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- •Preface
- •Contents
- •About the Authors
- •Further Reading
- •2.1.1 HA Fillers
- •2.1.2.4 PLLA (Poly-L-Lactic Acid) Fillers
- •2.1.2.5 PMMA (Polymethyl Methacrylate) Fillers
- •2.1.2.6 PAAG (Polyacrylamide Gel) Fillers
- •2.2.3 Cross-Linking Process
- •2.2.4 Dialysis or Washing
- •2.2.5 Cutting
- •2.2.6 Filling
- •2.2.7 Sterilization Process
- •2.3.1.2 Fluid Mechanics
- •2.1.2 Non-HA Fillers
- •2.1.2.1 Collagen Fillers
- •2.1.2.2 Ca Fillers
- •2.1.2.3 PCL (Polycaprolactone) Fillers
- •2.3.1.3 Rheology
- •2.3.2.1 G′: Elastic Modulus
- •2.3.2.2 G″: Viscous Modulus
- •2.3.2.3 G*: Complex Modulus
- •2.3.2.4 Phase Angle (Tangent δ)
- •2.3.2.5 Cohesion
- •Perceived Cohesion Test
- •Dispersion Test
- •Drop Weight Test
- •Compression Force Test
- •Flexibility Test
- •Further Reading
- •3.3 Retaining Ligaments
- •3.5.1 Subgalea-Frontalis Space
- •3.5.6 Prezygomatic Space
- •3.5.9 Prebuccal Space
- •3.5.11 Premental Space
- •Further Reading
- •4.1 Design Guidelines
- •4.1.4 Lateral View: Ricketts Line
- •4.2 Anesthesia: Nerve Block
- •4.2.1 Supratrochlear Nerve/Supraorbital Nerve
- •4.3 Cannula or Needle Selection
- •4.3.1 Cannula
- •4.4 Injection Techniques
- •4.4.1.8 Mantoux Injection Technique
- •4.4.1.9 Sandwich Technique
- •4.5 Basic Techniques by Area
- •4.6.1.2 Key Methodological Steps
- •4.6.1.3 Study Result
- •4.7.1 Filler Molding
- •4.7.2 Filler Degradation Test
- •Further Reading
- •5.1 Upper Face
- •5.1.2 Temple
- •5.2 Midface
- •5.2.2.1 Terminology
- •5.2.2.4 Injection Skill
- •Needle Injection
- •Cannula Injection
- •5.2.4.1 Design
- •5.2.4.2 Anesthesia
- •5.2.4.4 Injection Technique
- •5.2.5 Midcheek Groove
- •5.2.5.2 Treatment
- •5.2.7 Nose
- •5.2.7.3 Injection Technique
- •5.2.8 Nasolabial Fold
- •5.3 Lower Face
- •5.3.3.2 Injection Technique
- •5.3.4.1 Design
- •5.3.4.2 Anatomy
- •5.4 Skin Booster Procedures
- •5.4.1 Manual Injection Techniques
- •Further Reading
- •6.1.2 Edema
- •6.1.5.2 Granuloma
- •6.1.6 Infection
- •6.2.1.1 Extravascular Compression
- •6.2.1.2 Intravascular Emboli
- •6.2.2 Skin Necrosis
- •Decompression
- •Revascularization
- •Scar Treatment
- •6.2.3 Vascular Complication: Blindness
- •6.3.1.1 Hyaluronic Acid Turnover
- •6.3.2.4 Clinical Implications
- •Further Reading

16
hyaluronic acid
hyaluronic acid
Cross-linker
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
Linear shape of noncross-linked
Fig. 2.2 Noncross-linked and cross-linked hyaluronic acid
Hyaluronic acid can attract and hold water
that is almost 1000 times bigger than its molecular size, being responsible for storing moisture in
the dermis tissues and keeping the skin volume.
There are important reasons for keeping the
moisture level in the skin. The appropriate
amount of moisture makes the skin supple and
helps it easily keep its elasticity. In addition,
hyaluronic acid facilitates the multiplication and
migration of broblasts for the better production
of collagen and elastin; in addition, it contributes
to the prevention of skin cell aging by removing
free oxygen radicals.
As people get older, the amount of hyaluronic
acid in the skin decreases. They maintain the
amount of hyaluronic acid that is given at birth
level until 20 years old, and then it begins to
reduce at the age of 20. In general, the amount of
hyaluronic acid in adult skin at the age of 55 is
half the amount of hyaluronic acid at 35. At an
older age, one can have hyaluronic acid, which is
insufcient in the skin, injected into the dermis to
ultimately benet from the increasing volume of
dermis and hypodermis tissues as hyaluronic acid
increases its volume by absorbing moisture, casing the alteration of neighboring broblasts by
pressing on them, and inducing the generation of
collagen. Hyaluronic acid in the human body is
dissolved by a natural enzyme called hyaluroni-
Interwined shape of cross-linked
dase and then disappears. Free HA, which refers
to hyaluronic acid in its natural state, needs a stabilization process called cross-linking between
HA molecules with a cross-linking agent so that
it can be used as a ller. Cross-linking is a process of linking the molecules of hyaluronic acid,
which is untied like a thread and linearized, physically or chemically so that they will not be dissolved easily by an enzyme in the human body
(Fig.2.2).
HA llers are medical llers based on natural
free HA whose physical and rheological properties are altered to prevent easy dissolution. Since
they should be used with human tissues, they
should have biocompatibility so as not to cause
any problems to the adjacent tissues of an injection. In the past, hyaluronic acid was made of raw
materials extracted from the tongue and cartilage
of a cow and the cockscomb. Animal-derived
hyaluronic acid has been replaced with microbial
process-derived hyaluronic acid due to the possibilities of allergic reactions and the issues of
mad cow disease and avian inuenza in modern
society. Streptococcus is usually used to cultivate
microorganisms such as bacteria to produce hyaluronic acid, with the most popular strain being
Streptococcus zooepidemicus. NASHA, which
refers to the method of the rst HA ller
Restylane, is actually the abbreviation of non-

2.1 Classication ofFillers According toRaw Materials
17
animal stabilized hyaluronic acid rather than a
certain physical linking method. Today, it is natural that non-animal raw materials are used for HA
llers. When the rst HA ller was developed
and produced, it was of huge importance to
decide which materials should be used.
When hyaluronic acid is made via microbial
multiplication, it has high purity and low possibilities of pathogens such as a virus, which is
problematic with animal-derived raw materials.
It is, however, high in the content of endotoxins
excreted from microorganisms and impurities
such as intracellular organelle and cell-derived
protein, which makes it essential to undergo a
proper distillation process. Several steps of ltering and distillation should be conducted, including dissolution in an NaOH solution,
centrifugation, ltering, precipitation, and
absorption to get hyaluronic acid as a raw material of HA llers. Going through this complex
distillation process, hyaluronic acid varies in
purity as a raw material according to the distillation methods and degrees. The grade of raw
material depends on its purity, and there are three
grades: food, cosmetics, and medicine. The distillation process of medical hyaluronic acid is, of
course, the most complex and produces the highest level of purity. Medical hyaluronic acid is further divided into ophthalmic and intravenous
hyaluronic acid. Intravenous hyaluronic acid is
used as a raw material for lens llers, intraarticular injections, anti-adhesion agents, scaffolds for tissue engineering, and HA llers. It is
said that intravenous hyaluronic acid is several
times more expensive than ophthalmic hyaluronic acid. Intravenous HA powder is the hyaluronic acid raw material of the highest purity.
an injection; hence, it stays in the body for years.
These permanent llers have extremely high possibilities of side effects due to a foreign body
reaction, so they are not used much in the nation.
These days PN (polynucleotide) extracted from
salmon sperm and PDRN (polydeoxyribonucleotide) extracted from trout sperm are used as llers
injected into the skin for the regeneration of damaged tissue cells and the restoration of skin tissue
itself rather than the highlight of volume as a
non-HA ller.
2.1.2.1 Collagen Fillers
In the history of llers, the early ones were known
to have side effects due to their biochemical matters and were banned accordingly. With the
development of modern medicine, llers made of
animal collagen extracted from cows, such as
Zyderm and Zyplast, were rst developed and
then obtained an approval from the U.S.FDA in
the 1980s. They were followed by llers made of
collagen extracted from pig (Permacol, Evolence,
etc.) and human collagen (Cymetra, etc.).
Collagen llers are made of animal collagen and
require a skin test before a procedure to check
whether the client has an allergic reaction or not.
Early collagen llers had a short duration and
were no longer used after the development and
full-scale use of HA llers. Today there are collagen ller products that last for a year or longer
thanks to the technological distillation of pigderived collagen, but there are no enzyme materials to melt and dissolve away collagen, which
means that cautions should be taken before use
(Fig.2.3).
2.1.2 Non-HA Fillers
Most non-HA llers are used for their advantages
of a longer duration and more collagen production than HA llers except for the early collagen
llers whose duration was shorter than HA llers. Non-HA llers comprised of biochemical
matters are not absorbed in the human body after
Fig. 2.3 Atelocollagen ller

18
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
2.1.2.2 Ca Fillers
Ca llers are made of two components: calcium
hydroxyl-apatite (CaHA)–Ca10(PO4)6(OH)2
and a gel carrier. CaHA is a biocompatible material present in the human body, which has been
used in the eld of medicine for decades.
Comprised of particles of 20~45μm, it accounts
for approximately 30% of the entire Ca llers
(Fig. 2.4). After a Ca ller is injected into the
skin, CaHA facilitates collagen production by
stimulating surrounding tissues over time. It
turns into calcium and phosphate ions after being
slowly dissolved in the metabolic process of the
human body and is eventually removed naturally
through the human metabolic process.
A gel carrier accounts for 70% of a Ca ller
dose. Being comprised of sodium carboxymethylcellulose, glycerin, and sterile water, it has a
large molecular weight and viscoelasticity. It
generates instant volume effects after a ller
injection and keeps its shape until collagen production by CaHA.
These llers have the following differences
from HA llers in the clinical aspect: new collagen grows into an empty space created by the
absorption of a gel carrier, which means that Ca
llers produce more collagen than HA llers. In
addition, they get absorbed slowly with more collagen produced, recording a longer duration than
HA llers. Unlike HA llers, however, Ca llers
have no enzyme materials that get dissolved
away when wished for. Ca llers basically have
good viscoelasticity and can be used for parts
where the satisfaction in the sense of volume is
low after a procedure with an HA ller. They can
also be used to improve skin texture in addition to
increasing the sense of volume in soft tissues for
their material characteristics.
2.1.2.3 PCL (Polycaprolactone) Fillers
There are polymer materials developed for medical purposes, such as PDO threads used in thread
lifting and various materials used as a scaffold in
nose and breast surgeries. PCL is one of these
medical polymers.
PCL llers are made up of PCL particles in a
spherical shape with a smooth surface in 30%
and CMC (carboxy methylcellulose) used as a
gel carrier in 70%. Both PCL and CMC are completely absorbed, being used as a component of
medical devices for many years (Fig.2.5).
After a PCL ller injection, the CMC gel carrier is absorbed by macrophages over weeks. The
Fig. 2.4 Ca ller Fig. 2.5 PCL ller

2.1 Classication ofFillers According toRaw Materials
19
PCL sphere is not absorbed by them due to its
certain size (25~50μm) and gets surrounded by
macrophages but its spherical shape keeps intact.
PCl then multiplies the collagen, which in turn
occupies a space created by the absorption of the
gel carrier around the particle.
Doctors who use PCL llers must be aware of
their volume changes due to these reactions.
Right after a PCL ller injection, the part may
seem a little bit swollen due to edema. Once the
swelling subsides, the volume will decrease.
Then the CMC gel carrier is absorbed and
replaced with collagen, during which the ller
volume will seem to decrease further. After a few
weeks, the collagen will multiply and increase
the volume. Patients may complain by saying that
their llers have gone too quickly when it is
2~4weeks after a PCL ller procedure. If doctors
do an additional procedure too early without
observing the progress enough, they may encounter overcorrection later, which calls for caution.
Long-term llers that are known to have a longer duration and produce collagen better than HA
llers have the possibilities of side effects due to
longer delayed immune reactions.
It is generally known that microspheres
smaller than 15μm are removed by phagocytosis
and that microspheres bigger than 15μm with an
irregular surface can form granuloma due to
inammatory and foreign body reactions.
One serious side effects of long-term llers is
foreign body granuloma. Injected llers show
chronic inammation. As giant cells by the fusion
of macrosphages surround llers, they form an
inammatory lump.
Doctors need to keep the possibilities of these
side effects in mind when choosing a long-term
ller, such as a PCL ller, to avoid using one for
parts that are too shallow as they produce collagen even though they last a long time. There are
no enzyme materials to dissolve llers like HA
llers, which raises a need to be careful not to
overdose one at a time. Some clinicians adjust the
doses of such llers and dilute Ca or PCL llers
by mixing them with a saline or lidocaine solution to prevent excessive collagen production. In
case of dilution, such llers become soft to use,
but the dilution process may lower the homogeneity of their components and cause damage to
ller particles. It is not desirable to dilute these
llers too much.
2.1.2.4 PLLA (Poly-L-Lactic Acid) Fillers
PLLA llers are made of PLA (polylacice acid),
a major biogenic substance. They are better
known as their product name Sculptra than the
component. PLLA llers garnered popularity as a
ller capable of restoring the facial volume of
AIDS patients who had become gaunt with
almost no soft tissues in their face, which made it
difcult for them to receive fat transplantation or
llers by producing the native collagen of the
human body. PLLA llers were rst developed in
Europe and received the European CE approval
in 1999 and later the US FDA approval in 2003.
They are a powder product to dilute in water.
Distilled water is used to dilute them instead of a
physiological saline solution. They create a volume by regenerating collagen, and there are no
volume effects immediately after a procedure as
it takes weeks after the procedure for collagen to
form. The effects will show gradually. It is difcult to predict accurately how much the volume
will be enhanced by certain amounts of collagen
over time. These days, PLLA llers are mainly
used to generate the effects of rmer and more
elastic skin through collagen production than a
noticeable sense of volume (Fig.2.6).
2.1.2.5 PMMA (Polymethyl Methacrylate) Fillers
PMMA llers are also better known as the product name Artecoll than the component. Developed
in 1992, they contain cow collagen and the highmolecular compound PMMA in a 3:1 ratio.
PMMA, which was used as an implant material,
was turned into a ller that would last semipermanently. The ller obtained approval from the
US FDA in the name of Artell in 2006 (Fig.2.7).
PMMA llers are semipermanent and have
concerns with side effects, which calls for caution. The manufacturer puts limits on the supply
of PMMA llers, which is why they are not
widely used among the public.

20
Fig. 2.6 PLLA ller
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
Fig. 2.8 PAAG ller
PAAG ller, received the European CE approval
around 2000 and was imported into the nation. In
China, PAAG llers were used in large quantities
for breast augmentation but caused several side
effects, so these llers faced a negative public
opinion similar to liquid silicone, which put an
end to their use. A few years ago, Aqualling
appeared, which could change the molecular formula structure of PAAG and excrete it from the
human body in the metabolic process by melting
it in a saline solution and making it mushy when
the expected outcome was not desirable (Fig.2.8).
This ller, however, failed to provide objective evidence that its particles could actually be
absorbed and eliminated. It just looked like it disappeared as it spread thin. Thus, it was not widely
used, either.
Fig. 2.7 PMMA ller
2.1.2.6 PAAG (Polyacrylamide Gel) Fillers
Like PMMA, PAAG is a biochemical highmolecular compound that is semipermanent.
Developed in Europe in the 1980s, it was
circulated in the name of Interfall. Aquamid, a
2.2 Manufacturing Process ofHA
Fillers
An important part of understanding the hyaluronic
acid ller manufacturing process is how each process plays a role in producing a good product. At
the same time, it is important to understand what
problems arise when the process is awed.
2.2.1 Preparation ofRaw Materials
ofHyaluronic Acid
Manufacturers should use good-quality raw
materials. Friedman etal. have found that the use
of high-quality raw materials signicantly

2.2 Manufacturing Process ofHA Fillers
Fig. 2.9 Dissolution of hyaluronic acid. (With kind permission of S.thepharm company)
reduces the frequency of side effects when preparing llers under the same conditions.
In conclusion, clinicians should check where
the raw material of the ller originates from.
2.2.2 Dissolution withStrong Base
(NaOH)
21
Fig. 2.10 BDDE cross-linking process. (With kind permission of S.thepharm company)
The pH should be maintained above 10 for effective BDDE binding. NaOH, which is a strong
base used for dissolution, must be thoroughly
removed during the manufacturing process
(Fig.2.9).
2.2.3 Cross-Linking Process
As mentioned above, the half-life of hyaluronic
acid in the body is 1–2days. However, hyaluronic
acid llers made from hyaluronic acid are stabilized through cross-linking and have a longer
half-life. Filler manufacturers have their own
cross-linking technology, which is the company’s
core technology. As binding materials, BDDE,
PAG, and DVS are used and called “crosslinkers” (Fig. 2.10). These cross-linkers are
highly toxic. Therefore, it would be most desirable if a minimum amount of cross-linker could
be used while obtaining the desired physical
properties. In general, llers with low crosslinking ratio and stable properties are good llers. Fillers with too high cross-linking ratios are
possibly dangerous. At the end of the cross-
Fig. 2.11 State after completion of cross-linking. (With
kind permission of S.thepharm company)
linking process, hyaluronic acid aggregates into
several masses (Fig.2.11).
2.2.4 Dialysis or Washing
Depending on the company, dialysis or washing
may be performed. However, the purpose of this
manufacturing process is the same which is
removal and neutralization of toxic and foreign
substances. Previously utilized NaOH is removed
by pH and osmotic pressure adjustment. In addition, the remaining BDDE is removed during this
process (Fig.2.12).

22
Fig. 2.12 Dialysis. (With kind permission of S.thepharm
company)
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
Dialysis is generally a two-step process.
Primary, dialysis is performed using NaCl solution, and secondary dialysis is performed using
PBS (phosphate buffer solution).
This process is closely related to the safety of
the product.
In general, to be licensed as a ller product,
the amount of endotoxin and residual BDDE
should be below a certain level. However,
empirically, we can’t be absolutely sure that
those standards are met even if the product is
licensed. Problems can still arise with products
that were determined to be safe during the
approval inspection process. This is one of the
reasons why choosing a good ller is very
difcult.
It is expensive to go through a sufcient dialysis process. Nevertheless, a company’s products,
which have been designed with sufcient dialysis
processes, are naturally safe and have fewer side
effects.
Since the manufacturing process is kept condential by each company, it is difcult to know
the exact process which is used.
However, it is not difcult to understand why
it is important to wash for a sufcient time. It is
essential to wash for a sufcient period until no
BDDE is detected. Although different from manufacturer to manufacturer, they usually have a
cleansing period of 10days or more.
In conclusion, it would be advisable to inquire
about the cleaning or dialysis process and conrm the results of BDDE and endotoxin tests.
Fig. 2.13 Cutting process. (With kind permission of S.
thepharm company)
2.2.5 Cutting
The cutting process will change the ller to the
appropriate size (Fig. 2.13). There is no major
difference in the cutting process depending on
the ller line-up. Filler line-up is determined by
dissolving and cross-linking hyaluronic acid. If
the cutting process is insufcient, the extrusion
force is not uniform during ller injection. If the
cutting period is too long, thermal damage may
occur to the ller, which may change the rheology of the product. It is important to nd appropriate process conditions to produce appropriate
rheology for the intended use of the product. The
validation of cutting should optimize the manufacturing process.
Depending on the company, the cutting and
pulverizing process may be separated or be done
simultaneously. This is because manufacturing

2.3 Rheological Properties ofHA Fillers asViscoelastic Materials
know-how varies from company to company. The
pulverizing process is mainly used in making
biphasic llers.
2.2.6 Filling
This is the process of inserting the completed
ller product into the syringe. Contamination is
the main issue needed to be controlled in this step
(Figs.2.14 and 2.15).
Fig. 2.16 Sterilizing process using autoclave. (With kind
permission of S.thepharm company)
2.2.7 Sterilization Process
23
In general, hyaluronic acid llers are produced in
single batches (i.e., LOT). Then there is a sterilization process after product lling. If it is sterilized in two separate processes, there may be a
difference in the rheology of the product. Because
Fig. 2.14 Filling system. (With kind permission of S.
thepharm company)
Fig. 2.15 Product lling system. (With kind permission
of S.thepharm company)
the ller is affected by the minute environmental
differences in the sterilization process. Crosslinking may be destroyed or viscoelastic values
may be lowered (Fig.2.16).
2.3 Rheological Properties ofHA
Fillers asViscoelastic
Materials
HA ller products are generally divided into
biphasic and monophasic llers according to the
different manufacturing processes explained
above, which gives them their respective
properties.
Methods based on rheology, which conducts
academic research on the properties of viscoelastic
materials like llers, are usually used to assess the
quality of each ller objectively. Fillers that are
clinically used are only one of the many different
aspects of viscoelastic properties that are used in
daily life. Different viscoelastic materials have
various rheological properties according to their
components and characteristics, molecular
weights, molecular formulas, and manufacturing
methods. It is only natural that we should understand the nature of llers as viscoelastic materials
before their peripheral data and numbers in order
to gure out the properties of the llers that we
use.
The study of rheology, which is taken for
granted these days, has a short history since it
was only born a few decades ago. In the past,

24
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
matters were assessed based on the theory of
elasticity, which investigates the rheological
properties of hard solid matters, and uid
mechanics, which investigates owing uids.
Matters were simply divided into solid matters
and uids and assessed accordingly. People,
however, gradually discovered viscoelastic materials, which have a natural presence and were a
different nature from solid matters or uids, and
realized their signicance. Entering a modern
society, people developed more and more new
viscoelastic materials that grew in the number of
types and faced a denite need for a study on viscoelastic materials with more complex structures
and nature than solid matters and liquids. One
should rst understand two elds of study as the
foundation of modern rheology in order to gure
out the nature of viscoelastic materials right.
There is the theory of elasticity, which originated
in the elastic law of Robert Hooke and uid
mechanics, which began with the law of viscosity
by Isaac Newton. Both laws were created in the
nineteenth century, which indicates that the
research on the nature of matters itself is not very
long in the history of humankind. After these two
laws were established, people realized that some
matters were subjected to the theory of elasticity
and started to investigate the characteristics of
solid matters and uid mechanics, which led to
investigation of the characteristics of uids. They
realized that such matters changed their nature
according to different conditions and called the
materials they were made of viscoelastic materials, which led to the discovery that there were
many viscoelastic materials around them.
Rheology was created to understand viscoelastic
materials whose rheological properties could not
be understood with Hooke’s theory of elasticity
or Newton’s law of viscosity. Today the world is
full of daily materials based on such rheological
properties investigated in the eld of rheology
(Fig.2.17).
People commonly think of the human skin, a
rubber ball, or springs when they are asked to
give an example of viscoelastic materials, but
these examples are not made of components that
can pass through a round pipe like owing uid
due to their properties. The researcher believes
that these are not proper viscoelastic materials to
be compared to llers. Examples of materials
with more similar rheological properties and
nature to llers include toothpaste for brushing
teeth, paint to color buildings, and soft jelly to be
enjoyed by kids. These materials can take the
form as an elastic material sometimes or a uid at
other times according to the given conditions.
Since the researcher believes that toothpaste
serves the most similar use as llers used in the
practice, the following explanations will be based
on a toothpaste example:
When we try to use toothpaste from a tube to
brush our teeth, we have to push it out through
the end of the tube by applying force. This is like
the process of pushing a ller out of a syringe or
cannula by applying force to the plunger and
injecting the ller into the human body. Here,
toothpaste has the rheological properties of a
owing viscous uid. Out of the tube, toothpaste
should form a certain shape like an elastic material on a toothbrush. If it keeps its nature as a
Fig. 2.17 Basic
difference between
elastic, viscous and
viscoelastic materials in
response to an object’s
deformation

2.3 Rheological Properties ofHA Fillers asViscoelastic Materials
uid, one cannot brush one’s teeth correctly with
mushy toothpaste. This resembles the nature of a
ller that forms a certain shape to highlight volume in the skin. Some toothpaste products make
users feel the particle shapes in a more resistant
manner according to the viscoelastic level of the
particles, and others seem to be pushed very
softly according to tooth brushing. The toothpaste products that are mixed with grain-like
particles to reinforce this feel of an elastic material further serve the same purpose as biphasic
HA llers.
This chapter will examine the academic
grounds based on which the rheological numbers
Fig. 2.18 Elastic force of rubber balls that grows due to
elastic limit higher than ordinary solid elastic materials
provided by manufacturers for their HA ller
products are calculated and explain the nature of
llers as a viscoelastic material from a rheological perspective.
5% or less and a very low elastic limit (X). The
human skin, rubber, and spring are solids, but
they have a different elastic limit (X) than those
solids. Thus, it is natural that one should face
limitations with assessing matters only with
2.3.1 The Disciplines Underlying
material mechanics for general solids (Fig.2.18).
theStudy ofViscoelastic
Materials
2.3.1.1 Theory ofElasticity
In the theory of elasticity, elastic force is the
force of an elastic material trying to return to its
original state. Elastic force is calculated in
Hooke’s law and generally expressed in the formula of F=k△X. Here, F means elastic force; k
the elastic modulus that digitizes the hardness of
a material; and X the degree of deformation (or
elastic limit).
For further explanations about the formula, the
elastic modulus k is a constant determined by the
quality and shape of a material. In case of deformation (X) to the same degree, materials of higher
elastic modulus are harder and thus require greater
force than their own elastic force to be deformed.
It is important to note here that Hooke’s law of
elasticity for solids can be applied only to materials that have a similar elastic limit (X) as a basic
condition or a molecular structure with a similar
deformation rate, which shows the degree of
deformation. Solids of average elasticity usually
mentioned in material mechanics such as hard
iron, cement, and trees have a deformation rate of
2.3.1.2 Fluid Mechanics
In uid mechanics, viscosity represents the
degree of a uid being sticky. When a uid is
thin, it has low viscosity and small resistance
against deformation. Viscosity works as stress to
resist and slow down the speed of a uid sliding
proportionately. This is Newton’s law of
viscosity.
Hooke’s law of elasticity is universally established in solids of a low deformation rate, and
Newton’s law of viscosity is universally established in common uids that require no big force
or speed to slide.
Fluids are basically divided into Newtonian
uids, to which Newton’s law of viscosity can be
applied, and non-Newtonian uids, to which the
law is hardly applicable (Fig.2.19).
Newtonian uids have constant viscosity
according to their sliding and traveling speed.
They form a straight line of certain proportionate
relations between their sliding speed and their
stress to resist it. Materials of higher-resistant
stress or viscosity require greater force to increase
their sliding speed. Common uids show certain
proportionate relations between the force
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