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Elongation (%)

Figure 4.4. The typical load-deformation (elongation) curve for human tendon is more complex than for many materials. Initial elongation is resisted by small force increases in the toe region, followed by the elastic region. Much of the physiological loading of tendons in normal movement are likely within the toe region (<5% strain: Maganaris & Paul, 2000), but elongation beyond the elastic limit damages the tendon.

application affects the strain response of the material. Figure 4.5 illustrates the response of a ligament that is stretched to a set length at two speeds, slow and fast. Note that a high rate of stretch results in a higher stiffness than a slow stretch. Muscles and tendons also have increasing stiffness with increasing rates of stretch. The viscoelasticity of muscles and tendons has great functional significance. A slow stretch will result in a small increase in passive resistance (high compliance) from the muscle, while the muscle will provide a fast increase in passive resistance (high stiffness) to a rapid stretch. This is one of the reasons that stretching exercises should be performed slowly, to minimize the increase in force in the muscle-tendon unit (MTU) for a given amount of stretch. The solid lines of the graph represent the loading response of the

Fast

Fast

Elongation

Figure 4.5. Load-deformation curves for tendon stretched at a fast and a slow rate to the same length. Force at any length in loading (solid line) are higher than in unloading (dashed line). A viscoelastic material has different stiffness at different rates of deformation. A faster stretch results in greater force in the tendon for a given length compared to a slow stretch. Hysteresis is the work and energy lost in the restitution of the tendon and can be visualized as the area between loading and unloading of the tendon.

Elongation

Figure 4.5. Load-deformation curves for tendon stretched at a fast and a slow rate to the same length. Force at any length in loading (solid line) are higher than in unloading (dashed line). A viscoelastic material has different stiffness at different rates of deformation. A faster stretch results in greater force in the tendon for a given length compared to a slow stretch. Hysteresis is the work and energy lost in the restitution of the tendon and can be visualized as the area between loading and unloading of the tendon.

Activity:Viscoelasticity

An extreme example of viscoelastic behavior that serves as a good demonstration for teaching stretching exercises is the behavior of Silly Putty™. Roll the putty into a cylinder, which serves as a model of muscle. The putty has low stiffness at slow stretching rates, so it gradually increases in length under low force conditions and has a plastic response. Now stretch the putty model quickly and note the much higher stiffness.This high stiffness makes the force in the putty get quite high at short lengths and often results in the putty breaking.You may be familiar with this complex (different) behavior of the material because the shape can be molded into a stable shape like a ball, but when the ball is loaded quickly (thrown at a wall or the floor) it will bounce rather than flatten out.

Application: Stress Relaxation

Guitar players will know that steel strings do not lose tension (consequently their tuning) as quickly as nylon strings; this phenomenon is not related to strength but to viscoelasticity. Steel guitar strings are much more elastic (stiffer) and have negligible vis-coelastic properties compared to nylon strings. In a similar fashion, nylon tennis strings lose tension over time. Skilled players who prefer a higher tension to grab the ball for making greater spin will often need to cut out and replace nylon strings before they break. Gut strings are more elastic than nylon and tend to break before there is substantial stress relaxation. Similarly, when a static stretch holds a muscle group in an extended position for a long period of time the tension in the stretched muscle group decreases over time. This stress relaxation occurs quickly (most within the first 15 seconds), with diminishing amounts of relaxation with longer amounts of time (see Knudson, 1998). How might a coach set up a stretching routine that maximizes stress relaxation of the athlete's muscles? If many people dislike holding stretched positions for a long period to time, how might kinesiology professionals program stretching to get optimal compliance and muscle stress relaxation?

ligament, while the dashed lines represent the mechanical response of the tissue as the load is released (unloading).

There are other important properties of viscoelastic materials: creep, stress relaxation, and hysteresis. Creep is the gradual elongation (increasing strain) of a material over time when placed under a constant tensile stress. Stress relaxation is the decrease in stress over time when a material is elongated to a set length. For example, holding a static stretch at a specific joint position results in a gradual decrease in tension in the muscle from stress relaxation. If you leave a free weight hanging from a nylon cord, you might return several days later to find the elongation (creep) in the cord has stretched it beyond it initial length. Creep and stress relaxation are nonlinear responses and have important implications for stretching (see application box on flexibility and stretching) and risk of injury in repetitive tasks. For example, work pos-

tures that stretch ligaments, reducing their mechanical and proprioceptive effectiveness, increase joint laxity and likely increase risk of injury (Solomonow, 2004).

Hysteresis is the property of viscoelas-tic materials of having a different unloading response than its loading response (Figure 4.5). Hysteresis also provides a measure of the amount of energy lost because the material is not perfectly elastic. The area between the loading and unloading is the energy lost in the recovery from that stretch. We will learn in Chapter 6 that energy and work are related, and that mechanical work is defined as force times displacement (F • d), so work can be visualized as an area under a force-displacement graph. If you want to visualize the failure strength (work) of the material in Figure 4.3, imagine or shade in the total area above zero and below the load-deformation graph.

All these mechanical response variables of biological materials depend on precise measurements and characteristics of the samples. The example mechanical strengths and strains mentioned in the next section represent typical values from the literature. Do not assume these are exact values because factors like training, age, and disease all affect the variability of the mechanical response of tissues. Methodological factors like how the human tissues were stored, attached to the machine, or preconditioned (like a warm-up before testing) all affect the results. Remember that the rate of loading has a strong effect on the stiffness, strain, and strength of biological materials. The following sections will emphasize more the strengths of tissues in different directions and how these are likely related to common injuries.

BIOMECHANICS OF THE PASSIVE MUSCLE-TENDON UNIT (MTU)

The mechanical response of the MTU to passive stretching is viscoelastic, so the response of the tissue depends on the time or rate of stretch. At a high rate of passive stretch the MTU is stiffer than when it is slowly stretched. This is the primary reason why slow, static stretching exercises are preferred over ballistic stretching techniques. A slow stretch results in less passive tension in the muscle for a given amount of elongation compared to a faster stretch. The load in an MTU during other movement conditions is even more complicated be cause the load can vary widely with activation, previous muscle action, and kind of muscle action. All these variables affect how load is distributed in the active and passive components of the MTU. Keep in mind that the Hill model of muscle has a contractile component that modulates tension with activation, as well as two passive tension elements: the parallel elastic and the series elastic components. The mechanical behavior of activated muscle is presented in the upcoming section on the "Three Mechanical Characteristics of Muscle."

Tendon is the connective tissue that links muscle to bone and strongly affects how muscles are used or injured in movement. Tendon is a well-vascularized tissue whose mechanical response is primarily related to the protein fiber collagen. The parallel arrangement of collagen fibers in tendon and cross-links between fibers makes tendon about three times stronger in tension than muscle. The ultimate strength of tendon is usually about 100 MPa (megapas-cals), or 14,500 lbs/in2 (Kirkendall & Garrett, 1997). Even though the diameter of tendons is often smaller than the associated muscle belly, their great tensile strength makes tendon rupture injuries rare. Acute overloading of the MTU usually results in strains (sports medicine term for overstretched muscle, not mechanical strain) and failures at the muscletendon junction or the tendon/bone interface (Garrett, 1996).

In creating movement, a long tendon can act as an efficient spring in fast bouncing movements (Alexander, 1992) because the stiffness of the muscle belly can exceed tendon stiffness in high states of activation. A muscle with a short tendon transfers force to the bone more quickly because there is less slack to be taken out of the tendon. The intrinsic muscles of the hand are well suited to the fast finger movements of a violinist because of their short tendons. The Achilles tendon provides shock absorption and compliance to smooth out the forces of the large calf muscle group (soleus and gastrocnemius).

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