Linear elasticity

Summary

Linear elasticity is the mathematical model of solid bodies that deform by small amounts and return to their shape when the loads are removed. It combines three linear relations. The first is the balance of forces for the Cauchy stress tensor. The second gives the small strain tensor as the symmetric part of the displacement gradient. The third is a linear stress–strain law. That law is given by the elasticity tensor. Because everything is linear, solutions can be superposed, and the theory has a rich set of exact solutions and energy theorems. It is the basis of structural engineering, seismology and much of materials science.