8 July 2019 Stress and strain

Our body, our organs, ours cells are submitted to mechanical stress. The influence of mechanical stress of living organisms is omnipresent. It depends not only on environmental and endogenous loads (pressure exerted by cavities and blood) but also on intrinsic mechanical factors of organs, such as shape, architecture, and mechanical properties of tissues. Mechanical stress could be the cause, the consequence, and/or might also simultaneously interact with biological processes. Cells are continuously subjected to mechanical forces that influence cell division, gene expression, cell migration, morphogenesis, cell adhesion, fluid homeostasis, ion channel gating, and vesicular transport.

Recent studies demonstrated that physical forces play a key role in plant and animal morphogenesis. The skin also possesses unique biomechanical properties that allow it to protect and conform to the body that it covers, the properties are also of great interest regarding dermatology surgery, aging skin and disease state. Aging-associating diseases of different mechanisms, such as cardiomyopathy, degenerative valvular disease, atherosclerosis, and osteoarthritis, and cataract present mechanical factors interacting with their pathogenesis. 

In order to understand the biological material properties and their mechanical behaviour, it is necessary to understand this concept of stress.

Stress (σ) is defined as the force per unit area of a material. There are several kinds of mechanical stresses and all these stresses induce deformation: the strain (ε):

• Tensile stress, which tends to stretch or lengthen the material
• Compressive stress, which tends to compress or shorten the material
• Shearing stress, which tends to shear the material  
• Torsional stress, which tends to twist the material
• Bending stress, which tends to bend the material.

Deformation is the reaction of a material when it is subjected to mechanical stress. It depends on the nature, the stiffness and the shape of the material and of the force (stress) applied.
Strain (ε) is a relative length induce by the deformation and characterize the deformation (elongation, shortening…) percentage of the material compared to the initial length.

Stress (σ) and strain (ε) are two concepts directly linked by a law known as : Hooke’s Law.

This law allows to study the evolution of the stress over the strain and the curve is composed of different regions: 

During the initial stages of loading, the materials deforms in direct proportion to the stress, as seen by the early straight-line relationship between stress and strain. This straight-line relationship follows the Hookes’law and the slope of the curve is the young modulus (E), a measure of the stiffness of an elastic material.

The second stage begins after the yielding point. A material loaded with stress beyond the yielding point will not completely return to its original shape upon removal of the stress. The yielding point, therefore, represents the elastic limit, and the region of the curve beyond this point is known as the plastic region. The increasing stress produces increasing strain but not in a linear fashion and induce a permanent deformation of the material.

After the maximum load is exceeded, the material deforms rapidly, and rupture occurs (failure point).

If we take as example the skin, during the initial stage of loading and up to a certain strain, the skin offers little resistance to deformation because elastic fibres dominate the behaviour, with a little involvement of the collagen fibres. If the stress is released, the skin returns to its initial stage. If loading continues into the plastic region, the increasing stress produces increasing strain. It is in this stage where the properties of collagen become relevant. In cutaneous surgery and wound closure, the surgeon seeks to find the optimal point on the stress-strain curve where application of stress produces the greatest strain but does not exceed the tensile strength of the skin.

References:

The biomechanical properties of skin, Hussain et al. 2013, American Society of Dermatologic Surgery.

Mechanical Stress as the Common Denominator between Chronic Inflammation, Cancer, and Alzheimer’s Disease, Nogueira et al. 2015, Front Onc.