A Review of Benchmark Experiments for the Validation of Peridynamics Models

Abstract

Peridynamics (PD), a non-local generalization of classical continuum mechanics (CCM) allowing for discontinuous displacement fields, provides an attractive framework for the modeling and simulation of fracture mechanics applications. However, PD introduces new model parameters, such as the so-called horizon parameter. The length scale of the horizon is a priori unknown and need to be identified. Moreover, the treatment of the boundary conditions is also problematic due to the non-local nature of PD models. It has thus become crucial to calibrate the new PD parameters and assess the model adequacy based on experimental observations. The objective of the present paper is to review and catalog available experimental setups that have been used to date for the calibration and validation of peridynamics. We have identified and analyzed a total of 39 publications that compare PD-based simulation results with experimental data. In particular, we have systematically reported, whenever possible, either the relative error or the R-squared coefficient. The best correlations were obtained in the case of experiments involving aluminum and steel materials. Experiments based on imaging techniques were also considered. However, images provide large amounts of information and their comparison with simulations is in that case far from trivial. A total of six publications have been identified and summarized that introduce numerical techniques for extracting additional attributes from peridynamics simulations in order to facilitate the comparison against image-based data.

Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

“…which is the exact analogue of that in 2D in (17). Thus, according to (51), ψ is given by ψ(x, t) = exp α • x + χ 2 κ 2 t .…”

“…Replacing (17) into (13) leads to modes capable of constructing semi-analytical solutions for the local diffusion as follows:…”

“…Therefore, PD models are effective tools in modelling material discontinuities, and they consider fracture and damage as natural parts of the solution. To this respect, many PD models have so far been proposed and applied to a broad range of problems in solids including fracture and crack propagation; to mention a few, see [7,16,40,52,57,59,66] and for a comprehensive review one may refer to [11,17].…”

An asynchronous and task-based implementation of peridynamics utilizing HPX—the C++ standard library for parallelism and concurrency

“…Peridynamics is a non-local generalization of continuum mechanics, tailored to address discontinuous displacement fields that arise in fracture mechanics [12,20]. Several peridynamics implementations utilizing the EMU nodal discretization [39] are available.…”

Comparison of peridynamic and phase-field models for dynamic brittle fracture in glassy materials

“…Peridynamics has been successful in modeling crack branching [8,26,47] and has been mathematically proven to recover both static and dynamic Griffith's fracture [48,49]. An extensive review and catalog of available experimental setups that have been used for calibration/validation of numerous peridynamic-based simulations has recently appeared in [50]. An implementation of PD based on the discontinuous-Galerkin method has recently been introduced in the commercial code LS-DYNA for simulating fracture in brittle materials [51].…”