Biomechanics - Chapter 9

1. Linear Strain (Tensile OR Compressive Stresses): Linear strain occurs as a result of a change in the object's length. 2. Shear Strain: Shear strain occurs as a result of a change in the orientation of the object's molecules.

We just learned what Strain is... "The quantification of the deformation of a material." What are the 2 types of Strains?

Rupture/Failure Strength

"An amount of stress is placed on an object, corresponding to the end of the stress-strain curve. Results in the failure of the object." "Usually occurs immediately after ultimate strength."

Stress-Strain Relationship

"The more force applied to an object, the greater the deformation." "The relationship between the amount of force applied to a structure and the structure's response."

Yield Point or Elastic Limit... - It often coincides with the proportional limit, the end of the linear elastic range of the curve. - Below this load, the material behaves elastically, and above this load it behaves plastically. Most materials exhibit some elastic and some plastic behavior.

"The point at which elasticity is exceeded. The point on the stress-strain curve where further stress will cause permanent deformation is called the ___________ _________ or the _________ __________."

Combined Load

Answer the following... - Certain anatomical structures, such as muscles, tendons, and ligaments, behave like ropes or cables and effectively carry only one type of load: uniaxial tension. - Bones and cartilage, on the other hand, may be loaded in a variety of ways, from uniaxial tension, compression, or simple shear loads that produce uniform stress to bending and torsion loads that produce more complex stress patterns. - Bones and cartilage often encounter a combination of these loading configurations. This type of load is called a __________ _________.

ANSWER: .02%

Answer this example of calculating linear strain...

1. Hyaline Cartilage: This is also called articular cartilage; this is the cartilage that covers the ends of long bones at joints. 2. Elastic Cartilage: This type of cartilage is found in the external ear and in several other organs that are not part of the musculoskeletal system. 3. Fibrous Cartilage: Also called fibrocartilage, is found within some joint cavities (the menisci of the knee), in the intervertebral discs, at the edges of some joint cavities, and at the insertions of tendons and ligaments into bone.

Cartilage, a connective tissue that is more flexible than bone and that protects the ends of bones and keeps them from rubbing together, has 3 subcategories... What are the 3 subcategories or cartilage?

NO! - Hyaline cartilage (as well as fibrous and elastic cartilage) has no nerve or blood supply, so it must be very thin to allow the diffusion of nutrients to cells for normal metabolism. - Human hyaline cartilage is usually only 1 to 3 mm thick.

Does cartilage have any nerve or blood supply?

Imagine a balloon filled with water. As you push down on the balloon, its sides bulge out and stretch. Because water doesn't compress, it pushes out on the sides of the balloon. The sides of the balloon are thus under tension. If the balloon is made of a material capable of resisting large tensile stress, you can push on the balloon with more force. Hyaline cartilage is similar. Collagen's tensile strength holds the cartilage together under compressive loads due to the arrangement of the collagen fibers near the exterior surface of the cartilage. Unlike a balloon, however, hyaline cartilage is not watertight, so some fluid is exuded (squeezed out) when it is loaded in compression. This behavior causes creep and stress relaxation effects. Hyaline cartilage loaded under a constant compressive stress will not experience a corresponding constant strain. The strain will increase with time as fluid is exuded from the cartilage until it reaches a point where no more fluid is exuded. This increase in strain under a constant stress is called creep. term-84 Creep rate is how quickly the cartilage reaches a constant strain. Creep rate depends on the magnitude of the compressive stress, the thickness of the articular cartilage, and the permeability of the cartilage. The time it takes to reach constant strain may range from 4 to 16 h for human articular cartilage.

Hyaline cartilage transmits the compressive loads from bone to bone at joints. But how does a material composed primarily of collagen and water resist compression loads, when collagen can withstand only small compressive stresses?

1. ACTIVE TENSION: From the contractile elements themselves... 2. PASSIVE TENSION: From the connective tissue sheaths that surround the muscle fibers and are connected to the tendons. - The stiffness of the passive contractile component caused by the filaments of the contractile elements sliding past each other is very low, so the resistance to this movement is small as well. - Stretching of the muscle past the point where the contractile filaments no longer overlap is resisted by the connective tissue component of the muscle. This connective tissue behaves like tendon.

If a passive muscle is slowly stretched, there will be some resistance to this stretching and thus some stress developed. Tension in muscle comes from 2 different sources: what are they?

Muscle Contractions = Tension! - This is because sarcomeres are pulling on tendons, which then in return pull on the bones, creating tension on the bones.

Is a muscle contraction cause tension or compression?

Toughness! - The tougher an object is, the more energy a material can absorb before it breaks. - The toughness of an object is represented as the shaded area under each curve. - An idea to take from this is that larger/healthier muscles have a larger area under the stress-strain curve (pictured in the included figure), and thus can absorb more energy before they break. - This idea can also include bones. Older people with brittle bones have a smaller area under the stress-strain curve compared to someone who has dense bones. Thus, older people will brittle bones require lesser stress for a strain (break) to occur.

Mechanically, ___________ is the ability of a material to absorb energy. It's how much energy a material can absorb before it breaks.

Yield Strength

Regarding a muscle or tendon, any amount of stress beyond the ______ _______ point of the muscle or tendon causes permanent changes, and the muscle or tendon will not return to its original length.

1. Compression; Shear - The high mineral content of bone, primarily calcium and phosphate, accounts for its high compressive strength. The collagen fibers intertwined with these mineral salts give bone its high tensile strength.

Regarding bones resisting forces... 1. Bones are strongest in ____________ and weakest in _________.

Stress-Strain Curve

Regarding the Stress-Strain Relationship, objects have 2 types of properties... 1. Elastic Properties: Removing the load off of the object will allow the object to return to its original shape/length. 2. Plastic Properties: If too large of a force is applied to an object, permanent or lasting changes in deformation will occur. This is the plastic property of the material. Example: Rubber bands have a larger elastic property than bones.

Poisson's Ratio

The ratio of lateral strain to the corresponding longitudinal strain in an elastic body under longitudinal stress

1. Yield Strength 2. Ultimate strength 3. Failure strength

Thus there are several quantifications for the strength of a material, depending on which function of the material is of interest. These are illustrated in the stress-strain curve shown in the included figure... 1. The stress at the elastic limit of a material's stress-strain curve is the ________ _________ of the material. Although no breakage or rupture of the material occurs, stresses beyond the ________ _________ will cause permanent changes in the dimensions of the material. Beyond this point, the material fails in the sense that it is unable to regain its shape. 2. The ___________ __________ of a material is the maximum stress the material is capable of withstanding. 3. The ___________ ________ of a material is the stress where failure actually occurs. Failure in this sense means breakage or rupture. __________ _________ (rupture strength or fracture strength) usually has the same value as ultimate strength.

Muscle Tissue

Unlike connective tissues, __________ tissue is capable of actively contracting to produce tension within itself and the structures to which it attaches.

1. Linear Strain: Changes in an object's length, due to tensile or compressive stresses. 2. Shear Strain: Change in the orientation of an object's molecules. Due to Shear stress.

What are 2 types of Strain? "Quantifying how much deformation of a material/tissue there is, by measuring a change in length."

1. Compression 2. Tension 3. Shear

What are 3 principal types of Mechanical Stress?

1. It may assist with lubricating the articular surfaces, and it is reabsorbed by the cartilage as the compressive stresses are reduced 2. Stress relaxation:

What are some of the effects of the fluid leaking out of Hyaline Cartilage as a constant compressive load is placed on the Hyaline Cartilage?

1. The porosity of the bone: 2. Rate of loading: - Bone is stronger and stiffer if a load is applied quickly but is weaker and less stiff if a load is applied slowly.

What are some of the main factors that affect the mechanical strength and stiffness of bone?

1. Cortical or Compact Bone: Found in the dense and hard outer layers of bone. 2. Cancellous (trabecular or spongy) Bone: The less dense, porous bone that is spongy in appearance and found deep to cortical bone near the ends of long bones

What are the 2 subcategories of bone that make up a whole bone?

1. Tension 2. Compression 3. Shear.

What are the 3 main types of mechanical stress?

The active contractile components of muscle thus determine the stiffness of the muscle at any instant. - Muscle stiffness varies as a function of the number of active contractile elements. More muscle = stiffer.

What determines the stiffness of a muscle?

Poisson's Ratio

What does this describe? "A rule that states when an object (rubber ball or intervertebral disc, for example) is compressed, it becomes wider in the lateral direction and shorter in the axial direction."

Ligament

What does this describe? "Connects bone to bone"

Tendon

What does this describe? "Connects muscle to bone"

Isotropic

What does this describe? "Having identical values of a property in all directions."

Material Strength

What does this describe? "How much stress, or strain, an object can withstand before failure."

Strain

What does this describe? "Objects deform when they are subjected to external forces. These deformations may be large or small, depending on the nature of the material and the stresses involved. __________ is the quantification of the deformation of a material."

Strain! - Strain occurs when a tissue changes length; this can be via either the tissue elongating, shortening, or re-orientation.

What does this describe? "Quantifying how much deformation of a material/tissue there is, by measuring a change in length."

Ultimate Strength

What does this describe? "The maximum amount of stress a material can withstand without breaking. The total load that can be carried."

Yield Strength

What does this describe? "The point at which a material begins to deform permanently, failing to regain original shape."

Mechanical Stress

What does this describe? "This is the internal force divided by the cross-sectional area of the surface on which the internal force acts."

Anisotropic! - Anisotropic behavior of a tendon. The tendon is stronger if the tensile load is aligned with the tendon fibers rather than transverse to the fibers.

What does this describe? "____________ materials have different mechanical properties depending on the direction of the load."

Creep

What property of Hyaline Cartilage does this describe? "Hyaline cartilage also exhibits a ________ and stress-relaxation response. When a constant compressive stress is applied to the tissue, its deformation increases with time, and it will deform or _____ until an equilibrium value is reached."

Compression! - Your femur and tibia are under compression when you are standing, as a result of your body weight pushing down on the proximal end of the bones. - When an object is axially loaded in compression with forces pushing on either end, compressive stress is produced within the object, and the object tends to deform by shortening in the direction of these external forces

What type of Mechanical Stress does this describe? "The axial stress that results when a load tends to push or squash the molecules of a material more tightly together at the analysis plane."

Shear Stress

What type of Mechanical Stress does this describe? "This is a transverse stress that acts parallel to the analysis plane as a result of forces acting parallel to this plane. These forces tend to slide the molecules of the object past each other."

Tensile Stress

What type of Mechanical Stress does this describe? "________ is one of the two axial stresses (also called normal or longitudinal stresses), and one of the three principal stresses. This stress is the axial or normal stress that occurs at the analysis plane as a result of a force or load that tends to pull apart the molecules bonding the object together at that plane."

External Forces! Example: Someone's fist lands against your jaw. This will deform the internal structures of your jaw.

What type of forces deform the internal structures of an object?

Shear Stress! - Shear stress is a very common cause of fractures.

What type of mechanical stress does this describe? "__________ stress is a transverse stress that acts parallel to the analysis plane as a result of forces acting parallel to this plane."

Compression; - The bones in our lower legs feel this force everyday; from gravity.

What type of mechanical stress does this describe? "_____________ stress is the axial stress that results when a load tends to push or squash the molecules of a material more tightly together at the analysis plane."

Torsion Load - In this example, the stresses become larger with increasing distance from the central axis of the pencil.

What type of stress does this describe? "A _________ load is another type of load that produces something other than uniaxial stresses. ________ loading occurs when torques act about the long axis of the object at each end. Take a pencil and hold it with one hand at each end. Now try to twist the pencil in one direction with your right hand and in the opposite direction with your left hand. Figure 9.11a shows a three-dimensional free-body diagram of the whole pencil."

Tension, or tensile stress. - Tension acts to pull/stretch/lengthen molecules.

What type of stress does this describe? "An axial or "normal" stress (stress that is perpendicular) that occurs at the analysis plane as a result of a force or load that tends to pull apart the molecules that bond the object together at the analysis plane." "Called Axial or Normal Stress."

Torsion! - In this type of stress, the orientation of the molecules are changing. - Objects with greater diameters can create greater "counter" torsion forces, and thus can withstand greater torsion loads before breaking.

What type of stress does this describe? "Occurs when an object is twisted. "Counter" torques created by a shear force act on the analysis plane."

Axial Loading

When an object or material is ________ loaded, the objects tends to deform by stretching or elongating in the direction of the external loads.

Muscle & Connective Tissue! - The specific connective tissues important to the structure of the musculoskeletal system are bone, cartilage, ligament, and tendon.

___________ and __________ tissue form the structural units of the musculoskeletal system.

Mechanical Stress

____________ ________ is the internal force divided by the cross-sectional area of the surface on which the internal force acts.

Elastin! - This ground substance consists of carbohydrates and proteins that, combined with water, form a gel-like matrix for the collagen and elastin fibers.

____________ is also fibrous component of connective tissue, but unlike collagen, it is pliant and very extensible (failure strain as high as 160%).

Collagen! - Molecules of collagen align together to form collagen fibrils that bind together to form collagen fibers. Collagen is thus very stiff (failure strain of 8% to 10%) and has high tensile strength. - On the other hand, collagen is unable to resist compression because its long fibers are not supported laterally. It collapses or buckles like a rope.

____________, which is a fibrous protein, is the most abundant substance in all connective tissue.