Resumen de Computational Algorithms for Cyclic Plasticity Based on Prager's Translation Rule
The focus of this thesis is to introduce the theory and a fully implicit integration algorithm for multisurface plasticity using Prager's rule with mixed isotropic and nonlinear kinematic hardening.
The model uses the idea from Mróz of discretizing the uniaxial stress-strain curve in several segments, resulting in a field of hardening surfaces. This approach is very simple in obtaining material parameters of the model. However, in contrast to Mróz's proposal, the model is based on the traditional Prager's rule and the yield surface is always the innermost surface. The outer surfaces are just hardening surfaces, a tool to describe an anisotropic history-dependent hardening modulus. The formulation and numerical algorithm naturally recover classical von Mises plasticity with mixed hardening in the case of uniaxial bilinear stress-strain curves, regardless of the number of surfaces being employed. Hence, the predictions are self-consistent.
The integration algorithm is based in the closest point projection algorithm. Both local and global consistent linearizations are included in order to preserve the asymptotic second order convergence of Newton schemes. Some stress-point and finite element simulations show both the applicability and the robustness of the stress integration algorithm. And the model is validated with predictions of the experimental results from both uniaxial and multiaxial tests taken from the literature, which include very different loading paths. The numerical efficiency of the fully implicit, Backward-Euler algorithmic formulation is demonstrated by the implementation in a finite element program and the simulation of a cyclic loading example from the literature.
Using this model has resulted in two important observations.
By predicting the exact offsets of probing plastic strain, the same probing loading paths of actual experiments about the evolution of subsequent yield surfaces, similar results about apparent yield surfaces are got compared to those from experiments, which brings out the most important purpose of this thesis: to show that a relevant part of the observations in the experiments may be attributed to (and hence modeled by anisotropic kinematic hardening developed during preloading.
Another one, not usually commented in the literature, is the influence of the size of the actual yield surface in the predictions under some loading paths, even if the same stress-strain curve is employed. Since an accurate determination of the actual size of the yield surface is difficult in some materials, the stress path during multiaxial loading may facilitate this determination.
