DOCSLIB.ORG

Modelling and Simulation of the Mechanical Behavior of Hydrogels

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Modelling and Simulation of the Mechanical Behavior of Hydrogels MODELLING AND SIMULATION OF THE MECHANICAL BEHAVIOR OF HYDROGELS ZHANG XIAOXIN (B. Eng., Tongji University, China) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 - 1 - Acknowledgements I first wish to express my sincere appreciation to my supervisor, A/P Zhang Yongwei, from Department of Materials Science and Engineering of NUS, for his guidance, advice, support and encouragement throughout the four years. Insightful discussion with him provides most of inspiration in this thesis. The range of knowledge and interests he provided was invaluable for the successful completion of this work. Working with him is one of the luckiest things in my life. I extend thanks to my co-supervisors, A/P Zeng Kaiyang from Mechanical Engineering and A/P Li Jun from Bio-Engineering, for sharing their experience and knowledge in experiments. Dr. Liu Zishun from Institute of High Performance Computing also deserves thanks for his inspiring discussion and guidance for numerical simulations. I would also like to acknowledge Dr. Guo Tianfu from Institute of High Performance Computing for reviewing part of the analysis and paper writing. Thanks also go to Department of Materials Science and Engineering of NUS for providing me the scholarship and devices, the Institute of High Performance Computing and the Institute of Materials Research and Engineering for providing resources to accomplish this work. Many friends have added much in my life in NUS. I would like to thank my senior Zhang Chunyu who taught me the first lesson in modeling and simulation. I would also like to thank Wu Zhaoxuan and Sun Lu for their supports and I collaboration within the four years. Koh Tiongsoon and Huang Zhijun also deserve thanks for their aid and suggestion in my initial way of research, and Wang Yu, Yuan Du, Gong Ying and Hu Guangxia, for their friendship. Finally, I would like to thank my family. Without their love and support, none of this would have been possible. To my grandma, my dad, my mom and especially my grandpa, I own you forever. Thank all of you. Zhang Xiaoxin National university of Singapore August 2010 II Contents Acknowledgements........................................................................................................ I Contents .......................................................................................................................III List of symbols.............................................................................................................VI List of figures................................................................................................................X Summary...................................................................................................................XVI Chapter 1: Introduction..................................................................................................1 1.1 Swelling behavior of hydrogels....................................................................1 1.1.1 Neutral hydrogel swelling equilibrium ..............................................3 1.1.2 Ionic hydrogel swelling equilibrium..................................................5 1.1.3 Physical hydrogel swelling ................................................................7 1.1.4 Patterns formation in hydrogel structures..........................................8 1.2 Motivations.................................................................................................11 1.3 Objectives...................................................................................................13 Chapter 2: Computational Methods.............................................................................16 2.1 Introduction ................................................................................................16 2.2 Existing models ..........................................................................................16 2.2.1 One phase model..............................................................................16 2.2.2 Multi-phase model ...........................................................................20 2.2.3 Transport model ...............................................................................23 2.2.4 Thermodynamics model...................................................................25 III 2.3 Model implementation ...............................................................................33 2.4 Instability investigations.............................................................................37 2.4.1 Introduction......................................................................................37 2.4.2 FEM approach..................................................................................37 Chapter 3: Hydrogel microlenses under concentrated loadings ..................................43 3.1 Introduction ................................................................................................43 3.2 Hydrogel model and numerical simulation ................................................45 3.3 Simulation results.......................................................................................46 3.3.1 Vertical inward indentation..............................................................47 3.3.2 Vertical outward indentation............................................................56 3.3.3 Lateral indentation ...........................................................................59 3.4 Discussion ..................................................................................................63 3.5 Conclusion..................................................................................................64 Chapter 4: Formation of gears through buckling multilayered film-hydrogel structures ......................................................................................................................................66 4.1 Introduction ................................................................................................66 4.2 Numerical simulation of gear formation ....................................................67 4.3 Three types of gears ...................................................................................69 4.4 Teeth number..............................................................................................73 4.5 Teeth amplitude ..........................................................................................77 4.6 Discussion and conclusion .........................................................................78 Chapter 5: Buckling behavior of a hydrogel plate with a space-varying cross-linking IV density under swelling .................................................................................................80 5.1 Introduction ................................................................................................80 5.2 Numerical simulations-three types of buckling patterns............................82 5.3 Simulation results.......................................................................................84 5.4 Scaling analysis ..........................................................................................90 5.5 Patterns for cylindrical hydrogel tube ........................................................94 5.6 Discussion ..................................................................................................96 5.7 Conclusion ..................................................................................................97 Chapter 6: Conclusion and future work.......................................................................99 6.1 Conclusion..................................................................................................99 6.2 Future work ..............................................................................................101 Bibliography ..............................................................................................................103 V List of symbols N Effective polymer chains per unit volume E Young’s modulus of hydrogel s Lame constant of hydrogel s Shear modulus of hydrogel Osmotic pressure k Boltzmann constant T Temperature N A Avogadro’s constant K Donnan coefficient F Faraday constant Flory Huggins interaction parameter v Volume of water molecule c Molar concentration of polymer units z Valence of the fixed charges Csalt Salt concentration in the external solution Stretch in principle directions s Stretch due to swelling m Stretch due to mechanical loading chain Principal stretch J Vo l u me st r a in VI W Energy of the hydrogel G Energy of the system m Number of links in polymer chains P Additional pressure by boundary condition S Cauchy stress Density of each phase Chemical potential f Frictional coefficient per unit volume vi Velocity of i phases Volume fraction of each phase e Strain tensor I Identity tensor Osmotic coefficient M Molecular weight Activity of each phase Electric potential D Water diffusivity 0 Dielectric constant iK Nominal stress with respect to dry states 'iK Nominal stress with respect to swollen states FiK Deformation gradient with respect to dry states FiK ' Deformation gradient with respect to swollen states VII I1 First invariance with respect to dry states I1 ' First invariance with respect to swollen states X K Coordinates of material point in reference configuration xi Coordinates of material point in deformed configuration
Load more

Recommended publications
  • Modeling the Chain Entropy of Biopolymers
    Journal of Computer Science & Systems Biology - Open Access Research Article JCSB/Vol.2 January-February 2009 Modeling the Chain Entropy of Biopolymers: Unifying Two Different Random Walk Models under One Framework Wayne Dawson* and Gota Kawai Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino-shi, Chiba 275-0016, Japan *Corresponding author: Wayne Dawson, Bioinformation Engineering Laboratory, Department of Biotechnology, Graduate School of Agriculture and Life Sciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-8657, E-mail: [email protected] Received December 18, 2008; Accepted January 31, 2009; Published February 03, 2009 Citation: Dawson W, Kawai G (2009) Modeling the Chain Entropy of Biopolymers: Unifying Two Different Random Walk Models under One Framework. J Comput Sci Syst Biol 2: 001-023. doi:10.4172/jcsb.1000014 Copyright: © 2009 Dawson W, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Abstract Entropy plays a critical role in the long range structure of biopolymers. To model the coarse-grained chain entropy of the residues in biopolymers, the lattice model or the Gaussian polymer chain (GPC) model is typically used. Both models use the concept of a random walk to find the conformations of an unstructured polymer. However, the entropy of the lattice model is a function of the coordination number, whereas the entropy of the GPC is a function of the root-mean square separation distance between the ends of the polymer.
    [Show full text]
  • From Symmetry to Entropy: Crystal Entropy Difference Strongly Affects Early Stage Phase Transformation
    From symmetry to entropy: Crystal entropy difference strongly affects early stage phase transformation Cite as: Appl. Phys. Lett. 115, 264103 (2019); https://doi.org/10.1063/1.5114974 Submitted: 14 June 2019 . Accepted: 21 November 2019 . Published Online: 27 December 2019 C. H. Hu, Y. C. Chen, P. J. Yu, K. Y. Fung, Y. C. Hsueh, P. K. Liaw, J. W. Yeh, and A. Hu COLLECTIONS This paper was selected as Featured ARTICLES YOU MAY BE INTERESTED IN Updated method considers system’s structure when calculating entropy Scilight 2019, 521107 (2019); https://doi.org/10.1063/10.0000495 High-voltage vertical Ga2O3 power rectifiers operational at high temperatures up to 600 K Applied Physics Letters 115, 263503 (2019); https://doi.org/10.1063/1.5132818 Influence of electric polarization on Coulomb blockade in a super-paraelectric clusters assembly Applied Physics Letters 115, 262901 (2019); https://doi.org/10.1063/1.5128846 Appl. Phys. Lett. 115, 264103 (2019); https://doi.org/10.1063/1.5114974 115, 264103 © 2019 Author(s). Applied Physics Letters ARTICLE scitation.org/journal/apl From symmetry to entropy: Crystal entropy difference strongly affects early stage phase transformation Cite as: Appl. Phys. Lett. 115, 264103 (2019); doi: 10.1063/1.5114974 Submitted: 14 June 2019 . Accepted: 21 November 2019 . Published Online: 27 December 2019 C. H. Hu,1 Y. C. Chen,2,3 P. J. Yu,3 K. Y. Fung,3 Y. C. Hsueh,4 P. K. Liaw,5 J. W. Yeh,6,a) and A. Hu3,4,7,a) AFFILIATIONS 1Department of Chemistry, University of Illinois Urbana-Champaign, Champaign, Illinois 61801,
    [Show full text]
  • Quick Review of Thermodynamics Plastic Deformation in Crystalline Materials
    Quick Review of Thermodynamics Plastic Deformation in Crystalline Materials Kamyar Davoudi Lecture 4 Fall 2015 Kamyar Davoudi Thermodynamics 1/21 Definitions ■ System: A collection of continuous matter ■ Isolated system: A system which does not exchange neither energy nor matter with its surrounding ■ Closed system: A system which does not exchange matter with its surrounding ■ State property: A property that depends only on the state of the system and not on how it reached that state (e.g.: volume, pressure, temperature, energy, and entropy) Kamyar Davoudi Thermodynamics 2/21 Intensive and Extensive Properties Intensive properties: properties that do not depend on the amount of material in a system such as temperature, pressure, chemical potential , specific energy, and specific entropy Extensive properties: properties that depend on the amount of material in a system such as volume, energy, entropy, and heat capacity https: //en.wikipedia.org/wiki/Intensive_and_extensive_properties Kamyar Davoudi Thermodynamics 3/21 Internal Energy U Internal energy arises from total kinetic and potential energies of the atoms within the system. Kinetic energy can arise from atomic vibration in solids or liquids and from translational and rotational energies of the atoms and molecules within a liquid or gas. Potential energy arises from the interactions and bonds between atoms within the system. Kamyar Davoudi Thermodynamics 4/21 The First Law of Thermodynamics Heat is a form of energy The change in the internal energy ¢U of a system is equal to the heat absorbed by the system ¢Qinput and the work done on the system ¢Winput by surface traction and body force ¢U Æ ¢Qinput Å ¢Winput For our purposes, we can treat them as infinitesimally small energy transfers and we can use their specific values (per unit mass): First Law of Thermodynamics du Æ ±q Å ±w R ■ Æ ½ Note that for example U V udV ■ ± represents inexact differential; that is there are no functions as q(P,V) and w(P,V) that depend only on the state of the system.
    [Show full text]
  • Fecrmnnic Amorphous Equiatomic Alloy Thin Film Abstract Keywords
    Demanding applications in harsh environment - FeCrMnNiC amorphous equiatomic alloy thin film W. Muftah*, N. Patmore and V. Vishnyakov Institute for Materials Research, University of Huddersfield, HD1 3DH, UK Abstract An amorphous equiatomic FeCrMnNiC alloy thin film was synthesised on silica and silicon substrates by ion beam sputter deposition. Scanning Electron Microscopy (SEM) Energy- dispersive X-ray spectroscopy (EDX), X-Ray Diffraction (XRD), Selected Area Electron Diffraction (SAED) and Nano indentation were used to investigate the material. The produced film is amorphous and uniform on the atomic level without any detectable element segregation. The corrosion properties were assessed in 3.5% NaCl solution. The FeCrMnNiC alloy has corrosion resistance better than corrosion resistance of 304 SS. The thin film has hardness at around 12.3 ± 0.5 GPa and reduced Young's modulus at around 222 ± 12 GPa. Keywords FeCrMnNiC, equiatomic alloy, high entropy alloy HEA, amorphous, thin film, microstructure, corrosion resistance, hardness *) Corresponding author: Waleed Muftah, [email protected] Introduction Demands for growth in efficiency, longer lifespan and emerging new applications all require development of more advanced alloys. Metal alloy properties are traditionally refined along the lines of atomic compositions and grain/boundary morphologies. The contemporary advance started with multicomponent alloys and then realisation that the entropy of mixing can be exploited as an engineering properties enhancement tool. [1-3]. The configurational entropy in this case is maximised at the equiatomic concentrations. The equiatomic alloys, from the entropy point of view, form a subset of highly concentrated alloys and are also known as High Entropy Alloys (HEA’s).
    [Show full text]
  • The Effects of Interstitials Clustering on the Configurational Entropy of Bcc Solid Solutions
    The effects of interstitials clustering on the configurational entropy of bcc solid solutions Jorge Garcés Centro Atómico Bariloche, CNEA, 8400 Bariloche, Río Negro, Argentina This work presents a simple model for describing the interstitials behavior in solid solutions enlarging the current random interstitial atoms paradigm. A general and parameter-free analytical expression to compute the configurational entropy, valid for any tetrahedral or octahedral interstitial solutions and suitable for the treatment of interstitials clustering, is deduced for that purpose. The effect of interstitials clustering on the configurational entropy is shown by applying the methodology to the Nb-H and bcc Zr-H solid solutions. The model for Nb-H presented in this work, based on the existence of H pairs in the α–phase and double pairs in the α’–phase, provides the basis to explain the unsolved controversies in this system. The unusual shape of the partial configurational entropy measured in bcc Zr-H can be accurately described if a small amount of H clusters are included in the solution. Keywords: entropy, solid solutions, interstitials, Hydrogen, clustering 1. Introduction one interstitial atom (named overlapping or soft blocking) and, therefore, not all lattice sites are equivalent. The Despite the significant advances in computational main consequence of the SRO is to produce an important material science in the last years, a quantitative and decrease in the number of configurations to be computed. parameter-free methodology to predict the material Boureau and Tetot [3] showed in their Ti-O study that the properties at finite temperature is still unavailable. number of configurations decreases from 2x1019 to 2x107 However, there are technological requirements to extend if the blocking effect is considered.
    [Show full text]
  • Temperature-Dependent Structures and Atomic Mixing Behaviors in High-Entropy Alloys
    University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 5-2016 Temperature-Dependent Structures and Atomic Mixing Behaviors in High-Entropy Alloys Louis J. Santodonato University of Tennessee - Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Metallurgy Commons Recommended Citation Santodonato, Louis J., "Temperature-Dependent Structures and Atomic Mixing Behaviors in High-Entropy Alloys. " PhD diss., University of Tennessee, 2016. https://trace.tennessee.edu/utk_graddiss/3743 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Louis J. Santodonato entitled "Temperature- Dependent Structures and Atomic Mixing Behaviors in High-Entropy Alloys." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Materials Science and Engineering. Peter K. Liaw, Major Professor We have read this dissertation and recommend its acceptance: Jaime Fernandez-Baca, David J. Keffer, James R. Morris Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Temperature-Dependent Structures and Atomic Mixing Behaviors in High- Entropy Alloys A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Louis J.
    [Show full text]
  • Configurational Entropy in Multicomponent Alloys
    entropy Article Configurational Entropy in Multicomponent Alloys: Matrix Formulation from Ab Initio Based Hamiltonian and Application to the FCC Cr-Fe-Mn-Ni System Antonio Fernández-Caballero 1,2 , Mark Fedorov 3, Jan S. Wróbel 3 , Paul M. Mummery 1 and Duc Nguyen-Manh 2,* 1 School of Mechanical Aerospace and Civil Engineering, University of Manchester, Manchester M13 9PL, UK; [email protected] (A.F.-C.); [email protected] (P.M.M.) 2 CCFE, United Kingdom Atomic Energy Authority, Abingdon OX14 3DB, UK 3 Faculty of Materials Science and Engineering, Warsaw University of Technology, Woloska 141, 02-507 Warsaw, Poland; [email protected] (M.F.); [email protected] (J.S.W.) * Correspondence: [email protected] Received: 7 November 2018; Accepted: 11 January 2019; Published: 15 January 2019 Abstract: Configuration entropy is believed to stabilize disordered solid solution phases in multicomponent systems at elevated temperatures over intermetallic compounds by lowering the Gibbs free energy. Traditionally, the increment of configuration entropy with temperature was computed by time-consuming thermodynamic integration methods. In this work, a new formalism based on a hybrid combination of the Cluster Expansion (CE) Hamiltonian and Monte Carlo simulations is developed to predict the configuration entropy as a function of temperature from multi-body cluster probability in a multi-component system with arbitrary average composition. The multi-body probabilities are worked out by explicit inversion and direct product of a matrix formulation within orthonomal sets of point functions in the clusters obtained from symmetry independent correlation functions. The matrix quantities are determined from semi canonical Monte Carlo simulations with Effective Cluster Interactions (ECIs) derived from Density Functional Theory (DFT) calculations.
    [Show full text]
  • A Probabilistic Description of the Configurational Entropy of Mixing
    Entropy 2014, 16, 2850-2868; doi:10.3390/e16052850 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article A Probabilistic Description of the Configurational Entropy of Mixing Jorge Garcés Simulation and Modeling of Materials Division, Nuclear Fuel Cycle Department, Centro Atómico Bariloche, 8400 Bariloche, Río Negro, Argentina; E-Mail: [email protected]; Tel./Fax: +54-294-445-100 Received: 27 February 2014; in revised form: 16 May 2014 / Accepted: 20 May 2014 / Published: 23 May 2014 Abstract: This work presents a formalism to calculate the configurational entropy of mixing based on the identification of non-interacting atomic complexes in the mixture and the calculation of their respective probabilities, instead of computing the number of atomic configurations in a lattice. The methodology is applied in order to develop a general analytical expression for the configurational entropy of mixing of interstitial solutions. The expression is valid for any interstitial concentration, is suitable for the treatment of interstitial short-range order (SRO) and can be applied to tetrahedral or octahedral interstitial solutions in any crystal lattice. The effect of the SRO of H on the structural properties of the Nb-H and bcc Zr-H solid solutions is studied using an accurate description of the configurational entropy. The methodology can also be applied to systems with no translational symmetry, such as liquids and amorphous materials. An expression for the configurational entropy of a granular system composed by equal sized hard spheres is deduced. Keywords: configurational entropy; analytical expressions; interstitial solid solutions; hard sphere fluids PACS Codes: 82.60.Lf; 65.40.gd; 61.72.jj; 61.66.Dk Entropy 2014, 16 2851 1.
    [Show full text]
  • Nanoscale Accepted Manuscript
    Nanoscale Accepted Manuscript This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after acceptance, before technical editing, formatting and proof reading. Using this free service, authors can make their results available to the community, in citable form, before we publish the edited article. We will replace this Accepted Manuscript with the edited and formatted Advance Article as soon as it is available. You can find more information about Accepted Manuscripts in the Information for Authors. Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains. www.rsc.org/nanoscale Page 1 of 9 Please doNanoscale not adjust margins Nanoscale Paper Heteroaggregation Assisted Wet Synthesis of Core-Shell Silver- Silica-Cadmium Selenide Nanowires a b a b *a Received 00th January 20xx, I. A. Pita, S. Singh , C. Silien , K. M. Ryan and N. Liu Accepted 00th January 20xx A method has been developed for the wet solution synthesis of core shell heterogeneous nanowires. An ultrathin silica layer DOI: 10.1039/x0xx00000x was first grown around plain silver nanowires to act as a suitable insulator. An outer nanoparticle layer was then attached through heteroaggregation by dispersing the un-functionalized nanowires in toluene solutions containing nanoparticles of www.rsc.org/ CdSe or Au.
    [Show full text]
  • Synthesis and Characterisation of High Entropy Alloy and Coating
    LICENTIATE T H E SIS Department of Engineering Sciences and Mathematics Division of Materials Science ISSN 1402-1757 ISBN 978-91-7790-394-9 (print) Synthesis and Characterisation of High ISBN 978-91-7790-395-6 (pdf) and Coating Alloy Alvi Synthesis and Characterisation of High Entropy Ali Sajid Luleå University of Technology 2019 Entropy Alloy and Coating Sajid Ali Alvi Engineering Materials Licentiate thesis Synthesis and Characterisation of High Entropy Alloy and Coating Sajid Ali Alvi Department of Engineering Sciences and Mathematics Division of Materials Science Luleå University of Technolgy Printed by Luleå University of Technology, Graphic Production 2019 ISSN 1402-1757 ISBN 978-91-7790-394-9 (print) ISBN 978-91-7790-395-6 (pdf) Luleå 2019 www.ltu.se Abstract High entropy alloys (HEAs) are a new class of alloys that contains five or more principal elements in equiatomic or near-equiatomic proportional ratio. The configuration entropy in the HEAs tends to stabilize the solid solution formation, such as body-centered-cubic (BCC), face-centered-cubic (FCC) and/or hexagonal-closed-pack (HCP) solid solution. The high number of principal elements present in HEAs results in severe lattice distortion, which in return gives superior mechanical properties compared to the conventional alloys. HEAs are considered as a paradigm shift for the next generation high temperature alloys in extreme environments, such as aerospace, cutting tools, and bearings applications. The project is based on the development of refractory high entropy alloy and film. The first part of the project involves designing high entropy alloy of CuMoTaWV using spark plasma sintering (SPS) at 1400 oC.
    [Show full text]
  • A Continuum Model for Progressive Damage in Tough Multinetwork Elastomers
    A continuum model for progressive damage in tough multinetwork elastomers Shawn R. Lavoie†, Pierre Millereau§, Costantino Creton§, Rong Long‡, Tian Tang†*, †Department of Mechanical Engineering, 10-203 Donadeo Innovation Centre for Engineering, 9211-116 Street NW, Edmonton, AB, T6G 1H9, Canada § Laboratoire de Sciences et Ingénierie de la Matière Molle, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France ‡ Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO, USA 80309. *Corresponding author E-mail: [email protected], Phone: 780-492-5467, Fax: 780-492-2378 Keywords: Multinetwork elastomer, fracture toughness, progressive damage Abstract Recently a class of multinetwork elastomers (MNEs) was developed by swelling a filler polymer network with monomers that are subsequently polymerized to form matrix networks. Such MNEs were reported to possess remarkable stiffness and fracture toughness while maintaining the ability to sustain large deformation as found in simple elastomers. The enhancement in toughness is attained by prestretching the chains of the filler network through the introduction of one or more matrix network(s), thereby promoting energy dissipation through chain scission in the filler network. In this work, a model to capture the mechanical response of MNEs is developed, and validated with experimental data. Prestrech of the polymer chains is incorporated into the model by basing the strain energy density function on the combined effect 1 of swelling and subsequent deformation of the completed MNE. The filler network is modeled as a polydisperse network of breakable polymer chains with nonlinear chain elasticity, while the matrix networks are modeled using the generalized neo-Hookean model.
    [Show full text]
  • A Continuum Model for Progressive Damage in Tough Multinetwork Elastomers
    A continuum model for progressive damage in tough multinetwork elastomers Shawn R. Lavoie†, Pierre Millereau§, Costantino Creton§, Rong Long‡, Tian Tang†*, †Department of Mechanical Engineering, 10-203 Donadeo Innovation Centre for Engineering, 9211-116 Street NW, Edmonton, AB, T6G 1H9, Canada § Laboratoire de Sciences et Ingénierie de la Matière Molle, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France ‡ Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO, USA 80309. *Corresponding author E-mail: [email protected], Phone: 780-492-5467, Fax: 780-492-2378 Keywords: Multinetwork elastomer, fracture toughness, progressive damage Abstract Recently a class of multinetwork elastomers (MNEs) was developed by swelling a filler polymer network with monomers that are subsequently polymerized to form matrix networks. Such MNEs were reported to possess remarkable stiffness and fracture toughness while maintaining the ability to sustain large deformation as found in simple elastomers. The enhancement in toughness is attained by prestretching the chains of the filler network through the introduction of one or more matrix network(s), thereby promoting energy dissipation through chain scission in the filler network. In this work, a model to capture the mechanical response of MNEs is developed, and validated with experimental data. Prestrech of the polymer chains is incorporated into the model by basing the strain energy density function on the combined effect 1 of swelling and subsequent deformation of the completed MNE. The filler network is modeled as a polydisperse network of breakable polymer chains with nonlinear chain elasticity, while the matrix networks are modeled using the generalized neo-Hookean model.
    [Show full text]