## Gabriel Hattori

Research Updates

__Update 1__

__September 30, 2018__

The workload of the previous 6 months has been divided between two complementary projects: 1) developing a model for reinforced concrete (RC) structures using the non-ordinary state-based (NOSB) peridynamics (PD) formulation; and 2) to implement an adaptivity framework for PD. In the first project, we have investigated a real RC beam (see Figure), initially in 2D, using an explicit integration scheme. The deformed shape is as expected, where the stresses are considerably higher in the reinforcement. However, we realised that some oscillations may arise at the interface steel-concrete. This may be related to the different wave speeds, which propagates faster in steel. Another issue is that the time step has to be very small, which implies that the problem is very computationally expensive. The adaptivity framework could be a solution for this issue.

Video: https://youtu.be/_trWYnVuNnc

Adaptivity in PD will permit to have different particle discretisations in different areas for the studied problem. We intend to use error estimators, which have been largely used for finite element (FE) analysis in adaptivity. Error estimators represent a measure of the quality of the solution of the analysis. We have employed a background finite element (FE) mesh to calculate the area of influence (horizon) of each particle. The FE mesh will also be used to calculate the error estimators. We investigated a simple example, a fixed bar subjected to an initial velocity, where the left side is refined, for two different horizon approaches: area (a circle centred in the particle of interest) and topological (where the horizon is defined by the mesh connectivity). One can verify that there are some small oscillations at the interface of the mesh, and this is still under investigation.

Video: https://youtu.be/787NX7D8MGw