Abstract
The most common discretization method for peridynamic models used in engineering problems is the node-based meshfree approach. This method discretizes peridynamic domains by a set of nodes, each associated with a nodal cell with a characteristic volume, leading to a particle-based description of continuum systems. The behavior of each particle is then considered representative of its cell. This limits the convergence rate to the first order. In this paper, we introduce a reproducing kernel (RK) approximation to the field variables in the peridynamic equations to increase the order of convergence of peridynamic numerical solutions. The numerical results demonstrate improved convergence rates in static peridynamic problems using the proposed method.
| Original language | English |
|---|---|
| Pages (from-to) | 1044-1078 |
| Number of pages | 35 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 340 |
| DOIs | |
| State | Published - Oct 1 2018 |
Funding
This work is supported in-part by the AFOSR MURI Center for Material Failure Prediction through Peridynamics (AFOSR Grant No. FA9550-14-1-0073 ). The support of this work by the U.S. Army Engineer Research and Development Center under contract PLA-0009 to University of California, San Diego and by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL) , managed by UT-Battelle, LLC., for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725 , is also greatly appreciated.
Keywords
- Domain integration
- Meshfree method
- Nonlocal
- Peridynamics
- Reproducing kernel approximation