Learning topic
Stress and Strain at a Point
Introduction to normal and shear stresses and normal and shear strains as local measures of the mechanical state of a material.
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Internal force resultants describe the total interaction between portions of a body across a section. To describe this interaction locally at a material point, stress is introduced. Local changes in geometry are described by strain.
Stress
The internal interaction acting on a small oriented area can be resolved into a component normal to the area and a component lying in its plane. These define normal stress $\sigma$ and shear stress $\tau$.
Stress is not a force. A force or internal resultant is an integrated quantity, while stress describes the intensity of distributed internal interaction. Its dimension is force per unit area.
Normal strain
Normal strain $\varepsilon$ describes the relative change in length of a material line element. For a one-dimensional small elongation, its average value is $\varepsilon=\Delta l/l$.
Shear strain
Shear strain $\gamma$ describes the change of an initially right angle between material directions. It is particularly important in shear and torsion.
State at a point
The values of $\sigma$, $\tau$, $\varepsilon$, and $\gamma$ depend on position and on the orientation of the plane or direction considered. A complete stress and strain state is multicomponent and is developed later in dedicated topics. At this introductory stage, the key distinction is between global internal resultants and local material measures.