The quasi-static transverse fracture behavior in unidirectional fiber-reinforced composites (FRCs) is investigated using a new intermediately-homogenized peridynamic (IH-PD) model and a fully homogenized peridynamic (FH-PD) model. The novelty in the IH-PD model here is accounting for the topology of the fiber-phase in the transverse sample loading via a calibration to the Halpin-Tsai model.Both models can capture well the measured load-displacement behavior observed experimentally for intraply fracture, without the need for an explicit representation of microstructure geometry of the FRC.The IH-PD model, however, is more accurate and produces crack path tortuosity as well as a nonmonotonic load-crack-opening softening curve, similar to what is observed experimentally. These benefits come from the preservation of some micro-scale heterogeneity, stochastically generated in the IH-PD model to match the composite's fiber volume fraction, while its computational cost is equivalent to that of an FH-PD model. We also present a three-point bending transverse loading case in which the two models lead to dramatically different failure modes: the FH-PD model shows that failure always starts from the off-center pre-notch, while the IH-PD model, when the pre-notch is sufficiently off-center, finds that the composite fails from the center of the sample, not from the pre-notch. Experiments that can confirm these findings are sought.
Imposing local boundary conditions in nonlocal/peridynamic models is often desired/needed. Fictitious nodes methods (FNMs) are commonly used techniques for this purpose but they are limited, in general, to domains with simple geometry. FNMs also mitigate the well-known peridynamic surface/skin effect at boundaries/surfaces. Here, we introduce a general algorithm that automatically locates mirror nodes for fictitious nodes in the mirror-based FNM, without requiring an explicit mathematical description of the boundary. The algorithm is based on computing a nonlocal gradient, at fictitious nodes, to determine the “generalized” normal direction to the boundary of a domain with arbitrary geometry. We test several FNMs on peridynamic diffusion problems with or without singularities, that exist in the corresponding local models, along the boundaries. We find that the mirror-based FNM works best in agreeing with the classical solutions. We then test the new algorithm with this FNM for diffusion problems in domains with complex geometries, including one with intersecting cracks. The algorithm is general and should work for any type of peridynamic model, including those for problems with moving boundaries and growing cracks, for which enforcement of local-type boundary conditions is desired. Since high accuracy is critical near boundaries of arbitrary shape (including corners, notches, crack tips) in a variety of problems, the new algorithm has potential for high impact.
Concrete fracture caused by corrosion of reinforcing bars may cause subsequent structure failure. To better predict this process, we introduce a partially-homogenized stochastic peridynamic model with the simplest constitutive relation (linear elastic with brittle failure). The model links microscale information (phase volume fractions of mortar, aggregates, interfaces) to macroscale fracture behavior, while costing the same as a fully homogenized model. We show, and explain why a fully-homogenized peridynamic model fails to capture the correct concrete fracture modes/patterns, while the new model succeeds. The multiscale model predicts the evolution of fracture in reinforced concrete caused by corrosion products expansion in samples with a single or multiple rebars. Non-uniform expansion of corrosion products is enforced here as preset, incremental radial displacements. The computed fracture patterns and the order in which various cracks develop match what is seen in experiments. The model's robustness is tested under different stochastic realizations and discretization grid types.
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