FURTHER DEVELOPMENT, MULTIAXIAL FORMULATION, AND IMPLEMENTATION OF THE BOUNDING SURFACE PLASTICITY MODEL FOR METALS

The concept of the bounding surface in stress space is used to formulate a generalized constitutive model for metals within the framework of rate independent plasticity. The model is implemented numerically and it is validated by comparing its predictions with uniaxial and multiaxial experimental data.;The new features added to the original formulation of Dafalias and Popov, (1975 and 1976) include the following. First, a new term is added to the kinematic hardening of the bounding surface which allows the simulation of the relaxation phenomenon under cycles of nonzero mean strain. Second, the distance-measure function for the plastic modulus between the actual and image stress point is redefined in order to reflect the directional character of this distance at the initiation of each loading segment. Finally, the isotropic hardening of the bounding surface is reformulated to capture the material response under out-of-phase multiaxial loading.;The model uses fifteen constants to realistically predict different phenomena such as the initial 'plateau' behavior of structural steel, monotonic, cyclic, in-phase and out-of-phase isotropic hardening, cyclic softening, and a number of response aspects related to kinematic hardening such as cyclic creep under nonzero mean stress loading, and stress relaxation under cycles of nonzero mean strain loading. The number of model constants is drastically reduced if only some of the aforementioned phenomena are to be depicted, without altering the basic constitutive formulation.;Both the 'two surface' and 'radial mapping rule' versions of the bounding surface model are studied, with the emphasis placed on the former. A subroutine package is prepared for the numerical solution of the rate equations provided by the model, using the successive approximation technique (this package can also be added to two and three dimensional finite element programs). Successful comparisons between the model predictions and experimental data are presented for four different metals under uniaxial and diverse complex multiaxial loading paths.;The computer memory (storage) requirements for a finite element implementation is minimal compared to that of other models which can describe the same phenomena, rendering the present model a very useful tool for purposes of analyzing boundary value problems.