Fast quasi-implicit NOSB peridynamic simulation based on FIRE algorithm

Abstract

The peridynamics is a particle methods considered superior to the finite element method in describing fracture phenomena since fracture can be simply expressed as bond breaking between the peridynamics particles. The Non-Ordinary State-Based (NOSB) peridynamics is a variant of the particle method which allows us to implement constitutive laws as in the finite element method. To maintain its computational accuracy, parameters used in the peridynamic simulations needs to be optimized through parameter searches, hence the peridynamics requires a fast quasi-implicit algorithm which allows to directly compare the results to the one obtained by the finite element method. The FIRE algorithm is such an algorithm well examined through molecular dynamics studies and is easy to implement existing explicit algorithms. The objective of this study is to describe the details of the implementation of the FIRE method to the peridynamic elastic and elasto-plastic computational codes and the effectiveness through the comparison with another quasi-static algorithm, the energy based relaxation method. The computational results show the effectiveness of the algorithm and some examples of the parameter search in simple problems such as elastic and elasto-plastic deformation analyses and a stress analysis near a crack.

Keywords

• peridynamics
• quasi-implicit algorithm
• elasto-plasticity
• finite element method
• continuum mechanics