An adaptive substepping explicit integration scheme with a novel loading-unloading decision method is developed here for the non-isothermal unified hardening (UH) model. The non-isothermal UH model includes a convex subloading surface in the $$p$$p-$$q$$q plane and a nonconvex subloading surface in the $$p$$p-$$T$$T plane. Because of the convex/nonconvex subloading surfaces, the conventional loading-unloading decision method used in stress integration schemes may lead to incorrect elasticity/elastoplasticity judgements. In addition, the conventional loading-unloading decision method is unable to determine the division point that separates the elastic segment from the elastoplastic segment. A simple but robust method, the double cosine (DC) method, is proposed in this paper to solve loading-unloading decision problems. The proposed DC method is then embedded into an adaptive substepping explicit integration scheme to implement the non-isothermal UH model. The accuracy and efficiency of the DC method are discussed by comparing the method with the conventional loading-unloading decision method (the CV method) and the root-finding loading-unloading decision method (the RF method). The performance of the proposed scheme with the DC method is also discussed.
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