Uniaxial ratcheting and ductile damage in structural steel with a stochastic spreading of experimental data

This paper provides new experimental data regarding inelastic strain accumulation in structural steel samples. The samples are subjected to stress‐controlled cyclic loading with positive mean stress within each cycle; the loading blocks are combined in a complex pattern to study the effect of load history. A large‐strain ratcheting model is constructed based on a material law with a nonlinear kinematic and isotropic hardening. A new rule of ductile damage accumulation is suggested and a class of models with hardening stagnation is introduced. We show that models which include the hardening stagnation describe the experimental data more accurately. Unfortunately, due to a large spread of mechanical properties from sample to sample, it is impossible to describe the entire set of experiments using a single set of parameters. To address this challenge, we have developed novel mathematical tools for parameter identification in the context of stochastic variations in mechanical properties. These tools include the concept of a collar of model responses and the notion of protrusion. We propose an extended parameter identification problem that rethinks the standard error functional. We demonstrate that the extended identification problem effectively accounts for the large spread observed in experimental data when applied to the developed ratcheting model.