Numerical verification of a bond-based softening peridynamic model for small displacements

Abstract

In this article we present a systematic numerical approach for calibration and numerical verification of peridynamics models. The approach is illustrated for a two parameter exponential bond softening model, which is calibrated using theoretical relations connecting its horizon-independent parameters to the shear modulus and fracture toughness of classic Linear Elastic Fracture Mechanics. The horizon is determined by Griffith’s brittle failure criterion given in terms of the critical failure stress which can be found experimentally. Computations with the calibrated peridynamic model are carried out to verify the linear behavior of the deformation for small strains and the Poisson effect. Numerical experiments identical to physical experiments are used to compute the Poisson ratio from samples subjected to linear time-dependent loading. The ratio observed in the experimental tensile test was reproduced in the simulations but becomes unstable after some time steps. We conclude that one explanation for this discrepancy that the simple peridynamic model has a peridynamically equivalent Poisson ratio of ¼ and the Poisson ratio of PMMA is 0.4. Our numerical results indicate that state-based peridynamics models with peridynamically equivalent Poisson ratios of 0.4 should be considered for a more stable recovery of material behavior for PMMA. As future work the same energy equivalence and comparison of material behavior with respect to experiments for the state-based softening peridynamic model will be considered.