Interfaces in the materials are known entities since last century described as early as in the interfacial excess energy formulations by Gibbs (Bobelmann et al. 2007). The interface effect (or surface effect) is also widely referred to as the interface stress (or surface stress) that consists of two parts, both arise from the distorted atomic structure near the interface (or surface): the first part is the interface (or surface) residual stress which is independent of the deformation of solids, and the second part is the interface (or surface) elasticity which contributes to the stress field related to the deformation. Plastic deformation, in particular, the initial yielding point (i.e., the yield surface), is sensitive to the local stress (or local strain) of a heterogeneous material, which includes both the local (surface/interface) residual stress and local stress-strain relationship. The plastic deformation at the interfaces also considers the tension and compression along the interface and stress mismatch because of the material property differences. In the nanomaterials, the surface and interface stresses become even more important owing to the nanoscale size of the particles and interface areas. © Springer Nature Switzerland AG 2019. All rights reserved.