  A yield surface of a material is a set of critical stress conditions beyond
which macroscopic plastic deformation begins. For crystalline solids, plastic
deformation occurs through the motion of dislocations, which can be captured by
discrete dislocation dynamics (DDD) simulations. In this paper, we predict the
yield surfaces and strain-hardening behaviors using DDD simulations and a
geometric manifold learning approach. The yield surfaces in the
three-dimensional space of plane stress are constructed for single-crystal
copper subjected to uniaxial loading along the $[100]$ and $[110]$ directions,
respectively. With increasing plastic deformation under $[100]$ loading, the
yield surface expands nearly uniformly in all directions, corresponding to
isotropic hardening. In contrast, under $[110]$ loading, latent hardening is
observed, where the yield surface remains nearly unchanged in the orientations
in the vicinity of the loading direction itself, but expands in other
directions, resulting in an asymmetric shape. This difference in hardening
behaviors is attributed to the different dislocation multiplication behaviors
on various slip systems under the two loading conditions.
