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The tensile properties of reduced activation ferritic/martensitic (RAFM) steels are significantly influenced by neutron irradiation. Here, a mechanism-based model taking account of the typical ductile damage process of void nucleation, growth, and coalescence was used to study the temperature and irradiation effects. The elastic–plastic response of RAFM steels irradiated up to 20 dpa was investigated by applying the GTN model coupled with different work hardening models. Through a numerical study of tensile curves, the GTN parameters were identified reasonably and satisfying simulation results were obtained. A combination of Swift law and Voce law was used to define the flow behavior of irradiated RAFM steels. The deformation localization could be adjusted effectively via setting the nucleation parameter εn close to the strain where necking occurs. Because εn changed with uniform elongation, εn decreased with the testing temperature and rose with an irradiation temperature above 300 °C. The nucleation parameter fn increased with the testing temperature for RAFM steels before irradiation. For irradiated RAFM steels, fn barely changed when the irradiation temperature was below 300 °C and then it rose at a higher irradiation temperature. Meanwhile, the ultimate strength of the simulated and experimental curves showed good agreement, indicating that this method can be applied to engineering design. [ABSTRACT FROM AUTHOR]

We propose and study a class of discrete-time commensalism systems with additive Allee effects on the host species. First, the single species with additive Allee effects is analyzed for existence and stability, then the existence of fixed points of discrete systems is given, and the local stability of fixed points is given by characteristic root analysis. Second, we used the center manifold theorem and bifurcation theory to study the bifurcation of a codimension of one of the system at non-hyperbolic fixed points, including flip, transcritical, pitchfork, and fold bifurcations. Furthermore, this paper used the hybrid chaos method to control the chaos that occurs in the flip bifurcation of the system. Finally, the analysis conclusions were verified by numerical simulations. Compared with the continuous system, the similarities are that both species' densities decrease with increasing Allee values under the weak Allee effect and that the host species hastens extinction under the strong Allee effect. Further, when the birth rate of the benefited species is low and the time is large enough, the benefited species will be locally asymptotically stabilized. Thus, our new finding is that both strong and weak Allee effects contribute to the stability of the benefited species under certain conditions. [ABSTRACT FROM AUTHOR]