Strain (mechanics)

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In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. Strain has dimension of a length ratio, with SI base units of meter per meter (m/m). Hence strains are dimensionless and are usually expressed as a decimal fraction or a percentage. Parts-per notation is also used, e.g., parts per million or parts per billion (sometimes called "microstrains" and "nanostrains", respectively), corresponding to μm/m and nm/m. Strain can be formulated as the spatial derivative of displacement: 𝜺≐∂∂𝐗(𝐱−𝐗)=𝑭′−𝑰, where I is the identity tensor. The displacement of a body may be expressed in the form x = F(X), where X is the reference position of material points of the body; displacement has units of length and does not distinguish...

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