Stress-wave distribution in a semi-infinite body due to an arbitrary heat flux at the surface

Abstract

A general solution is given to the uncoupled one-dimensional equations for the stress wave in a semi-infinite body due to an absorbed heat flux that is spatially uniform but varies in an arbitrary manner with time. The solution is in the form of a convolution integral that is applicable when both the thermal conductivity and the exponential absorption depth of the material are nonzero. Analytical results in terms of real and complex error functions are given for the cases where the flux is steady or varies in an impulsive, linear or exponential manner with time.