What are stress and strain in continuum mechanics?

In continuum mechanics, stress describes the internal forces that neighboring particles of a continuous material exert on each other during deformation, measured in force per unit area. Strain, by contrast, is the measure of the relative deformation of the material resulting from these forces or other changes. Together with strain rate, their relationships are fundamental to modeling the physical behavior of both solids and fluids.

What we know

• Stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. [1, 2]
• Strain is the measure of the relative deformation of a material. [2]
• Stress has the dimension of force per area, with SI units of newtons per square meter or pascals. [2]
• Deformation of a solid material generates an internal elastic stress that tends to restore the material to its original non-deformed state. [2]

Where to go next

• the bigger pictureHow does solid mechanics study deforming materials?
• a case in pointWhat is fluid mechanics?
• how it workedHow do mathematical tensors describe physical properties?
• compared withHow do solids and fluids differ in their response to stress?
• what followedWhat causes permanent deformation or material fracture?
• an unexpected connectionHow does dental prosthesis design rely on continuum mechanics?Solid mechanics provides the fundamental tools to understand the deformation of solid materials under forces, extending its practical applications directly into biomedical engineering for designing dental prostheses and surgical implants.

Sources

• [1]mechanical stress (Wikidata Q206175) · CC0 1.0
• [2]Stress (mechanics) · CC BY-SA 4.0
• [3]Solid mechanics · CC BY-SA 4.0
• [4]Continuum mechanics · CC BY-SA 4.0
• [5]Fluid mechanics · CC BY-SA 4.0