Chaotic Dynamics in Generalized Rabinovich System

The article is devoted to the study of the global behavior of the generalized Rabinovich system describing the process of interaction between waves in plasma. For this generalized system, we obtain the positive invariant set (ultimate bound) and globally exponential attractive set using the approach where we transform the initial problem of finding the corresponding set to the conditional extremum problem and solve this problem. Furthermore, the rate of the trajectories going from the exterior of the attractive set to the interior of the attractive set is also obtained. Numerical localization of attractor is presented. Meanwhile, the volumes of the ultimate bound set and the global exponential attractive set are obtained, respectively. The main innovation of this article lays in considering the generalized form of the Rabinovich system with [Formula: see text] and obtaining the results on the ultimate bound set and globally exponential attractive set for this general case.

A delayed damage model for the prediction of dynamic fracture experiments

A delayed damage model was recently introduced to avoid artificial localization and mesh dependence in a softening material during a finite element analysis. This model is also interesting for transient applications because it requires only local information to predict damage and plastic strain rates. The physical idea behind this model is that the void growth rate cannot be infinite and hence the damage rate must be bounded. This paper shows that such a model does not require artificial numerical parameters and can be identified using classical spall fracture experiments. It was applied successfully to experiments performed on two aluminum alloys and one titanium alloy. The identification of the delayed damage parameters is presented. The model is applied to a simple numerical experiment which shows clearly that it avoids artificial numerical localization.