The development of residual stress distributions in thermoviscoelastic materials due to surface cooling is considered. They arise because the nonuniform thermal contraction generates irreversible viscoelastic deformation, which tends to become permanent as the temperature falls due to the rapid growth of relaxation times with temperature reduction. Examples of a cooled solid sphere of polymethylmethacrylate are evaluated, and the results are compared with previous analyses based on an elastic-inviscid fluid model. For application in design to generate beneficial residual stress distributions, the need to assess the entire stress history is pointed out, and relevant features of the phenomenon are discussed.

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