Response Of Tissues To Forces

The immediate response of tissues to loading depends on a variety of factors. The size and direction of forces, as well as the mechanical strength and shape of the tissue, affect how the material structure will change. We will see in this section that mechanical strength and muscular strength are different concepts. This text will strive to use "muscular" or "mechanical" modifiers with the term strength to

Figure 4.1. The principal axial loads of (a) compression, (b) tension, and (c) shear.

help avoid confusion. There are several important mechanical variables that explain how musculoskeletal tissues respond to forces or loading.

Stress

How hard a load works to change the shape of a material is measured by mechanical stress. Mechanical stress is symbolized with the Greek letter sigma (a) and is defined as the force per unit area within a material (a = F/A). Mechanical stress is similar to the concept of pressure and has the same units (N/m2 and lbs/in2). In the SI system one Newton per meter squared is one Pascal (Pa) of stress or pressure. As you read this book you are sitting in a sea of atmospheric gases that typically exert a pressure of 1 atm, 101.3 KPa (kilopascals), or 14.7 lbs/in2 on your body. Note that me chanical stress is not vector quantity, but an even more complex quantity called a tensor. Tensors are generalized vectors that have multiple directions that must be accounted for, much like resolving a force into anatomically relevant axes like along a longitudinal axis and at right angles (shear). The maximum force capacity of skeletal muscle is usually expressed as a maximum stress of about 25-40 N/cm2 or 36-57 lbs/in2 (Herzog, 1996b). This force potential per unit of cross-sectional area is the same across gender, with females tending to have about two-thirds of the muscular strength of males because they have about two-thirds as much muscle mass a males.

Strain

The measure of the deformation of a material created by a load is called strain. This de-

Figure 4.2. Combined loads of (a) bending and (b) torsion. A bending load results in one side of the material experiencing tension and the other compression.

formation is usually expressed as a ratio of the normal or resting length (L0) of the material. Strain (e) can be calculated as a change in length divided by normal length: (L - L0)/ L0. Imagine stretching a rubber band between two fingers. If the band is elongated to 1.5 times its original length, you could say the band experiences 0.5 or 50% tensile strain. This text will discuss the typical strains in musculoskeletal tissues in percentage units. Most engineers use much more rigid materials and typically talk in terms of units of microstrain. Think about what can withstand greater tensile strain: the shaft of a tennis racket, the shaft of a golf club, or the shaft of a fiberglass diving board?

Stiffness and Mechanical Strength

Engineers study the mechanical behavior of a material by loading a small sample in a materials testing system (MTS), which simultaneously measures the force and displacement of the material as it is deformed at various rates. The resulting graph is called a load-deformation curve (Figure 4.3), which can be converted with other measurements to obtain a stress-strain graph. Load-deformation graphs have several variables and regions of interest. The elastic region is the initial linear region of the graph where the slope corresponds to the stiffness or Young's modulus of elasticity of the material. Stiffness or Young's modulus is defined as the ratio of stress to strain in the elastic region of the curve, but is often approximated by the ratio of load to deformation (ignoring the change in dimension of the material). If the test were stopped within the elastic region the material would return to its initial shape. If the material were perfectly elastic, the force at a given deformation during restitution (unloading) would be the same as in loading. We will see later that biological tissues are not like a perfectly elastic spring, so they lose some of the energy in restitution that was stored in them during deformation.

Beyond the linear region is the plastic region, where increases in deformation occur with minimal and nonlinear changes in load. The yield point or elastic limit is the point on the graph separating the elastic and plastic regions. When the material is deformed beyond the yield point the material will not return to its initial dimensions. In biological materials, normal physiological loading occurs within the elastic region, and deformations near and beyond the elastic limit are associated with microstructural damage to the tissue. Another important variable calculated from these measurements is the mechanical strength of the material.

Deformation

Figure 4.3. The regions and key variables in a load-deformation graph of an elastic material.

Deformation

Figure 4.3. The regions and key variables in a load-deformation graph of an elastic material.

Activity: Failure Strength

Two strong materials are nylon and steel. Nylon strings in a tennis racket can be elongated a great deal (high strain and a lower stiffness) compared to steel strings. Steel is a stiff and strong material. Take a paper clip and apply a bending load. Did the paper clip break? Bend it back the opposite way and repeat counting the number or bends before the paper clip breaks. Most people cannot apply enough force in one shearing effort to break a paper clip, but over several loadings the steel weakens and you can get a sense of the total mechanical work/energy you had to exert to break the paper clip.

(force at the end of the elastic region) of healthy and healing ligaments. Sports medicine professionals may be more interested in the ultimate strength that is largest force or stress the material can withstand. Sometimes it is of interest to know the total amount of strain energy (see chapter 6) the material will absorb before it breaks because of the residual forces that remain after ultimate strength. This is failure strength and represents how much total loading the material can absorb before it is broken. This text will be specific in regards to the term strength, so that when used alone the term will refer to muscular strength, and the mechanical strengths of materials will be identified by their relevant adjective (yield, ultimate, or failure).

The mechanical strength of a material is the measurement of the maximum force or total mechanical energy the material can absorb before failure. The energy absorbed and mechanical work done on the material can be measured by the area under the load deformation graph. Within the plastic region, the pattern of failure of the material can vary, and the definition of failure can vary based on the interest of the research. Conditioning and rehabilitation professionals might be interested in the yield strength

Viscoelasticity

Biological tissues are structurally complex and also have complex mechanical behavior in response to loading. First, biological tissues are anisotropic, which means that their strength properties are different for each major direction of loading. Second, the nature of the protein fibers and amount of calcification all determine the mechanical response. Third, most soft connective tissue components of muscle, tendons, and liga ments have another region in their load-deformation graph. For example, when a sample of tendon is stretched at a constant rate the response illustrated in Figure 4.4 is typical. Note that the response of the material is more complex (nonlinear) than the Hookean elasticity illustrated in Figure 2.4. The initial increase in deformation with little increase in force before the elastic region is called the toe region. The toe region corresponds to the straightening of the wavy collagen fiber in connective tissue (Carlstedt & Nordin, 1989). After the toe region, the slope of the elastic region will vary depending on the rate of stretch. This means that tendons (and other biological tissues) are not perfectly elastic but are viscoelastic.

Viscoelastic means that the stress and strain in a material are dependent on the rate of loading, so the timing of the force

Ultimate Strength

Ultimate Strength

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