Table Of ContentElsevier Series in Mechanics of Advanced
Materials
The Mechanics of
Hydrogels
Mechanical Properties, Testing, and
Applications
Edited by
Hua Li
School of Mechanical and Aerospace
Engineering, Nanyang Technological University,
Singapore
Vadim Silberschmidt
Wolfson School of Mechanical, Electrical and
Manufacturing Engineering, Loughborough
University, Loughborough, United Kingdom
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Elsevier Series in Mechanics of Advanced
Materials
Editor-in-Chief
Vadim V. Silberschmidt
LoughboroughUniversity,UK
Series Editors
Thomas B€ohlke
KarlsruheInstituteofTechnology,Germany
David McDowell
GeorgiaInstituteofTechnology,USA
Chen Zhong
NanyangTechnologicalUniversity,Singapore
List of contributors
Mark Ahearne Department of Mechanical, Manufacturing and Biomedical Engi-
neering, School of Engineering, Trinity College Dublin, The University of Dublin,
Dublin,Ireland;TrinityCentreforBiomedicalEngineering,TrinityBiomedicalScien-
ces Institute,TrinityCollege Dublin, The University of Dublin, Dublin,Ireland
Xing Gao Research Centre for Medical Robotics and Minimally Invasive Surgical
Devices, Shenzhen Institutes of Advanced Technology, Chinese Academy of Scien-
ces, Shenzhen, Guangdong, China
K.B. Goh School of Engineering, Monash University Malaysia, Bandar Sunway,
Selangor, Malaysia
Mohammad R. Islam Department of Ophthalmology, University of Pittsburgh,
Pittsburgh, PA, United States
J.JinchengLei InternationalCenterforAppliedMechanics,StateKeyLaboratory
forStrengthandVibrationofMechanicalStructures,Xi’anJiaotongUniversity,Xi’an,
Shaanxi,China
Hua Li School of Mechanical & Aerospace Engineering, Nanyang Technological
University, Singapore, Republic ofSingapore
Ziqian Li International Center for Applied Mechanics, State Key Laboratory for
Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an,
Shaanxi,China
Qimin Liu School of Civil Engineering and Architecture, Wuhan University of
Technology,Wuhan, Hubei,PR China
Zishun Liu International Center for Applied Mechanics, State Key Laboratory for
Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an,
Shaanxi,China
TongqingLu StateKeyLaboratoryforStrengthandVibrationofMechanicalStruc-
tures, International Center for Applied Mechanics, Department of Engineering
Mechanics, Xi’anJiaotong University, Xi’an, Shannxi,China
Lianhua Ma College of Quality and Technical Supervision, Hebei University,
Baoding, PR China
Yinggang Miao Joint International Research Laboratory of Impact Dynamics and
ItsEngineeringApplications,SchoolofAeronautics,NorthwesternPolytechnicalUni-
versity,Xi’an, Shaanxi, China
x Listofcontributors
Michelle L. Oyen Department of Biomedical Engineering, Washington University
in St.Louis, St. Louis, MO, United States
Zhi-JunShi CollegeofLifeScienceandTechnology,HuazhongUniversityofSci-
ence and Technology, Wuhan, Hubei,China
Vadim V. Silberschmidt Wolfson School of Mechanical, Electrical and Manufac-
turingEngineering,Loughborough University, Leicester, United Kingdom
Emrah Sozumert Wolfson School of Mechanical, Electrical and Manufacturing
Engineering, Loughborough University, Leicester, United Kingdom
WilliamToh SchoolofMechanicalandAerospaceEngineering,NanyangTechno-
logical University, Singapore,Singapore
Xingquan Wang Department of Engineering Mechanics, Faculty of Materials and
Manufacturing,Beijing University ofTehnology,Beijing, PR China
Tao Wu School of Mechanics, Civil Engineering and Architecture, Northwestern
PolytechnicalUniversity,Xi’an,Shaanxi,PRChina;MIITKeyLaboratoryofDynam-
ics andControl of Complex Systems,Xi’an, Shaanxi,PR China
Shuai Xu International Center for Applied Mechanics, State Key Laboratory for
Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an,
Shaanxi, China
Qingsheng Yang Department of Engineering Mechanics, Faculty of Materials and
Manufacturing,Beijing University ofTehnology,Beijing, PR China
Jianxun Zhang State Key Laboratory for Strength and Vibration of Mechanical
Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an,
Shaanxi, China
QiangZhang SchoolofElectricPower,CivilEngineeringandArchitecture,Shanxi
University, Taiyuan, Shanxi, China
Wenlei Zhang State Key Laboratory for Strength and Vibration of Mechanical
Structures, International Center for Applied Mechanics, Department of Engineering
Mechanics, Xi’an Jiaotong University, Xi’an, Shannxi, China
Wei-Wei Zhao School ofMechanicalandElectronicEngineering, Wuhan Univer-
sityof Technology, Wuhan, Hubei,China
ShoujingZheng InternationalCenterforAppliedMechanics,StateKeyLaboratory
forStrengthandVibrationofMechanicalStructures,Xi’anJiaotongUniversity,Xi’an,
Shaanxi, China
YifanZhou StateKeyLaboratoryforStrengthandVibrationofMechanicalStruc-
tures, International Center for Applied Mechanics, Department of Engineering
Mechanics, Xi’an Jiaotong University, Xi’an, Shannxi, China
Preface
Inrecent years, hydrogels eoneoftheadvanced materials e haveattracted increas-
ingly more attention thanks to their suitability for a wide range of emerging applica-
tions. For example, hydrogels are adopted in various biological systems due to their
unique properties such as biocompatibility and biostability, biomimetic applications
such as soft robots, as well as medical/pharmaceutical applications such as drug
delivery systems, articular cartilage, biomaterial scaffolds, corneal replacement, and
tissue engineering. However, a common and serious concern regarding hydrogels is
their mechanical properties. A large amount of interstitial water within networked
structure of cross-linked hydrophilic polymer chains results in the hydrogels’ soft
mechanicalbehavior.Thisoftenbecomesanobviouslimitationtotheirvariousappli-
cations,especiallyinbiologicalandmedicalfields.Assuch,itiscriticallyimportantto
develop the mechanics of hydrogels, in order to obtain a deep understanding of the
fundamentalmechanismsofdeformation,damageandfracture,mechanicalcharacter-
istics of soft hydrogels, and also to provide a bridge between the mechanical and
biologicalperformanceofhydrogelssoastopushthemechanicalapplicationofhydro-
gels beyondtheircurrent boundaries.
Thisbookispreparedbyagroupofleadingacademicsandexpertsfromdifferent
institutionsandcountries,includingthemostactiveresearchersgloballyintheareaof
hydrogelmechanics.Theirresearchinterestscoveralmostallrelevanttopicsintheme-
chanics of hydrogels, from theoretical modeling and numerical simulation to experi-
mental tests and further to various applications, from micro to macro scales.
Examples of the research topics include mechanical characterization of hydrogel at
differentscales;elasticandinelasticbehaviorsofhydrogels;rheologicalcharacteriza-
tionofhydrogels;fatigueandfractureofhydrogels;indentationtestingofhydrogels;
phasetransitionsinhydrogels;responsesofsmarthydrogelstovariousenvironmental
stimuli;mechanicalpropertiesofcellularlyresponsivehydrogels;multiscalemodeling
ofhydrogels;applicationsofhydrogelsincornealreplacementandartificialmuscles;
soft robots; and manufacturing of hydrogels with controlled mechanical properties.
These topics are covered in this collection of such contributions, with each written
by world-leading experts in the relevant research areas. The volume’s contributors
not only present their own pioneering work in their research fields, but also provide
valuable literature reviews andrecommend thesignificant futurework.
Therefore, this book covers the most advanced knowledge on the mechanics of
hydrogels, making it informative reading for experts; concurrently, it can serve as a
rich reference source for graduate students intending to work in this area. It will be
xii Preface
alsousefulforscientistsandengineersinthebroadareasofpolymermaterialsscience,
mechanicsofmaterials,biomaterialsengineering,biomedicalengineering,biosensors/
actuators,microelectro-mechanicalsystem(MEMS)andbioMEMS,artificialmuscles
and soft robotics, microfluidic control, physics, chemistry, biophysics, biochemistry,
andbioengineering.Itwillbeespeciallyusefulformedicalpractitionersandbiomed-
ical companies as a reference source with benchmark results to compare and verify
their experimental data against the mechanical properties of hydrogels. The book
also provides key guidance for medical practitioners planning to conduct further
studies to extend their work into practical mechanical applications of soft materials
anddesignaswellastooptimizevariousapplicationssuchashydrogel-basedsoftro-
bots, orperformnumericalstudies,where theknowledge ofmechanical propertiesis
crucial.
Hua Li
School ofMechanical and Aerospace Engineering
Nanyang Technological University
Republic ofSingapore
Vadim V.Silberschmidt
WolfsonSchool ofMechanical, Electrical and Manufacturing Engineering
LoughboroughUniversity
UnitedKingdom
1
Mechanical characterization of
hydrogels
Mohammad R. Islam1 andMichelle L.Oyen2
1Department of Ophthalmology, University of Pittsburgh,Pittsburgh, PA, United States;
2DepartmentofBiomedicalEngineering,WashingtonUniversityinSt.Louis,St.Louis,MO,
United States
1.1 Introduction
Hydrogels are polymeric materials consisting of a sparse network of polymer chains
embeddedinanaqueousmedium.Hydrogelscanretainlargeamountsofwaterwithin
theirintermolecularspaceduetostronghydrophilicityofthepolymerchainsandlarge
porosity.As such, hydrogelscan undergo significant swelling inwater, from 10% to
1000 times of their dry weight [1]. The polymer network does not dissolve in water
as interchain cross-linking prohibits water flow at scales larger than network pore
size,preservingthestructuralintegrityofthematerial.Hydrogelstructureandswelling
behaviorlargelydependonpolymercomposition,natureofcross-linking,fabrication
routes, and external environment, making gel properties exquisitely tunable over a
broadrange.Thisdiversityinhydrogels’chemical,physical,andmechanicalproper-
tiesoffersanexcitingavenueofsoftmaterialdesignformultidisciplinaryapplications.
Hydrogels are ubiquitous around us. The extracellular matrix (ECM) of most soft
tissues inourbodysuchascartilage,cornea,heart vessels, andskin tissueareessen-
tially fibrous hydrogel composites, consisting of a hydrated proteoglycan gel rein-
forced with biopolymer (i.e., collagen or elastin) fibers. Bacterial biofilms are also
hydrogels [2] and marine plant tissues (i.e., kelp) are fiber-reinforced polysaccharide
gels[3].Gelatin,agar,andalginategelshavebeenusedinfoodindustryfor decades
[4]. Beyond these traditional hydrogels, the technological advantage of synthesizing
hydrogels as engineering materials was not realized until 1960. Wichterle and Lim
[5] first developed a hydrogel for soft contact lenses by polymerizing poly(2-
hydroxyethyl methacrylate) (polyHEMA) with cross-linking agents in the presence
ofwaterandothersolvents.Sincethisimportantdiscovery,alargevarietyofhydrogels
with intriguing chemical, physical, and mechanical properties have been developed.
Buwaldaetal.[6]presentedasystematicreviewofthishistoricalevolutionofhydro-
gel asmaterial.
Hydrogels have found diverse and rapidly increasing applications in recent years.
Theyarewidelyusedinconsumerproductssuchascontactlenses,cosmeticimplants,
hairgels,anddiapers[7].Hydrogelsloadedwithpharmaceuticallyactivecompounds
are used as drug carriers to achieve controlled and targeted drug release into human
body [8]. Hydrogels act as debriding agent and provide a moist condition in wound
TheMechanicsofHydrogels.https://doi.org/10.1016/B978-0-08-102862-9.00014-2
Copyright©2022ElsevierLtd.Allrightsreserved.
2 TheMechanicsofHydrogels
dressingstofacilitatewoundhealing[9].Intissueengineering,hydrogelsarecultured
withcellsandgrowthfactorstobeusedasartificialscaffoldsfordamagedtissuerepair
and regeneration [10,11]. Hydrogels are used as urinary catheter coatings to prevent
bacterial colonization on the surface [12]. Hydrogels are also increasingly used for
in vitro experiments to study the role of matrix elasticity on stem cell differentiation
[13e15]. Several biomimetic machines and functional devices are also developed
fromhydrogelsbyleveragingtheiruniquepropertiesandstimuliresponsivecharacter-
istics.Examplesincludehydrogelactuators[16],stretchablehydrogelelectronics[17],
hydrogelvalvesformicrofluidics[18],color-tunablehydrogelcolloidalcrystals[19],
and artificial muscles [20].
Advancementinhydrogeltechnologyhasalsodrawnconsiderableresearchinterest
onhydrogelmechanics.Inseveralimportantapplications,ahydrogelactsasaprimary
load-bearing component, which often requires an optimal combination of elasticity,
strength, and toughness as a material. For example, hydrogel scaffolds for cartilage
replacement must possess both high strength and fracture toughness [21]. Artificial
skinsmadefromhydrogelsneedtosustainlargestrainwithoutdamage[22].Hydrogel
actuators,suchasroboticarms,oftenfunctionunderrepeatedcyclicloading[23].Me-
chanicalpropertiesofhydrogelsarealsoimportantforfunctionalapplications.Incell
culturestudies,ithasbeenobservedthatthestiffnessofhydrogelsubstrateaffectscell
behavior,includingproliferation,migration,anddifferentiation[13].Mechanicalchar-
acterization of hydrogels under in situ loading conditions is therefore an important
considerationin design of hydrogelmaterials.
Hydrogelsaremultiphasecompositematerialsconsistingofanaqueousmatrixrein-
forced by solid polymer network. Fig. 1.1 illustrates schematically the structure of
hydrogels at different length scales. At macroscale, they resemble continuum solids
withdefinedshapedespitelargewatercontent.Microscopically,hydrogelsarediscrete
randomnetworksofflexibleorsemiflexiblepolymerchains.Atmolecularscale,they
allow diffusion of solute molecules just like pure liquid. Hydrogel mechanics is also
strongly multiscale. When subjected to far field loading, individual polymer chains
deform in a manner dependent on bulk polymer properties, connectivity with the
neighboring chains, interaction with solvent molecules, and the test environment.
The collective deformation of all such chains leads to a nonuniform deformation at
the network scale, and thereby a nonlinear stressestrain behavior at the macroscale.
While theliquid matrix does notsupportanyload, it introduces anincompressibility
constraint that prevents lateral contraction of the polymer network under stretch.
Hydrogels demonstrate strong time-dependent relaxation behavior that involves two
distinct mechanisms associated with viscoelastic and poroelastic deformation [24].
Viscoelastic relaxation occurs due to topological fluctuations of flexible polymer
chains under fixed strain, whereas poroelastic relaxation emerges from the migration
of liquid over time. Poroelasticity of hydrogels is strongly dependent on material
length-scale, whereasviscoelasticityislargelylength-scale independent [25].
Multiscalestructureandmechanicsofhydrogelsnecessitateevaluationoftheirme-
chanicalpropertiesatdifferentlength-andtime-scalesaswell.Alargevarietyofme-
chanicaltestingmethodsareusedforhydrogelsdependingonthemateriallength-scale
and mechanical property of interest (Fig. 1.1b). Elastic and fracture properties (i.e.,
