Huang et al 2023c - Revision history

Rimni at 10:55, 29 January 2024

2024-01-29T10:55:48Z

Rimni at 09:28, 25 January 2024

2024-01-25T09:28:56Z

Rimni at 13:32, 19 January 2024

2024-01-19T13:32:43Z

Rimni at 10:24, 19 January 2024

2024-01-19T10:24:07Z

Rimni at 10:22, 19 January 2024

2024-01-19T10:22:31Z

Rimni at 10:20, 19 January 2024

2024-01-19T10:20:46Z

Rimni at 15:14, 17 January 2024

2024-01-17T15:14:45Z

Rimni: /* Conclusion */

2024-01-17T14:51:40Z

‎Conclusion

Rimni at 14:50, 17 January 2024

2024-01-17T14:50:53Z

Rimni: /* 4.5 Effect of particle agglomeration */

2024-01-17T14:48:52Z

‎4.5 Effect of particle agglomeration

@@ Line 499: / Line 499: @@
 ==Acknowledgements==
-This work was supported by Natural Science Foundation Project of Fujian Province (Grant No. 2020J05179））, and Science and Technology Project of FuJian University of Technology (Grant No. GY-Z20012).
+This work was supported by Natural Science Foundation Project of Fujian Province (Grant No. 2020J05179), and Science and Technology Project of FuJian University of Technology (Grant No. GY-Z20012).
 ==References==

@@ Line 531: / Line 531: @@
 [13] Li X.H., Li Z., Xia Y. Test and calculation of the carbon black reinforcement effect on the hyper-elastic properties of tire rubbers. Rubber Chemistry and Technology, 88:98-116, 2015.
-[14] Li Xiaofang, and Yang Xiaoxiang. "Hyperelastic Constitutive Models for Rubber Materials." Elasticity 15.1 (2005): 9.
+[14] Chen W., Wierzbicki T. Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption. Thin-Walled Structures, 39(4):287-306, 2001.
 [15] Khajehsaeid H.,   Arghavani J., Naghdabadi R. A hyperelastic constitutive model for rubber-like materials. European Journal of Mechanics/A Solids,  38:144-151, 2013.

@@ Line 525: / Line 525: @@
 [10] Tomita Y.,  Lu  W.,   Furutani Y. Numerical evaluation of micro- to macroscopic mechanical behavior of carbon-black-filled rubber. Key Engineering Materials, 274-276(2):19-24, 2004.
-[11] Akutagwa, K , et al. "Mesoscopic mechanical analysis of filled elastomer with 3D-Finite Element Analysis and transmission electron microtomography." Rubber Chemistry and Technology 2(2008):81, 182–189.
+[11] Akutagwa K., et al. Mesoscopic mechanical analysis of filled elastomer with 3D-Finite Element Analysis and transmission electron microtomography. Rubber Chemistry and Technology, 81(2):182–189, 2008.
-[12] Li, Qing , and  X. X. Yang . "Numerical Simulation for Mechanical Behavior of Carbon Black Filler Particle Reinforced Rubber Matrix Composites." Applied Mechanics & Materials 137(2011):1-6.
+[12] Li Qing,    Yang X.X. Numerical simulation for mechanical behavior of carbon black filler particle reinforced rubber matrix composites. Applied Mechanics & Materials, 137:1-6, 2011.
-[13] Xia, et al. "Test and calculation of the carbon black reinforcement effect on the hyper-elastic properties of tire rubbers." Rubber Chemistry and Technology (2015).
+[13] Li X.H., Li Z., Xia Y. Test and calculation of the carbon black reinforcement effect on the hyper-elastic properties of tire rubbers. Rubber Chemistry and Technology, 88:98-116, 2015.
-[14] Li, Xiaofang, and Yang Xiaoxiang. "Hyperelastic Constitutive Models for Rubber Materials." Elasticity 15.1 (2005): 9.
+[14] Li Xiaofang, and Yang Xiaoxiang. "Hyperelastic Constitutive Models for Rubber Materials." Elasticity 15.1 (2005): 9.
-[15] Khajehsaeid, H. ,  J. Arghavani , and  R. Naghdabadi . "A hyperelastic constitutive model for rubber-like materials." European Journal of Mechanics / A Solids 38.none(2013):144-151.
+[15] Khajehsaeid H.,   Arghavani J., Naghdabadi R. A hyperelastic constitutive model for rubber-like materials. European Journal of Mechanics/A Solids,  38:144-151, 2013.
-[16] Hüsnü Dal,  K. Acikgoz , and  Y. Badienia . "On the Performance of Isotropic Hyperelastic Constitutive Models for Rubber-Like Materials: A State of the Art Review." Applied Mechanics Reviews (2021).
+[16] Dal H.,  Acikgoz K.,  Badienia Y. On the performance of isotropic hyperelastic constitutive models for rubber-like materials: A state of the art review. Applied Mechanics Reviews,  73(2), 020802, 2021.
-[17] Attard, Mario M , and  G. W. Hunt . "Hyperelastic constitutive modeling under finite strain." International Journal of Solids & Structures 41.18-19(2004):5327-5350.
+[17] Attard M.M.,    Hunt G.W. Hyperelastic constitutive modeling under finite strain. International Journal of Solids & Structures, 41(18-19:5327-5350, 2004.
-[18]Khisaeva, Z. F., and M. Ostoja-Starzewski. "On the size of RVE in finite elasticity of random composites." ''Journal of elasticity'' 85 (2006): 153-173.
+[18]Khisaeva Z.F.,   Ostoja-Starzewski M. On the size of RVE in finite elasticity of random composites. Journal of Elasticity, 85:153-173, 2006.
-[19] Savvas, Dimitrios ,  G. Stefanou , and  M. Papadrakakis . "Determination of RVE size for random composites with local volume fraction variation." Computer Methods in Applied Mechanics & Engineering 305.jun.15(2016):340-358.
+[19] Savvas D.,   Stefanou G.,  Papadrakakis  M. Determination of RVE size for random composites with local volume fraction variation. Computer Methods in Applied Mechanics & Engineering, 305:340-358, 2016.
-[20] Omairey, et al. "Development of an ABAQUS plugin tool for periodic RVE homogenisation.".
+[20] Omairey S.L., Dunning P.D.,   Sriramula S. Development of an ABAQUS plugin tool for periodic RVE homogenisation. Engineering with Computers, 35:567–577, 2019.
-[21] Catalanotti, G . "On the generation of RVE-based models of composites reinforced with long fibres or spherical particles." Composite Structures 138.mar.(2016):84-95.
+[21] Catalanotti G. On the generation of RVE-based models of composites reinforced with long fibres or spherical particles. Composite Structures, 138:84-95, 2016.

@@ Line 247: / Line 247: @@
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
-! !! RMSE !! SSE !! <math>{R}^{2}</math>
+! style="text-align: left;"| Model !! RMSE !! SSE !! <math>{R}^{2}</math>
 |-
-|  style="text-align: center;vertical-align: top;"|Mooney-Rivlin
+|  style="text-align: left;vertical-align: top;"|Mooney-Rivlin
 |  style="text-align: center;vertical-align: top;"|0.0015089
 |  style="text-align: center;vertical-align: top;"|2.98E-04
 |  style="text-align: center;vertical-align: top;"|0.99989
 |-
-|  style="text-align: center;vertical-align: top;"|Yeoh
+|  style="text-align: left;vertical-align: top;"|Yeoh
 |  style="text-align: center;vertical-align: top;"|0.0023356
 |  style="text-align: center;vertical-align: top;"|7.15E-04
 |  style="text-align: center;vertical-align: top;"|0.99974
 |-
-|  style="text-align: center;vertical-align: top;"|Ogden
+|  style="text-align: left;vertical-align: top;"|Ogden
 |  style="text-align: center;vertical-align: top;"|0.012336
 |  style="text-align: center;vertical-align: top;"|0.0199

@@ Line 157: / Line 157: @@
 The constitutive model is the basis for studying the mechanical properties of rubber materials, and its geometric nonlinear relationship must be considered when establishing the constitutive relationship of hyperelastic materials. In engineering practice, strain energy function [14-17] is commonly used to represent the hyperelastic constitutive relationship of rubber materials, three common constitutive models are listed below.
-'''1. Mooney-Rivlin Model'''
+'''1. Mooney-Rivlin model'''
 The Mooney-Rivlin model, a more classical intrinsic model in which the mechanical behavior of all rubber materials can be simulated almost all the time, is suitable for describing small and medium deformations, and its strain energy density function is as follows:
@@ Line 185: / Line 185: @@
 where <math display="inline">W</math> is the strain energy density function of the rubber-like nonlinear material model, <math display="inline">{I}_{1}</math>and <math display="inline">{I}_{2}</math> are the first and second invariants of the Green deformation tensor, respectively, and <math display="inline">{C}_{10}</math> and <math display="inline">{C}_{01}</math> are the intrinsic parameters, which are determined by experiments.
-'''2. Yeoh Model'''
+'''2. Yeoh model'''
 The Yeoh model has an additional term containing exponential decay compared to the Mooney-Rivlin model, and its strain energy function is expressed as:
@@ Line 213: / Line 213: @@
 where <math display="inline">N</math>, <math display="inline">{C}_{i0}</math> and <math display="inline">{D}_{k}</math> are material constants.
-'''3. Ogden Constitutive Model'''
+'''3. Ogden constitutive model'''
 The Ogden intrinsic model is based on the concept of the strain energy density function, which describes the mechanical behavior of a material by expressing the strain energy density function as a power series expansion of the strain. It assumes that the strain energy of a material can be described by higher order terms of strain which have different weights in different strain directions. Its strain energy density function is as follows:

@@ Line 503: / Line 503: @@
 ==References==
-[1] Ramesan, M. T. ,  R. Alex , and  N. V. Khanh . "Studies on the cure and mechanical properties of blends of natural rubber with dichlorocarbene modified styrene–butadiene rubber and chloroprene rubber." Reactive & Functional Polymers 62.1(2005):41-50.
+<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
-[2] Payne, A. R. . "The Dynamic Properties of Carbon Black-Loaded Natural Rubber Vulcanizates. Part I." Journal of Applied Polymer Science 6.19(2010):57-63.
+[1] Ramesan M.T., Alex R., Khanh N.V. Studies on the cure and mechanical properties of blends of natural rubber with dichlorocarbene modified styrene–butadiene rubber and chloroprene rubber. Reactive & Functional Polymers, 62(1):41-50, 2005.
-[3] Hubert, et al. "Theory of the Elastic Properties of Rubber." Journal of Chemical Physics 11(1943).
+[2] Payne A.R. The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I. Journal of Applied Polymer Science, 6(19):57-63, 2010.
-[4] Elizabeth, K. I ,  R. Alex , and  S. Varghese . "Evaluation of blends of natural rubber and hydrogenated nitrile rubber containing chemically modified natural rubber." Plastics Rubber & Composites 37.8(2008):359-366.
+[3] Hubert M.J., Guth E. Theory of the elastic properties of rubber. Journal of Chemical Physics, 11(10):455–481, 1943.
-[5] Sumita, Masao . "Characterization of Disporsion of Filler and Polymer-Filler Interaction in Rubber-Carbon Black Composites." (1996).
+[4] Elizabeth K.I, Alex  R., Varghese S. Evaluation of blends of natural rubber and hydrogenated nitrile rubber containing chemically modified natural rubber. Plastics Rubber & Composites, 37(8):359-366, 2008.
-[6] Zhong Xian Ooi,  H. Ismail , and  A. A. Bakar . "Optimisation of oil palm ash as reinforcement in natural rubber vulcanisation: A comparison between silica and carbon black fillers." Polymer Testing (2013).
+[5]    Karásek  L.,  Sumita M.  Characterization of disporsion of filler and polymer-filler interaction in rubber-carbon black composites.  Journal of Materials Science, 31:281–289, 1996.
-[7] Jean, A. , et al. "A multiscale microstructure model of carbon black distribution in rubber." Journal of Microscopy (2011).
+[6] Zhong X.O., Ismail  H.,    Bakar A.A. Optimisation of oil palm ash as reinforcement in natural rubber vulcanisation: A comparison between silica and carbon black fillers. Polymer Testing, 32(49.625-630, 2013.
-[8] Figliuzzi, Bruno , et al. "Modelling the microstructure and the viscoelastic behaviour of carbon black filled rubber materials from 3D simulations." (2016).
+[7] Jean A., et al. A multiscale microstructure model of carbon black distribution in rubber. Journal of Microscopy, 241(3):243-60, 2011.
-[9] Li, Qing, and Yang Xiaoxiang. "Numerical Study on the Mechanical Behavior of N330 Carbon Black Reinforced Rubber Composites." Journal of Composite Materials Science and Engineering 7 (2019): 16-20.
+[8] Figliuzzi B., et al. Modelling the microstructure and the viscoelastic behaviour of carbon black filled rubber materials from 3D simulations. Technische Mechanik, 32(1-2):22-46, 2016.
-[10] Tomita, Yoshihiro ,  W. Lu , and  Y. Furutani . "Numerical evaluation of micro- to macroscopic mechanical behavior of carbon-black-filled rubber." Key Engineering Materials 274-276.2(2004):19-24.
+[9] Li Q., Yang X. Numerical study on the mechanical behavior of N330 carbon black reinforced rubber composites. Journal of Composite Materials Science and Engineering, 7:16-20, 2019.
 [11] Akutagwa, K , et al. "Mesoscopic mechanical analysis of filled elastomer with 3D-Finite Element Analysis and transmission electron microtomography." Rubber Chemistry and Technology 2(2008):81.

@@ Line 485: / Line 485: @@
 |}
-==Conclusion==
+==Conclusions==
 In this study, a two-dimensional plane strain model was developed for elliptical carbon black particles, and simulations and analyses of uniaxial tension were performed. The effects of carbon black volume fraction, particle distribution angle, and agglomeration on the stress-strain relationship and stress distribution in the Representative Volume Element (RVE) of the composite material were investigated. The following conclusions were drawn:

@@ Line 449: / Line 449: @@
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a) 1 agglomeration
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(b) 2 agglomerations
 |-
@@ Line 456: / Line 455: @@
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(c) 3 agglomerations
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(d) 4 agglomerations
 |}
@@ Line 464: / Line 462: @@
-{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
+<div id='img-17'></div>
 |-
-|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_lihong_849542190-image21.png|258px]]
+|style="text-align: center;padding:10px;"|[[Image:Draft_lihong_849542190-image25.png|258px]]
+|style="text-align: center;padding:10px;"| [[Image:Draft_lihong_849542190-image26.png|258px]]
-(a)1 agglomeration
-|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_lihong_849542190-image22.png|258px]]
-−
-(b)2 agglomerations
 |-
-|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_lihong_849542190-image23.png|258px]] (c)3 agglomerations
+|style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a) 1 agglomeration
-|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_lihong_849542190-image24.png|258px]] (d)4 agglomerations
+|style="text-align: center;font-size: 75%;padding-bottom:10px;"|(b) 2 agglomerations
-|}
-−
-−
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-<span style="text-align: center; font-size: 75%;">Fig.16  Mise stress cloud map under different aggregate numbers of NR3</span></div>
-−
-{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
 |-
-|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_lihong_849542190-image25.png|258px]]
+|style="text-align: center;padding:10px;"|[[Image:Draft_lihong_849542190-image27.png|258px]]
+|style="text-align: center;padding:10px;"| [[Image:Draft_lihong_849542190-image28.png|264px]]
-(a)1 agglomeration
-|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_lihong_849542190-image26.png|258px]] (b)2 agglomerations
 |-
-|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_lihong_849542190-image27.png|258px]]
+|style="text-align: center;font-size: 75%;padding-bottom:10px;"|(c) 3 agglomerations
+|style="text-align: center;font-size: 75%;padding-bottom:10px;"|(d) 4 agglomerations
-(c)3 agglomerations
+|}
-|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_lihong_849542190-image28.png|264px]] (d)4 agglomerations
+|-
 |}
 ==Conclusion==

@@ Line 417: / Line 417: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Draft_lihong_849542190-image19.jpg|330px]]
+|style="text-align: center;"| [[Image:Draft_lihong_849542190-image19.jpg|450px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 14'''. Stress-strain curves of NR3 under different aggregate numbers
@@ Line 426: / Line 426: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Draft_lihong_849542190-image20.jpg|306px]]
+|style="text-align: center;"| [[Image:Draft_lihong_849542190-image20.jpg|450px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 15'''. Stress-strain curves of NR4 under different aggregate numbers
@@ Line 437: / Line 437: @@
 Mises stress cloud map in [[#img-16|Figures 16]] and [[#img-17|17]] show similar results for both volume fraction RVE models. The stress concentration becomes more pronounced as the agglomeration increases, this can be attributed to the idealization of agglomerates, i.e., larger carbon black particles with a larger contact area with the matrix.
 {| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"