Modeling the Yield Surface of a Composite Made from Rigid-Plastic Materials Using Piecewise Quadratic Yield Criteria 1. The General Case of a Plane Multidirectional Reinforcement

A structural model of the mechanics of composites for calculating their yield surfaces in the 3D space of averaged stresses in the plane stress state (PSS) is developed. The composite is multidirectionally reinforced in the parallel planes with continuous fibers of different physical nature (a hybrid composite). The materials of composition constituents are isotropic and have different yield strengths in tension and compression. In all constituents, a complex stress state is taken into account. The mechanical behavior of materials of the composition is described by the associated flow law for an ideal rigid-plastic body with piecewise quadratic and piecewise linear yield conditions in the space of principal stresses of the PSS. In addition to average stresses, the average strain rates in the limit state of the composite are also determined. The conditions under which the flow curves of constituents of the composition in the PSS satisfy the Drucker postulate, i.e., are convex, are analyzed.