Samuel Heroy, Dane Taylor, F Bill Shi, M Gregory Forest, Peter J Mucha
{"title":"刚性图压缩:无序光纤网络的基于图案的刚性分析。","authors":"Samuel Heroy, Dane Taylor, F Bill Shi, M Gregory Forest, Peter J Mucha","doi":"10.1137/17M1157271","DOIUrl":null,"url":null,"abstract":"<p><p>Using particle-scale models to accurately describe property enhancements and phase transitions in macroscopic behavior is a major engineering challenge in composite materials science. To address some of these challenges, we use the graph theoretic property of rigidity to model mechanical reinforcement in composites with stiff rod-like particles. We develop an efficient algorithmic approach called <i>rigid graph compression</i> (RGC) to describe the transition from floppy to rigid in disordered fiber networks (\"rod-hinge systems\"), which form the reinforcing phase in many composite systems. To establish RGC on a firm theoretical foundation, we adapt rigidity matroid theory to identify primitive topological network motifs that serve as rules for composing interacting rigid particles into larger rigid components. This approach is computationally efficient and stable, because RGC requires only topological information about rod interactions (encoded by a sparse unweighted network) rather than geometrical details such as rod locations or pairwise distances (as required in rigidity matroid theory). We conduct numerical experiments on simulated two-dimensional rod-hinge systems to demonstrate that RGC closely approximates the rigidity percolation threshold for such systems, through comparison with the pebble game algorithm (which is exact in two dimensions). Importantly, whereas the pebble game is derived from Laman's condition and is only valid in two dimensions, the RGC approach naturally extends to higher dimensions.</p>","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/17M1157271","citationCount":"5","resultStr":"{\"title\":\"RIGID GRAPH COMPRESSION: MOTIF-BASED RIGIDITY ANALYSIS FOR DISORDERED FIBER NETWORKS.\",\"authors\":\"Samuel Heroy, Dane Taylor, F Bill Shi, M Gregory Forest, Peter J Mucha\",\"doi\":\"10.1137/17M1157271\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Using particle-scale models to accurately describe property enhancements and phase transitions in macroscopic behavior is a major engineering challenge in composite materials science. To address some of these challenges, we use the graph theoretic property of rigidity to model mechanical reinforcement in composites with stiff rod-like particles. We develop an efficient algorithmic approach called <i>rigid graph compression</i> (RGC) to describe the transition from floppy to rigid in disordered fiber networks (\\\"rod-hinge systems\\\"), which form the reinforcing phase in many composite systems. To establish RGC on a firm theoretical foundation, we adapt rigidity matroid theory to identify primitive topological network motifs that serve as rules for composing interacting rigid particles into larger rigid components. This approach is computationally efficient and stable, because RGC requires only topological information about rod interactions (encoded by a sparse unweighted network) rather than geometrical details such as rod locations or pairwise distances (as required in rigidity matroid theory). We conduct numerical experiments on simulated two-dimensional rod-hinge systems to demonstrate that RGC closely approximates the rigidity percolation threshold for such systems, through comparison with the pebble game algorithm (which is exact in two dimensions). Importantly, whereas the pebble game is derived from Laman's condition and is only valid in two dimensions, the RGC approach naturally extends to higher dimensions.</p>\",\"PeriodicalId\":49791,\"journal\":{\"name\":\"Multiscale Modeling & Simulation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1137/17M1157271\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Multiscale Modeling & Simulation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/17M1157271\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2018/8/21 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Multiscale Modeling & Simulation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/17M1157271","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/8/21 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
RIGID GRAPH COMPRESSION: MOTIF-BASED RIGIDITY ANALYSIS FOR DISORDERED FIBER NETWORKS.
Using particle-scale models to accurately describe property enhancements and phase transitions in macroscopic behavior is a major engineering challenge in composite materials science. To address some of these challenges, we use the graph theoretic property of rigidity to model mechanical reinforcement in composites with stiff rod-like particles. We develop an efficient algorithmic approach called rigid graph compression (RGC) to describe the transition from floppy to rigid in disordered fiber networks ("rod-hinge systems"), which form the reinforcing phase in many composite systems. To establish RGC on a firm theoretical foundation, we adapt rigidity matroid theory to identify primitive topological network motifs that serve as rules for composing interacting rigid particles into larger rigid components. This approach is computationally efficient and stable, because RGC requires only topological information about rod interactions (encoded by a sparse unweighted network) rather than geometrical details such as rod locations or pairwise distances (as required in rigidity matroid theory). We conduct numerical experiments on simulated two-dimensional rod-hinge systems to demonstrate that RGC closely approximates the rigidity percolation threshold for such systems, through comparison with the pebble game algorithm (which is exact in two dimensions). Importantly, whereas the pebble game is derived from Laman's condition and is only valid in two dimensions, the RGC approach naturally extends to higher dimensions.
期刊介绍:
Centered around multiscale phenomena, Multiscale Modeling and Simulation (MMS) is an interdisciplinary journal focusing on the fundamental modeling and computational principles underlying various multiscale methods.
By its nature, multiscale modeling is highly interdisciplinary, with developments occurring independently across fields. A broad range of scientific and engineering problems involve multiple scales. Traditional monoscale approaches have proven to be inadequate, even with the largest supercomputers, because of the range of scales and the prohibitively large number of variables involved. Thus, there is a growing need to develop systematic modeling and simulation approaches for multiscale problems. MMS will provide a single broad, authoritative source for results in this area.