From Fibers to Materials and Viscoelasticity

Question 1

What factors need to be considered for a composite?

Answer 1

Material selection, configuration, and scale

Question 2

What are the possible arrangements for fibrous biological materials?

Answer 2

-Unidirectional
-Orthogonal
-Planar random
-Twisted orthogonal
-Cylindrical helicoidal
-Helicoid
-Pseudo-orthogonal

Question 3

What are three examples of materials with an unidirectional fiber structure?

Answer 3

Tendons, insect cuticles, hair

Question 4

What are two examples of materials with a planar random fiber structure?

Answer 4

Parts of plant cell walls, skin dermis

Question 5

What are two examples of materials with an orthogonal fiber structure?

Answer 5

Basement lamella in vertebrates, cuticles of cylindrical animals

Question 6

What are two examples of materials with a pseudo-orthogonal fiber structure?

Answer 6

Wood tracheids, insect cuticles

Question 7

What are two examples of materials with a twisted orthogonal fiber structure?

Answer 7

Fish scales, cornea

Question 8

What are two examples of materials with a helicoid fiber structure?

Answer 8

Insect and arthropod cuticles, some plant cell walls

Question 9

What is an example of a material with a cylindrical helicoidal structure?

Answer 9

Bone haversian system

Question 10

What type of bonding holds the fibers together in chitin?

Answer 10

H bonds

Question 11

What type of bonding holds the fibers together in cellulose?

Answer 11

Cellulose is held together by hemicelluloses and reinforced by lignin

Question 12

What holds the fibers together in a tendon?

Answer 12

The collagen fibrils are bonded by proteoglycans

Question 13

What holds the fibers together in skin?

Answer 13

The skin collagen fibers are coated with collagen III and crosslinked by proteoglycans

Question 14

What equation describes the elastic modulus of a layered composite for a force applied parallel to the bonding interfaces?

Answer 14

Rule of mixture/constant strain model/Voigt model
The elastic modulus is the sum of (volume fraction)*(material modulus) for all materials used in the composite.

Question 15

What equation describes the elastic modulus of a layered composite for a force applied perpendicular to the bonding interfaces?

Answer 15

Reuss model/constant stress model
1/(elastic modulus) = sum of (volume fraction)/(material modulus) for all materials used in the composite

Question 16

How are the upper and lower bounds on composite properties defined?

Answer 16

The upper bound is the Voigt approximation
The lower bound is the Reuss approximation

Question 17

What model other than Reuss and Voigt can be used to describe the elastic modulus of a composite?

Answer 17

Elastic modulus = (volume fraction 1)(material modulus 1)+(empirically define modifier)(volume fraction 2)(material modulus 2)

Question 18

How is a representative volume element used to calculate elastic modulus?

Answer 18

The stresses and strains are solved within a representative subset of the material (RVE) and then used to compute E

Question 19

What happens when the fibers in a composite rub or glide against each other?

Answer 19

-Generates rate effects and viscoelasticity
-Can generate large deformations

Question 20

What happens when force is applied to a viscoelastic material very slowly vs very quickly?

Answer 20

When force is applied very slowly, it behaves liquid like

When force is applied very fast, it behaves like a solid

Question 21

What two components are used to model the viscoelastic response?

Answer 21

Hookean spring - elastic response (sigma = k*epsilon)
k is a spring constant (N/m^2) analogous to Young’s modulus

Newtonian dashpot - viscous response (sigma = eta*deltaepsilon)
eta is viscosity (Ns/m^2) analogous to Young’s modulus

Question 22

What models describes an ideal viscoelastic solid?

Answer 22

Maxwell fluid - spring and dashpot in series

Voigt solid - spring and dashpot in parallel

Question 23

What model describes the standard linear solid?

Answer 23

A spring in parallel with a spring and a damper in series

Question 24

What causes hysteresis in polymers?

Answer 24

Molecules rub against each other during deformation and dissipate energy through friction in the form of heat. The interchain resistance is due to molecular side branches that are obstacles to sliding of polymeric chains.

Question 25

How can the viscous effects be avoided in some cases?

Answer 25

Selecting a loading rate that is in the rubbery or glassy range of materials