A two-complementary-trio material model for cyclic plasticity is proposed in this paper. In this formulation we consider a contact surface to confine the motion of contact stress. While the on-off switching criteria of plasticity are derived from the first complementary trio, the switching criteria of kinematic hardening rules are derived according to the second complementary trio. In terms of the new concept of contact stress and contact surface, it becomes easier to derive the governing rule of back stress during the contact of yield surface and bounding surface. The validity of the new model is confirmed by comparing the computational results with the experimental data for materials of SAE 4340 and RHA under uniaxial cyclic tests and biaxial cyclic tests. Even though the material constants used in the new model are parsimonious (with only 12), it is immediately recognized that the cyclic response curves described by the new model are in good agreement with the experimental data.

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Developed herein is an analysis procedure based on closed-form solutions to elastoplastic bilinear model of building structures accounted for different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels due to the layout of buildings and the complexity of structural members. The seismic design often considers earthquake forces on multiple floor levels but usually only in a single direction. However, in reality, the direction of the earthquake is not limited to one particular direction. Therefore, studying the influence of a two-way, furthermore multi-dimensional, earthquake on buildings is of great value. To estimate the total seismic demand on inelastic building structures subjected to multi-dimensional loading, this paper aims to find closed-form solution responses to an input rectilinear force path for the elastoplastic bilinear model of Hong and Liu (1999) which already has available closed-form solution responses to an input rectilinear displacement path. In this paper the elastoplastic bilinear model of building structures and Minkowski spacetime are adapted to accommodate such situations as different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels.