Determination of the Length Scale Parameter in Peridynamics
Abstract
To obtain accurate results from a peridynamic analysis, it is essential to choose a suitable size for the horizon. Hence, the primary objective of this project is to develop concrete ways to determine the size of the horizon for different conditions including (1) classical deformation behavior in problems without damage, (2) non-classical (non-local) deformation behavior in problems without damage, and (3) non-locality in problems with damage. Both ordinary state based and non-ordinary state based peridynamic formulations will be considered. The first task focuses on problems which do not require a length scale parameter as in Cauchy’s continuum mechanics formulation. For such a condition, peridynamics and Cauchy’s formulation should yield same set of results. Although this is true in the limit as horizon approaches zero, this requires additional care in practice since numerical techniques, mainly meshless methods, are utilized for the solution of peridynamic equations. Due to finite distance between material points in the solution domain, the horizon value also takes a finite value rather than an ideal infinitely small value. Second task focuses on problems showing non-local characteristics which cannot be accurately modelled using Cauchy’s formulation. Such problems are especially common at small scales including analysis of carbon nanotubes, graphene sheets, self-assembly processes, etc. In this case, horizon corresponds to a physical parameter which requires a careful selection of this parameter to capture the actual physics of the problem. Final task focuses on problems with damage occurrence. Although the original problem may not require a length scale parameter as mentioned earlier, the spontaneous occurrence of damage inside the structure may require definition of a length scale parameter to accurately describe the physics around the damage region.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 19, 2018
- Source ID
- FA95501817004
Entities
People
- Erkan Oterkus
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Strathclyde