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We introduce PeriFast/Corrosion, a MATLAB code that uses the fast convolution-based method (FCBM) for peridynamic (PD) models of corrosion damage. The FCBM uses the convolutional structure of PD equations and employs the Fast Fourier transform (FFT) to achieve a computational complexity of O(NlogN). PeriFast/Corrosion has significantly lower memory allocation needs, O(N), compared with, for example, the meshfree method with direct summation for PD models that requires O(N2). The PD corrosion model and the fast convolution-based method are briefly reviewed, and the detailed structure of the code is presented. The code efficiently solves 3D uniform corrosion (example for copper) and pitting corrosion (example for stainless steel) problems with multiple growing and merging pits, set in a complicated shape sample. Discussions on possible immediate extensions of the code to other corrosion damage problems are provided. PeriFast/Corrosion is a branch of PeriFast codes and is freely available on GitHub [1].

We present PeriFast/Dynamics, a compact and user-friendly MATLAB code for fast peridynamic (PD) simulations for deformation and fracture. PeriFast/Dynamics uses the fast convolution-based method (FCBM) for spatial discretization and an explicit time marching scheme to solve large-scale dynamic fracture problems. Different from existing PD solvers, PeriFast/Dynamics does not require neighbor search and storage, due to the use of the Fast-Fourier transform and its inverse to compute the integral operator. Run-times and memory allocation are independent of the number of neighbors inside the PD horizon, leading to faster computations and lower storage requirements. The governing equations and discretization method are briefly reviewed, the code structure explained, and individual modules described in detail. A demonstrative example on dynamic brittle fracture in 3D, with multiple crack branching events, is solved using three different constitutive models: a bond-based, an ordinary state-based, and a correspondence model. The small differences between results with the three different constitutive models are explained. Users are provided with a step-by-step description of the problem setup and execution of the code. PeriFast/Dynamics is a branch of the PeriFast suite of codes, and is available for download at the GitHub link provided in reference [1].

Formulations for diffusion processes based on graph Laplacian kernels have been recently used to solve linear transient heat transfer problems with insulated boundary conditions by way of a spectral-based semi-analytical approach. This has been called the “spectral graph” (SG) approach. In this paper, we show that the meshfree discretization for corresponding peridynamic (PD) models leads to a graph structure that allows us to introduce the “graph Laplacian PD” (GL-PD) method using the semi-analytical approach employed in the SG approach to solve the transient heat diffusion problems. The new method, GL-PD, can be seen as a “hybrid” between SG and PD with meshfree discretization. We discuss the similarities and differences between the GL-PD and the SG approaches. Main differences are related to calibration and discretization procedures. We use a 1D heat diffusion example to highlight some limitations the spectral-based semi-analytical method in the SG approach has compared with the direct time-integration normally used in computing solutions to transient diffusion problems. We then propose an extension of the semi-analytical approach to solve transient diffusion problems with Dirichlet boundary conditions, using a recent scaling and squaring algorithm that calculates the matrix exponential of non-symmetric matrices.

This study evaluates the effectiveness of GN (Graphene Nanoplatelets) salt inhibitor-treated concrete in inhibiting chloride ion diffusion and corrosion compared to untreated concrete under various erosion conditions. Through an accelerated indoor chloride erosion test lasting 180 days, we examined the temporal changes in internal chloride ion concentration with and without the GN salt inhibitor. Quantitative assessment of the inhibitor's impact was achieved by introducing reduction factors for surface chloride concentration and diffusion coefficient. Our findings reveal a significant reduction of 31.3% in chloride ion diffusion coefficient and 22.67% in surface chloride concentration in concrete treated with GN salt inhibitor. This indicates the inhibitor's potential to extend the service life of gearbox and substation foundations exposed to chloride ion erosion environments.