Biomechanics Exam 4

Viscosity

resistance to flow; ability to dissipate energy

• usually referred to liquids

• governed by Newton’s Law

viscosity is caused by…

internal friction

Newton’s Viscosity law

sigma is stress

n is coefficient of viscosity

gamma . = strain rate

constitutive: Double strain rate, double stress

elasticity

the ability to return to its original shape; ability to

• usually referred to solids

• governed by Hookes law

Hooke’s law

sigma = stress

E = elastic modulus

epsilon = strain

constitutive: Double strain, double stress 

ELASTIC deformation is effectively….

INSTANTANEOUS

• total deformation occurs the INSTANT stress is applied, and completely disappears the instant it is released

viscous behavior

deformation is not instantaneous

• deformation delayed in response to stress (NOT fully reversible or completely recovered)

viscoelasticity

combination of viscous and elastic properties

• posses FLUID and SOLID properties

viscoelastic models

springs and dashpots

• connected in various forms

for a viscoelastic material, at CONSTANT STRESS…

STRAIN INCREASES with TIME (creep)

for a viscoelastic material, AT CONSTANT STRAIN…

STRESS DECREASES WITH TIME (relaxation)

for a viscoelastic material, the EFFECTICE STRESS DEPENDS ON…

the RATE of APPLICATION OF LOAD

• fast, little to no deformation

• slow, higher deformation

for a viscoelastic material, if CYCLIC LOADING is applied…

there is a PHASE LAG between the APPLIED STRESS and RESULTING STRAIN

there is a corresponding DISSIPATION of MECHANICAL ENERGY (hysteresis)

for a viscoelastic material, ACOUSTIC WAVES experience

ATTENUATION (reduction of amplitude)

for a viscoelastic material, REBOUND of an object following an impact is…

LESS THAN 100%

This figure describes what viscoelastic phenomenon?

Hysteresis = AREA BETWEEN loading and unloading curve

• dissipation of energy

• loading portion MUST be HIGHER than unloading curve

This figure describes what viscoelastic phenomenon?

RATE DEPENDENCY

creep

SLOW, PROGRESSIVE deformation of a material under constant stress

Creep Compliance

in linearly viscoelastic materials, this is INDEPENDENT of Stress level

in viscoelastic materials, if load is released at a later time…

the strain WILL EXHIBIT RECOVERY

AKA Progressive decrease of deformation

this figure best shows which viscoelastic phenomenon? 

Creep and Recovery

stress relaxation

the gradual DECREASE of STRESS when the material is held at CONSTANT STRAIN

relaxation modulus

in linear materials, INDEPENDENT of STRAIN level

this figure best shows which viscoelastic phenomenon? 

stress relaxation and recovery

sinusoidal oscillation applied stress waveform

sigma = stress

sigma 0 = stress amplitude

omega = 2*pi*f or angular frequency

t = time

sinusoidal oscillation applied strain waveform

gamma = strain

gamma 0 = strain amplitude

omega = 2*pi*f or angular frequency

t = time

delta = PHASE LAG (loss angle)

this figure best shows which viscoelastic phenomenon? 

sinusoidal wave forms for stress and strain functions

the phase lag and amplitude ratio (sigma 0/gamma0) vary with….

FREQUENCY

• considered material properties under LINEAR VISCOELASTIC CONDITIONS

for an ideal solid, the phase lag (delta) angle is…

0 degrees

response is purely ELASTIC

for a NEWTONIAN FLUID, the phase lag (delta) angle is…

90 degrees

• yields a purely VISCOUS response

mechanical testing of viscoelastic materials

machine applies a SINUOSIDAL LOAD to specimen

measures load (stress) and position (strain) as functions of time (phase angle, delta)

the “as measured” stress is the COMPLEX STRESS (0<delta<90)

this figure represents what for a viscoelastic material?

Phase Angle (Delta)

0<delta<90 degrees

this phase angle diagram represents what kind of material and phase angle value?

a purely ELASTIC material

delta = 0

(Hookean Solid)

this phase angle diagram represents what kind of material and phase angle value?

a purely VISCOUS material

delta = 90

(Newtonian Liquid)

storage modulus

G’

represents the IN PHASE (ELASTIC) component

equation of storage modulus

sigma 0 = stress amplitude

gamma 0 = strain amplitude

delta = phase angle

loss modulus

G”

represents the OUT OF PHASE (VISCOUS) component

indicated capacity to DISSIPATE energy as heat

equation of loss modulus

sigma 0 = stress amplitude

gamma 0 = strain amplitude

delta = phase angle

complex shear modulus

G*

represents the overall resistance to deformation

equation of complex modulus

G’ = storage modulus

G” = loss modulus

j = square root(-1)

tan(delta) = G”/G’

is a measure of material dampening

this diagram represents what?

the energy loss (loss modulus) in internal motion and the elastic response (storage modulus)

What can be determined from this diagram?

1. Storage modulus and Loss modulus are HIGH at LOW temperatures, while phase angle is LOW at LOW temperatures

2. As a material is heated, storage modulus and loss modulus DECREASE, while phase angle INCREASE

from this graph, it can be concluded that…

1. Dynamic stiffness and Storage modulus INCREASE WITH FREQUENCY

2. Phase angle and Loss modulus DECREASE WITH FREQUENCY

3. Everything is sensitive to frequency

what are the 3 spring and dashpot models?

1. Maxwell Model

2. Kelvin-Voight Model

3. Standard Solid Model

Maxwell Model

spring and dashpots in SERIES

represents a FLUID since it relaxes completely to 0 stress and undergoes CREEP INDEFINITELY

These graphs represent which spring and dashpot model?

Maxwell Model

Standard Solid Model

a three parameter model used to describe VISCOELASTIC behavior of biological materials

Kelvin Voight Model

spring and dashpots in PARALLEL

dashpot does NOT allow INSTANTANEOUS deformation to occur, but overtime, the DISPLACEMENT creeps to an ASYMPTOTIC level

These graphs represent which spring and dashpot model?

Kelvin-Voight Model

ligaments connect…

BONE TO BONE

tendons connect…

BONE TO MUSCLE

both tendons and ligaments are composed of…

Closely packed, PARALLEL COLLAGEN FIBER BUNDLES

Type 1 collagen is how much percent of tendon and ligament dry weight?

70-80%

What is collagen embedded in?

Ground substance of proteoglycans (PGs), glycolipids, and water

• water and PGs provide LUBRICATION and SPACING for gliding function at intercept points where fibers CROSS in tissue matrix

the functions of LIGAMENTS

1. augment mechanical stability of joints

2. guide joint motion

3. prevent excessive motion

the functions of TENDONS

1. attach bone to muscle

2. transmit tensile loads from muscle to bone

in addition to collagen, ligaments may contain a small amount of…

ELASTIN

structure and chemical composition of ligaments and tendons is…

HIGHLY CONSERVED among species

collagen is synthesized by…

fibroblasts

• 1st as larger precursor (procollagen), then secreted and cleaved to become collagen

collagen molecular structure

3 helical, about 1000 amino acid polypeptide chains

• 2 alpha-1 chains

• 1 alpha-2 chain

the molecular weight of collagen is?

340 kDa

the collagen chains are combined in

a Right-handed triple helix

gives rod-like shape

280 nm LENGTH

1.5 nm DIAMETER

This diagram represents

the structure of collagen

these diagram represent

the hierarchy and components of collagen as well as view points

the diagram shows

the tendon hierarchy

tropocollagen<microfibril<sub-fibril<fibril<fascicle<tendon

percentages of collagen

2/3 Glycine (33%)

Proline (15%)

Hydroxyproline (15%)

every THIRD amino acid in each alpha chain of collagen is…

GLYCINE

• small size allows tight helical packing of molecule

glycine

amino acid that is 33% of collagen

small, allows for tight helical packing of molecule

enhances stability by forming HYDROGEN BONDS among the three chains of collagen

interchain crosslinks

hydrogen bonds with glycine among the three chains

essential to aggregation of the collagen molecules at the FIBRIL level

intrachain crosslinks

proline and hydroxyproline form hydrogen bonds within each chain

collagen fibril

formed by aggregation of several collagen molecules in a quaternary structure, in which molecules overlap

• causes BANDING pattern

collagen fibers

further aggregation of collagen fibrils which are visible under light microscope

1-20 micrometer diameter, many cm long

fibroblasts are aligned in ROWS..

BETWEEN FIBER BUNDLES

the fibroblast cells are…

elongated along an axis in the direction of l

collagen fibers of tendons

More orderly with PARALLEL orientation

collagen fibers of ligaments

Less orderly without parallel orientation

the half-life of collagen

Very LONG

• same collagen molecule can exist throughout an entire life

ground substance

mixture of water and organic molecules

highly HYDROPHILLIC

contributes to:

• diffusion of metabolites

• spacing between fibers

• strength and elasticity

ground substance consists of

1. Glycoproteins: adhesive between cells and cells to collagen

2. Proteoglycans: proteins (5%) and GAG chains (95%) covalently linked → binds Water

This figure describes what?

a tendon cut LONGITUDINALLY

• collagen fibers = pink, lined parallel to each other in response to stress

• fibroblasts = black lines displaying stretched nuclei

  • squeezed between fibers and line up in parallel rows

this figure describes what?

a tendon cut in CROSS SECTION

• pale pink background = cut ends of bundles of thick collagen fibers

• wispy lines/”cracks" = place where fibroblasts are 

  • triangular or stellate due to being squeezed between fibers

similarities between ligaments and tendons

1. fibroblasts surrounded by GROUND SUBSTANCE and fibers

2. fibers primarily TYPE 1 AND 2

3. PGs important for organizing ECM

   • chondroitin and keratan sulfate exert swelling pressure

   • dermatan sulfate affects ECM and fibril formation

4. Insertional Morphology

this diagram shows what?

INSERTIONAL MORPHOLOGY of LIGAMENTS AND TENDONS

1. is collagen fibers

2. is unmineralized fibrocartilage

3. is mineralized fibrocartilage

4. is cortical bone

tendon and ligament insertions to bone are functionally adapted to…

distribute and dissipate the forces they carry by passing through fibrocartilage to bone

characteristics of ligaments ONLY

1. MORE TYPE 2 collagen (and elastin)

2. LESS perfectly aligned fiber orientation

3. MORE GAGs and water

4. MORE cells and metabolically active

characteristics of tendons ONLY

1. THINNER collagen fibrils

2. MORE parallel fiber arrangement

3. structural hierarchy: FASICLES

this diagram shows

the differences between the FIBER ORIENTATION of tendons and ligaments

• tendons: MORE PARALLEL BUNDLES

• ligaments: not as parallel bundles of collagen

paratenon

loose membrane that surrounds TENDONS, forms sheath that protects the tendon and enhances gliding

epitenon

synovium-like membrane that may exist beneath the paratenon where friction forces are very high

• the cells in this produce synovial fluid that facilitates gliding of the tendon 

this diagram represents?

the tendon sheath

• contains the paratenon and epitenon

tendon/ligament tensile test

exist in toe region and somewhat in linear region

• toe-in region = “uncrimping” of collagen fibrils → backbone is stretched making it STIFF (linear region)

• when failure of fibrils start: damage accumulates, and stiffness is REDUCED causing ligaments/tendons to fail

tendon mechanical properties

Tensile Strength: 50-150 MPa

Elastic Modulus: 1.2-1.8 GPa

True or False: Ligaments are LESS strong and stiff than tendons

TRUE

• they have LOWER COLLAGEN CONTENT

• MORE woven collagen structure compared to tendon’s parallel arrangement

Viscoelastic characteristics

1. Creep

2. Stress-Relaxation

3. Hysteresis

ligaments and tendons are what kind of materials?

viscoelastic

rate dependent functions have…

1. Increased stiffness with Increased loading rate

2. stores MORE potential energy

3. requires MORE force to rupture

hysteresis

if a viscoelastic material is loaded and unloaded, the unloading curve will NOT follow the loading curve

the difference between the two represents the amount of energy that is dissipated during loading

tendons and ligaments are

rate dependent and age dependent functions

age dependent functions

stronger with age

stiffer with age

less strain required for rupture