Maxwell's stress functions

Maxwell's stress functions

[′mak‚swelz ′stres ‚fəŋk·shənz]
(mechanics)
Three functions of position, φ1, φ2, and φ3, in terms of which the elements of the stress tensor σ of a body may be expressed, if the body is in equilibrium and is not subjected to body forces; the elements of the stress tensor are given by σ11=∂2φ2/∂ x32+∂2φ3/∂ x22, σ23= -∂2φ1/∂ x2x3, and cyclic permutations of these equations.