Ch 9: Biomechanics of Brittle vs Ductile Materials, Toughness, Connective Tissues (Collagen & Elastin), Bone & Cartilage (4/11/25)

Brittle vs. Ductile Materials

• Brittle materials have a small strain at fracture, meaning they don't deform much before breaking.
• Ductile materials have a larger strain at fracture, indicating they can deform more before breaking.

Temperature Influence

• Materials tend to become more brittle as they get colder.
• This applies to metals as well, and the specific composition of the metal influences its behavior.
• The Titanic disaster is theorized to be partly due to the rivets becoming brittle in the cold water, leading to the unzipping of the hole plates.

Construction of Ships

• Large plates are held together by rivets, and failure of these rivets can lead to catastrophic water leaks.

Toughness

• Toughness is technically defined as the ability of a material to absorb energy.
• A tougher material requires more energy to break.
• On a stress-strain diagram, toughness is represented by the area under the curve.

Hard and Brittle Materials

• Hard and brittle materials can withstand a lot of stress but do not deform much before failing.
• Dry bone is an example of a hard and brittle material.
• Living bone, which is more hydrated, is less brittle.
• Ligaments and tendons are relatively tough compared to bone, capable of absorbing more energy and handling larger deformations.

Musculoskeletal System

• Muscle is an active element that can change in length.
• Passive elements like bone, tendons, ligaments, and cartilage do not actively change length. Stress-strain diagrams will differ considerably for each structure.

Connective Tissue Building Blocks

• Collagen and elastin influence how much and how quickly connective tissues deform under stress.
• Ground substance, minerals, and water are also components, but collagen and elastin are key to understanding deformation.

Collagen

• Collagen is a fibrous protein, the most abundant in connective tissue.
• It is a stiff material with a relatively low failure strain (8-10%). $\varepsilon_{failure} = 0.08 - 0.10$
• Collagen has high tensile strength, meaning it can withstand a lot of pulling force.
• It is not very good at resisting compression. Collagen is ideally suited to resist tension rather than compression.

Elastin

• Elastin's structure is more disorganized compared to collagen.
• It doesn't take much force to deform elastin initially.
• Once the fibers are stretched and aligned, it takes more stress to deform it further.
• Elastin is a very pliant and extensible material with a high failure strain. > 100 \%.

Similarities and Differences of Collagen and Elastin. $Collagen \Leftrightarrow Elastin$

• Both are fibrous proteins.
• Collagen is stiff, while elastin is pliant and extensible.
• Collagen is strong in tension, while elastin is easily deformed initially. Failure Strain $\varepsilon_{failure}$

Isotropic vs. Anisotropic Materials

• Isotropic materials have the same properties in all directions.
• Anisotropic materials have different mechanical properties depending on the direction of loading.
• Connective tissue behaves similarly to the grain of wood; it is stronger when pulled parallel to the fibers.

Muscle Terminology

• A bands and I bands within a sarcomere: these terms will be used later when discussing muscle.

Influence of Activity and Age on Connective Tissue

• Activity and age affect the mechanical properties of connective tissue.
• Strength typically increases until around 25-30 years old due to regular loading and unloading cycles.
• This increased strength is related to an increase in the cross-sectional area of the tissue.

Inactivity and Aging

• Inactivity and immobilization negatively influence material strength.
• Bones become more brittle with age, while tendons and ligaments become less stiff.
• Older individuals are at higher risk of rupturing tendons or ligaments due to decreased mechanical strength.

Bone Composition and Strength

• Bone is composed of minerals, water, and collagen.
• It is the strongest and stiffest material in the musculoskeletal system.

Bone Loading and Strength

• Bone is strongest in compression, weaker in tension, and weakest in shear.
• Strength{compression} > Strength{tension} > Strength_{shear}
• Mineral content contributes to compressive strength.
• Collagen helps resist tension.

Bone Health considerations. Influences to overall mechanical properties.

• Bone strength is also affected by the rate of loading.
• Slow loading rates: bone is relatively weak and less stiff, increasing the risk of avulsion fractures (tendon pulling off a chunk of bone).
• Fast loading rates: bone is stronger and stiffer, but there is a higher risk of ligament rupture.

Cartilage

General Composition

• Cartilage is composed of 60-80% water and largely collagen.
• Articular cartilage (hyaline cartilage) is found at joints, in the nose, and in the ribs.
• Fibrocartilage is specialized in joints and at points of insertion of tendons and ligaments into bone.

Nutrient Supply

• Cartilage has limited blood and nerve supply, receiving nutrients primarily through diffusion.
• It must be relatively thin (1-3 mm) to allow for diffusion.

Load Response

• Cartilage withstands compressive, tensile, and shear loads.
• Collagen resists tension, but cartilage must also handle compressive stresses.

Hyaline/Articular Cartilage Compression

• Articular cartilage transmits loads from bone to bone.
• Under compression, the sides of the cartilage experience tension.
• The cartilage is not watertight, allowing fluid to move in and out.

Intervertebral Discs and Pressure

• Intervertebral discs can be compressed, leading to lateral bulging.
• Different movements affect the pressure on the discs differently.
• Sitting generally increases pressure on the lumbar discs compared to standing.
• Maintaining the natural curvature of the lumbar region while sitting can reduce pressure.

Cartilage: Creep Effect

• The creep effect refers to the behavior where strain increases over time under constant stress.
• There is an initial increase in deformation of the articular cartilage that seemingly levels off for a period of time before it then starts to increase again over time.
• Fluid is exuded from the cartilage, leading to increased deformation over time.
• The fluid helps lubricate the joint and can be reabsorbed when the load is removed.
• The creep rate is the rate at which the cartilage reaches a point of constant strain.
• It can take 4-16 hours for strain to level off in different parts of the body. Different locations inside of the human body will have different tolerance and recovery rates.

Creep Effect Conclusions

• Just because there is a constant load/stress, does not mean there will be a constant strain.

Cartilage: Stress Relaxation Effect

• Stress relaxation effect indicates that just because there is a constant strain does not mean that stress will remain the same.
• Stress can initially increase rapidly and then decrease over time.
• This is due to slow deformation in the cartilage, increasing the contact area and reducing stress at the initial point of deformation.

Stress Relaxation Effect Conclusions

• Just because there is a constant strain, does not mean the stress will be constant as well.

Tendons vs Ligaments

• Tendons attach muscle to bone, while ligaments attach bone to bone.

General Makeup

• 70% water, primarily collagen.
• Ligaments have more elastin than tendons.

Fiber Arrangement

• Tendon: relatively parallel fiber arrangement.
• Ligament: nearly parallel fiber arrangement, slightly offset to handle shearing and torsional loads.

Mechanical Properties

• Ligaments are slightly less stiff and weaker than tendons.
• They can carry non-axial loads.
• Tendons have high tensile strength but are not good at resisting compression and shear stresses.

Flexibility

• Slow stretching can lead to a slow elongation of both tendon and ligament due to the creep and stress relaxation effect.

Toe Region

• The toe region of the stress-strain diagram represents the initial phase where it is easy to deform/stretch a material.
• Collagen molecules un-crimp, and elastin fibers straighten out, allowing for more deformation without much stress.

Order of Stretching of the Toe Region Elements

• Elastic Band $\Leftrightarrow$Collagen stretching followed by elastin stretching. $Elastic_Band \Leftrightarrow Collagen \rightarrow Elastin$

Muscle Stress-Strain Diagram

• Muscle also has a toe region due to the construction of the sarcomere.
• The passive component of muscle (connective tissue) contributes to the overall strain potential.
• Relaxed muscle has a relatively long toe region compared to tendon and ligament.
• There is a low stiffness of those passive contractile elements at first.