Session: 12-03-01: Minisymposium on Peridynamic Modeling of Materials’ Behavior

Paper Number: 77161

Start Time: Monday, 11:35 AM

77161 - Overall Equilibrium in the Coupling of Peridynamics and Classical Continuum Mechanics 

The unavoidable presence of small or large cracks in many aeronautical and aerospace structures still represents a major challenge for engineers who want to simulate a full structural life cycle. Even though classical continuum mechanics (CCM) based numerical methods are extensively used for the simulation of different structural problems, their application in fracture problems is challenging due to the presence of spatial derivatives of displacements in the governing equations, which are undefined when the displacement fields are discontinuous. 

In recent years, innovative computational methods based on peridynamics have been proposed and implemented in order to solve complex problems involving damage initiation and crack propagation. The peridynamic (PD) theory is a nonlocal reformulation of CCM based on integro-differential equations, which allows for a natural modeling of the evolution of cracks, including their nucleation, their propagation direction, and the points where they start and stop, without having to define any criteria for triggering, bifurcation, and deviation phenomena. Despite the effectiveness of PD models in solving problems concerning crack propagation, PD models are computationally more expensive than CCM models due to their nonlocal nature. Therefore, the considerable computational cost of PD models hinders their application in large-scale, geometrically complex simulations. Furthermore, PD numerical implementations may be affected by some additional difficulties related to the definition of nonlocal boundary conditions. In nonlocal theories the boundaries are fuzzy, so that prescribed displacement or load conditions have to be imposed in finite volumetric regions rather than on boundary surfaces. Most of the time, such extension of classical boundary conditions is not clearly defined. Hence, it would be convenient to couple PD and CCM models in order to take advantage of the benefits of both models while avoiding their aforementioned drawbacks.

In CCM-PD coupled modeling, usually small areas of a domain, which might be affected by the presence of discontinuities, are described with a PD model, whereas the remaining parts of the domain are represented through a more efficient CCM model. CCM-PD coupling has led to a great research effort resulting in the development of a variety of techniques, and it is still an area in which active research is carried out because most of the coupling methods proposed are affected by some kind of arbitrariness or spurious effects that need to be overcome. 

In this presentation, we will provide an overview of CCM-PD coupling methods, and we will discuss the problem of the overall equilibrium in CCM-PD coupled models. We will present a new analysis of out-of-balance forces, which sheds some light on how to control the lack of overall equilibrium in CCM-PD coupled problems.

Presenting Author: Pablo Seleson Oak Ridge National Laboratory

Authors:

Greta Ongaro University of Padova
Pablo Seleson Oak Ridge National Laboratory
Ugo Galvanetto University of Padova
Tao Ni Hohai University
Mirco Zaccariotto University of Padova