Effective plastic properties of laminates made of isotropic elastic plastic materials

The effective elastic behavior of laminates is well understood. In this contribution, we make use of the fact that the elastic homogenization can be extended relatively easy to the plastic case (He and Feng, 2012), which is interesting for bilayer metallic structures. With the aid of stress concentration tensors, the effective yield limit is calculated, and its properties are examined. It turns out to be anisotropic, pressure-dependent, non-smooth, and evolves with the plastic deformation. Using the constitutive equations of von Mises elastic plastic materials, the effective plastic flow behavior is obtained as a set of coupled nonlinear ordinary differential equations with algebraic conditions. A general solution can hardly be given, but it can be integrated numerically. Further, it is possible to examine some properties of its solution without explicitly stating it, such as its poles. The latter allow to extract closed form-expressions for the ultimate loading stress in monotonic stress-driven tests. All analytical results are compared to representative volume element simulations, and found to match very well.