lett.89 185503
[11]Arcangelis L,Redner S,Herrmann H J 1985 J.Phys.Lett.46585
[12]Schramm O 2000 Israel J.Math.118 221
[13]Claudio M,Ashivni S,Nukala P K V V,Alava M J,Sethna JP,Zapperi S 2012 Phys.Rev.Lett.108 065504
[14]Duxbury P M,Beale P D,Leath P L 1986 Phys.Rev.Lett.59 155
[15]Nukala P K V V,Srdan S,Zapperi S 2004 J.Stat.Mech.8P08001
[16]Toussaint R,Hansen A 2006 Phys.Rev.E 73 046103
[17]Jan?ystein H B,Hansen A 2008 Phys.Rev.Lett.100 045501
[18]Davis T A,Hager W W 1999 Siam J.Matrix Anal.A 22 997
[19]Family F,Vicsek T 1985 J.Phys.A 18 L75
[20]Xun Z P,Tang G,Han K,Xia H,Hao D P,Li Y 2012 Phys.Rev.E 85 041126
[21]Xun Z P 2017 The Dynamic Scale Properties of the Surface Roughness of the Discrete Growth Model(Xuzhou:China Mining University Press)p88(in Chinese)[寻之朋2017离散模型表面界面粗化的动力学标度性质(徐州:中国矿业大学出版社)第88页]
[22]Raychaudhuri S,Cranston M,Przybyla C,Shapir Y 2001Phys.Rev.Lett.87 136101
[23]Foltin G,Oerding K,Racz Z,Workman R L,Zia R K P 1994Phys.Rev.E 50 639
[24]Majumdar S N,Comtet A 2004 Phys.Rev.Lett.92 225501
[25]Derrida B,Lebowitz J L 1998 Phys.Rev.Lett.80 209
[26]Majumdar S N,Comtet A 2005 Stat.Phys.119 777
[27]Fisher R A,Tippett L H C 1928 Proc.Cambridge Philos.Soc.24 180
[28]Bramwell S T,Christensen K,Fortin J,Holdsworth P C W,Jensen H J,Lise S,Lopez J M,Nicodemi M,Pinton J F,Sellitto M 2000 Phys.Rev.Lett.84 3744
[29]Antal T,Droz M,Gyorgyi G,Racz Z 2001 Phys.Rev.Lett.87 240601
[30]Lee D S 2005 Phys.Rev.Lett.95 150601
[31]Lee S B,Jeong H C,Kim J M 2008 J.Stat.Mech.9 P12013
[32]Wen R J,Tang G,Han K,Xia H,Hao D P,Xun Z P,Chen Y L 2011 Chin.J.Comput.Phys.28 933
[33]Cui L J,Zhang Y,Zhang M Y,Li W,Zhao X S,Li S G,Wang Y F 2012 J.Environ.Mont.14 3037
[34]Brar J 2011 M.S.Thesis(Ottawa:University of Ottawa)pp6-9
[35]Yang Y,Tang G,Song L J,Xun Z P,Xia H,Hao D P 2014Acta Phys.Sin.63 150501(in Chinese)[杨毅,唐刚,宋丽建,寻之朋,夏辉,郝大鹏2014物理学报63 150501]
[36]Yang Y,Tang G,Zhang Z,Xun Z P,Song L J,Han K 2015Acta Phys.Sin.64 130501(in Chinese)[杨毅,唐刚,张哲,寻之朋,宋丽建,韩奎2015物理学报64 130501]
[37]Wang X F,Yang X L,Liu Y 2018 Chemical Engineer.Sum.274 7(in Chinese)[王晓芳,杨小玲,刘洋2018化学工程师274 7]
[38]Wu H H,Xiao L N,Wang J,Wang Y D 2018 Laser Opt.Prog.55 011417(in Chinese)[吴海华,肖林楠,王俊,王亚迪2018激光与光电子学进展55 011417]
[39]McGregor D J,Sameh T,William P K 2019 Addit.Manuf.25 10
[40]Gibson L J,Ashby M F 1997 Cellular Solids:Structure and Properties(2nd Ed.)(Cambridge:Cambridge University Press)(Cambridge:Cambridge University Press)pp13-19
[41]Soriano J,Ramasco J J,Rodriguez M A,Hernandez-Machado A 2002 Phys.Rev.Lett.89 026102