In another form, this law can be written with Lamé coefficients and Kronecker's delta.
This law can be extended using an 81 coefficient 4th order tensor named for Green. In another form, this law can be written with Lamé coefficients and Kronecker's delta. Augustin Cauchy would extend this law to three dimensions using a compliance matrix. In isotropic form, it can be written generally using Poisson's ratio, or alternatively using Young's modulus and the bulk modulus. One can use it to show the linear relationship between the components of stress and strain, and for materials like steel it is only valid for its elastic range. FTP, identify this law that gives the restoring force on a spring, typically written as F equals the opposite of k times x. 
This law can be extended using an 81 coefficient 4th order tensor named for Green.
{Hooke's} law