A review of benchmark experiments for the validation of peridynamics models

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 set-ups 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 6 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.

A mechanical model to interpret distributed fiber optic strain measurement at displacement discontinuities

Distributed fiber optic (strain) sensing, which provides the unique advantage of sensing damage (e.g. cracking) at locations that are not known a priori, has been increasingly used in civil engineering. Quantitative crack measurement requires the translation of a discontinuous displacement field at the crack to a continuous strain deformation in the fiber. The main purpose of this article is to develop a mechanical model to explain the fiber deformation in the presence of a displacement discontinuity. The proposed mechanical model is validated with experimental results from cable calibration tests and concrete cracking tests. The model is extended to simulate the effects of multiple closely spaced cracks on fiber optic strain measurement, and this model is used to create an algorithm to automatically distinguish multiple cracks in distributed fiber optic (strain) sensing strain distributions. Using the model and two shape parameters, kurtosis and standard variation, the effects of cable properties (i.e. shear stiffness between cable and fiber, cable radius, elastic modulus, and interface cohesion) on the shape of fiber optic strain distributions across cracks are also quantified. The results provide an indication of beneficial cable properties for various measurement objectives.

Crack development assessment using modal analysis in peridynamic theory

If structural damage remains undetected and is allowed to grow, structure's load-bearing capacity deteriorates, which can lead to costly repairs or in extreme cases its collapse. Modal analysis is widely used to detect structural damage because, when damage, such as cracks, is introduced, structure's geometrical and/or mechanical properties change, and these changes can be used for damage detection. Peridynamics is a non-local alternative to the continuum mechanics theory that represents forces and displacements using integral equations, which are defined even with discontinuous displacement fields, thus making this theory an attractive option for damage modeling. In this paper, authors verify peridynamic (PD) modal analysis against finite-element (FE) results, and validate it against experimental modal analysis results. The modal solver was implemented in the open-source program Peridigm and four different damage configurations were considered for verification and validation. The results show close agreement between the PD and the FE results, and the PD and the experimental results. Moreover, PD modal frequencies are shown to have similar accuracy to experimental data as the FE results. It is also shown that the frequency shifts are comparable between all three types of modal analysis. The PD mode shapes agreed well with both the FE and the experimental mode shapes at all considered damage configurations. Furthermore, the change in mode shapes from the introduced damage is similar in all three analyses.

Isothermal extrusion of ribs on plate

Technological schemes and relationships are given for calculating of operating modes during isothermal heating of workpieces. The conditions of viscoplastic non-stationary deformation are accepted. The energy form equilibrium equation as applied to the discontinuous displacement velocity fi eld and material damage kinetics equations are used. The calculation results and product samples are presented.