Infinitesimal strain theory

Summary

Infinitesimal strain theory is the approximation of the kinematics of deformation in which displacement gradients are small. Strain is then described by the linear strain tensor $\varepsilon = \tfrac12 (\nabla u + (\nabla u)^T)$, and the reference and deformed shapes are not distinguished. It is the kinematic basis of linear elasticity and of most engineering calculations for stiff materials such as steel and concrete.