Question

Answer following questions:

a) Explain the difference between an isotropic material and an anisotropic material. Give one example of abiological material other than bone that is anisotropic and explain how it is anisotropic.

b) It is well documented that humans are typically taller first thing in the morning, but get progressively shorter (by very small amounts) as the day goes on. Based on what you know about the viscoelastic properties of human body tissues, can you explain this phenomenon?

c) Explain how the creep response of a viscoelastic material is different than the stress-relaxation response of that material. Provide an example of one biological material for which creep is a significant issue to deal with and one biological material for which stress-relaxation is a significant issue to deal with.

Answer 1

a) Materials are considered to be isotropic if the properties are not dependent on the direction while“Anisotropic” refers to the properties of a material that is dependent on the direction. Another condition that can fit the anisotropic definition is the presence of different properties in different directions.

Cartilage is an anisotropic material. The anisotropy results in part from the structural variations that are Interactions take place among the fl uid, proteoglycan molecules, and various electrostatic charges, providing superior quality of lubrication and shock absorption. The cartilaginous tissue is extremely well adapted to glide. Its coefficient of friction is several times smaller than that between ice and an ice skate. There are electrostatic attractions between the positive charges along the collagen molecules and the negative charges that exist along the proteoglycan molecules. Hydrostatic forces also exist as forces are applied to cartilage and the fluid tries to move throughout the tissue. It is the combined effect of all these interactions that gives rise to anisotropy.

b)  Biological tissues are viscoelastic materials; their behavior is both viscous, meaning time- and history-dependent, as well as elastic. A viscoelastic material possesses characteristics of stress-relaxation, creep, strain-rate sensitivity, and hysteresis . Force-relaxation (or stress-relaxation ) is a phenomenon that occurs in a tissue stretched and held at a fixed length. Over time the stress developed within the tissue continually declines. Stress-relaxation is force- or strain-rate–sensitive. In general, the higher the strain or loading rate, the larger the peak force/stress and subsequently the greater the magnitude of the force-relaxation. In contrast to stress- relaxation, which occurs when a tissue’s length is held fi xed, is creep. Creep occurs with time when a constant force/stress is applied across the tissue. If subjected to a constant tensile force, then a tissue elongates with time. The general shape of the displacement-time curve depends on the past loading history.

c) Another important aspect of ligament/tendon behavior is viscoelasticity. Viscoelasticity indicates time dependent mechanical behavior. Thus, the relationship between stress and strain is not constant but depends on the time of displacement or load. There are two major types of behavior characteristic of viscoelasticity. The first is creep. Creep is increasing deformation under constant load. This contrasts with an elastic material which does not exhibit increase deformation no matter how long the load is applied. Creep is illustrated schematically below:

                         

The second significant behavior is stress relaxation. This means that the stress will be reduced or will relax under a constant deformation. This behavior is illustrated below:

                                     

The other major characteristic of a viscoelastic material is hysteresis or energy dissipation. This means that if a viscoelastic material is loaded and unloaded, the unloading curve will not follow the loading curve. The difference between the two curves represents the amount of energy that is dissipated or lost during loading. An example of hysteresis is shown below: