For an anisotropic, elastic medium with elastic energy density

integrate this energy density over a 3-dimensional region V (not necessarily small) to get the total elastic energy E. Now consider a small variation δξ_i in the displacement field. Evaluate the resulting change δE in the elastic energy without using the relation

Convert to a surface integral over ∂V, and thence infer the stress strain relation

Transcribed Image Text:

U = Ši;j Yijkl Šk;l>