A meshless IRBFN-based numerical simulation of adiabatic shear band formation in one dimension

Abstract

[Abstract]: In this paper, we describe an integrated radial basis function network (IRBFN) method for the numerical modelling of the dynamics of strain localization in elasto-thermo-viscoplastic materials with coupled heat conduction. A new coordinate mapping for the IRBFN method is introduced in this paper to resolve the steep temperature, velocity, strain and strain-rate gradients associated with the strain localization (shear band). The discrete governing PDEs are integrated in time using an implicit 5th-order Runge-Kutta method with automatic time step selection. Numerical results demonstrate the e±ciency of the present IRBFN approach in solving steep (singularity-like behaviour) nonlinear PDEs encountered.