SUMMARYAn analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper. Reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well-known trapezoidal and midpoint rules to fit the present context. Other integration schemes such as the radial return, mean normal and closest point procedures are particular cases of this general formulation. The meaning of first and second-order accuracy in the presence of the plastic consistency condition is examined in detail, and the criteria derived are used to identify two second-order accurate members of the proposed algorithms. A general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed. With the aid of this methodology, the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule. Finally, numerical examples are presented that illustrate the performance of thc algorithms.

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The notion of Plastic Internal Variables (PIVJ is used in reformulating, in a general form, the equations of rate-independent plasticity. The stress, temperature, and the PIV are the state variables for the present development. Loading-unloading is defined in terms of the usual loading function of classical plasticity. The concept of discrete memory parameters entering the constitutive equations for the PIV is introduced, in order to describe realistically the material behavior under cyclic loading. Within the framework of the general development, a simple model is constructed. By generalizing uniaxial experimental observations the concept of the "bounding surface" in stress space is introduced, defined in terms of appropriate PIV. This surface always encloses the yield surface, and their proximity in the course of their coupled translation and deformation in stress space during plastic loading determines an appropriate quantity function of the state variables and a corresponding discrete memory parameter on which the value of the plastic modulus depends. The model is compared with experimental results in a uniaxial case.

Slotted Bolted Connections (SBCs) are modified bolted connections designed to dissipate energy through friction during rectilinear tension and compression loading cycles. Experimental results on two types of SBCs are reported. In one type, friction occurs between clean mill scale steel surfaces; in the other, friction is between clean mill scale steel and brass surfaces. The behavior of connections with brass on steel frictional surfaces is found to be more uniform and simpler to model analytically than that with steel on steel surfaces. These connections maintain essentially constant slip force, and unlike those with steel on steel surfaces, require minimal overstrength of the system in design. The frictional mechanisms giving rise to the observed behavior are explained. As an example of application a one story diagonally braced frame was designed and its behavior determined for four different earthquakes. Experimental results are presented for the fabricated SBC for this frame subjected consecutively to the four displacement histories derived from these earthquakes. The agreement between the analytical and experimental results is found to be excellent. Because of the intrinsic simplicity of the SBCs and their very low cost, their use in seismic design and retrofit applications appears to be very promising.

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