**CONTEXT**

Over the centuries, many devices have been invented to **basically understand mechanics** before it can be so widely understood and studied. A great understanding of skin mechanics is then a gateway to **characterize mechanics properties of human skin and allows to observe its behavior** under laws of elasticity*, torsion and force, which together are known as **« Hooke’s law »**.

### Definition

Hooke’s law, applied on skin, is a **principle of physics** modeling its deformation* under external stretching, compressing, or bending. This law of elasticity is a link between the displacement or size of the deformation and the deforming force or load. This is why skin **returns to its original shape removal of the load**.

This ability to return to a normal shape after experiencing distortion is named **« restoring force »**. Refering to Hooke’s Law, this restoring force is generally **proportional to the amount of stretch*** experienced by the skin. The law may also be expressed in terms of stress and strain.

**Hooke’s law can be formulated as:**

## F = -kx

Where :

- F is
**the force** - X is
**the length of extension/compression*** - k is
**a constant of propotionality, which is usually given in N/m.**Its value depends not only on the kind of elastic material under consideration, but also on its dimension and shape.

**Figure 1 :** Illustration of Hooke’s law, showing the relationship between force and distance when applied to a spring.

### Hooke’s law story

Behind this law, Robert Hooke, a 17th century British physicist who gave his name to it, demonstrated a relationship between the forces applied to a spring and its elasticity. Thanks to this experience, he noticed that the stress vs strain curve for materials such as skin, has a **linear region**. This law was first extracted in 1660 from a latin anagram, and then used as a solution in 1678 under the form *« ut tensio, sic vis »*, that means in english *« as the extension, so the force »* or *« the extension is proportional to the force »*.

One century later, Hooke’s law could **relate strain to stress in the linear elastic domain, thanks to a modulus named… Young’s modulus.**

### Young’s modulus

Young’s modulus is a **numerical constant**, named by the 18th century english physician Thomas Young. It describes the **object’s resistance to being deformed elastically while an external force is applied to it.** Young’s modulus is equal to the longitudinal stress divided by the strain.

*What is the difference between Hooke’s law and Young ‘s modulus ?*

Hooke’s law is a fondamental rule of thumb applied on skin that describes a **direct proportionality link between the force applied on an object and the induced strain.** Young’s Modulus is a constant coefficient stiffness*, named k, which describes **how stiff is the skin or how likely it is to deform.** Young’s modulus can be derived by compressing the skin then measuring the stress and strain.

**Figure 2:** Stress and strain curve at the Hooke’s law scale.

### Application on skin

According to Hooke’s law, elastic behaviour of a material is **partly due to small displacements of its constituent molecules.** These displacements are also proportional to the force caused by displacements themselves.

The skin is defined as perfectly elastic as it returns to its initial shape after applied forces. **Then skin plays under mechanical laws that might redefine its own properties.**

**WHY AFM?**

AFM aquires any information about skin mechanical properties that are **measured with an optical system spotted on a cantilever.** From the deflection of the AFM, the force can then be calculated with the Hooke’s law, when the spring constant is known.

**On the scale of a more than 300 years old’s law, AFM represents one of the most modern and efficient methods to characterize elastic properties of the skin.**

**Two famous physicists from respectively 17th and 18th century, many developments on skin research and a vibrant BioMeca’s team to bring you powerful tools to revolutionize in vitro and ex vivo efficacy tests.**

### LEXICAL

**Deformation:**change in size or shape of an object.**Elasticity (or elastic deformation):**temporary change in length, volume, or shape produced in an elastic substance by a stress.**Stiffness (or rigidity):**the extent to which an object resists deformation in response to an applied force (measured in N/m).**Stretch:**cause a material to become longer or wider than usual as a result of pulling at the edges.**Compression:**the act of pressing a material into a smaller space or putting pressure on it from different sides until it gets smaller.