What is stiffness?

Chris Beardsley
Apr 23, 2018 · 6 min read

Stiffness can simply defined as the resistance of an object or a system to a change in length. It is calculated by dividing the applied force by the resulting length change.

Very stiff objects or systems only change length by a small amount when a large force is applied. They are stiff.

Less stiff objects or systems change length substantially when the same amount of force is applied. They are compliant.


How can we calculate stiffness?

Stiffness can be calculated for objects that are inert and have no moving parts (like elastic bands), and also for systems that have engines and moving parts (like the lower body of humans).

When we stretch an elastic band, it changes length because we apply a force by pulling on either end of it. The amount of force that we need to apply to stretch the elastic band can be measured by a load cell, and the distance that the elastic band is stretched can be measured with a ruler. This allows us to calculate its stiffness, as the applied pulling force divided by the change in length.

When we perform a drop landing, our lower body system does not remain exactly the same length. Upon hitting the ground, our ankles, knees, and hips all bend, and this shortens the vertical distance between our hip joint and the ground. Our center of mass continues traveling vertically downwards even after our feet hit the ground.

The vertical distance that our center of mass travels downwards after our feet hit the ground can be measured with a video camera. This is the change in length of the system in our stiffness calculation. The amount of force exerted (in addition to our bodyweight), can be measured if we put a force plate in the landing zone. This is the force applied to cause the change in length of the system. Now, we can calculate the vertical stiffness of our lower body system, as the applied force divided by the change in length.


When can we calculate stiffness? — part 1

Stiffness can be calculated for a wide variety of objects and systems in human movement.

For example, it can be measured for the whole lower body system during a drop landing (as explained above), or for each joint in the system (either the ankle, knee, or hip). To measure stiffness at a joint, we divide the joint moment by the change in joint angle, rather than dividing the forces by the change in linear distance, since we are working in a rotational system.

Stiffness can also be measured for the muscle-tendon unit (MTU), the tendon, and the muscle itself.

We can measure the stiffness of the MTU by taking the same measurements as if we were calculating the stiffness of a single joint. Once we have the joint moment and the change in joint angle, we can estimate the force applied at the tendon (based on what we know about the internal moment arm length of the muscle), and the change in length of the MTU.

Measuring stiffness of the muscle and tendon separately is a harder project, since they can each move independently of each other. To measure muscle or tendon stiffness, we need to record their actual movements when an outside force is applied to a joint, usually using ultrasound scanning, which allows us to see through the skin.


When can we calculate stiffness? — part 2

Stiffness can be measured passively (when muscles are not producing force) and actively (when muscles are producing force).

Passive stiffness is less interesting than active stiffness, because most lower body sporting movements involve muscles producing force, and it is muscle force that contributes the most to the stiffness of the lower body system.

This is quite easy to appreciate — just imagine what would happen if someone did a drop landing without exerting any force with their muscles. They would collapse to the floor in response to the force that the ground exerted on their feet upon landing. Their center of mass would travel a long way in response to a lower applied force, and this would mean that their lower body system was very compliant.

If we consider active and passive stiffness at the joint level, we can make a less disturbing but more useful observation.

  • Passive joint stiffness — we can measure passive joint stiffness in a dynamometer, by simply extending a joint to its maximum range of motion while the subject keeps the limb relaxed, and recording the joint moment produced. This moment is called passive resistive torque, and is often used as a measure of stretch tolerance in static stretching research.
  • Active joint stiffness — we can measure active joint stiffness in exactly the same way, by simply extending a joint to its maximum range of motion in a dynamometer while the subject tries to exert as much muscle force as possible, and measuring the joint moment produced. This is more normally called measuring eccentric strength.

When we talk about “stiffness” in sporting movements, we should really refer to “active stiffness,” since we are really just talking about the application of force while the muscle-tendon unit is lengthening, which is very similar if not identical to eccentric strength in many situations.

N.B. If a leg muscle is not activated at the point when the foot hits the ground in a sporting movement, then there is a short period of time over which the muscle must be activated before can produce maximal force. This is why “preactivation” is helpful, because it brings the muscle to a point where it can immediately exert eccentric force when the external load is applied. Failing to trigger preactivation early enough before the external load is applied can therefore lead to reduced active stiffness.


Why “eccentric strength” and not just “strength”?

Although “active stiffness” in sport is closer to a strength quality than it is to a passive property of muscles and tendons, we must avoid falling into the opposite error, which is to think that eccentric strength is the same thing as maximum concentric strength (one repetition-maximum) or maximum isometric strength.

In fact, rodent research has shown that we can increase eccentric strength without changing isometric strength. Also, most eccentric training studies in humans have shown that eccentric strength increases to a greater extent than concentric strength, while the opposite happens after concentric-only training, or stretch-shortening cycle strength training.

The interesting thing about the rodent research is that it shows that eccentric strength increased more than isometric strength, despite measurements being taken during maximal electrical stimulation. Thus, while neural adaptations are a big part of how eccentric strength (and therefore active stiffness) changes after strength training, they cannot explain everything.

When muscles lengthen while also producing force, they can exert far greater forces than when they shorten or remain the same length. This happens because when a muscle fiber is activated, it activates titin, which is a long molecule that runs alongside the actin-myosin myofilaments. When titin is activated, it strongly resists any lengthening of the muscle. Thus, the force produced by a muscle during lengthening is provided both by the actin-myoin crossbridges and *also* by titin. In contrast, when a muscle shortens, force is only provided by the actin-myoin crossbridges.

Animal studies have shown that the amount of titin inside a muscle can increase after exercise, and titin is broken down and damaged after eccentric exercise in humans, suggesting that it may later adapt. If the amount or nature of titin does indeed alter in humans after eccentric training, this could partly explain the specific gains in eccentric strength that result, and therefore the preferential gains in active stiffness.

N.B. It is worth pointing out that much of the confusion about the effects of eccentric training on “stiffness” arise due to a failure to define whether the type of stiffness is active or passive. Eccentric training actually decreases passive muscle stiffness, probably because of an increase in fascicle length. But it must by definition increase active muscle stiffness, because it increases the capacity for force production during muscle lengthening.


What is the takeaway?

Stiffness is the resistance of an object or a system to a change in length. It is calculated by dividing the applied force by the resulting length change. It can be calculated for objects that are inert and have no moving parts (like elastic bands), and for systems that have engines and moving parts (like the lower body of humans).

Stiffness can be calculated for many objects and systems in human movement, including the lower body system in a drop landing, for each joint in the system (such as the ankle, knee, or hip), and for the muscle-tendon unit (MTU), the tendon, and the muscle itself. Measurements of stiffness can be made while the muscle is not actively producing force (passive), and while the muscle is actively producing force (active). Active stiffness is more relevant to sporting movement, since most such movements involve active force production.

Active stiffness (of the lower body system, joint, or muscle) is determined largely by the ability of the muscle to produce force while lengthening, which is called eccentric strength. Eccentric strength increases preferentially after eccentric-only strength training, and this is probably partly because of neural mechanisms, but may also be caused by increases in titin content.