Farshid Mossaiby

Peridynamic (PD) models are commonly implemented by exploiting a particle-based method referred to as standard scheme. Compared to numerical methods based on classical theories (e.g., the finite element method), PD models using the meshfree standard scheme are typically computationally more expensive mainly for two reasons. First, the nonlocal nature of PD requires advanced quadrature schemes. Second, non-uniform discretizations of the standard scheme are inaccurate and thus typically avoided. Hence, very fine uniform discretizations are applied in the whole domain even in cases where a fine resolution is per se required only in a small part of it (e.g., close to discontinuities and interfaces). In the present study, a new framework is devised to enhance the computational performance of PD models substantially. It applies the standard scheme only to localized regions where discontinuities and interfaces emerge, and a less demanding quadrature scheme to the rest of the domain. Moreover, it uses a multi-grid approach with a fine grid spacing only in critical regions. Because these regions are identified dynamically over time, our framework is referred to as multi-adaptive. The performance of the proposed approach is examined by means of two real-world problems, the Kalthoff–Winkler experiment and the bio-degradation of a magnesium-based bone implant screw. It is demonstrated that our novel framework can vastly reduce the computational cost (for given accuracy requirements) compared to a simple application of the standard scheme.

In the published studies, peridynamics has been used to simulate crack growth in brittle and quasi-brittle materials, simulation of plastic behaviour and solution of differential equations. With such achievements, the extent of problems which can be solved using peridynamics is growing. Peridynamics was intended to analyze the impact and the wave propagation problems since its introduction. Due to existence of the characteristic length in peridynamics relations, it has been used to solve problems in various scales. Some researchers have also used peridynamics multiphysics models to analyze heat transfer, diffusion and fluid behavior problems. Analyzing the damage growth in composite materials and investigation of geomechanical problems are among other achievements of using peridynamics. In addition to all these cases, application of peridynamics to biological problems has also received attention in recent years. This paper reviews the studies on the applications of peridynamics in the solution of different problems.

This study is a first attempt to provide an effective tool for crack prediction in beam-type structures using the peridynamics (PD) theory and metaheuristic-based optimization. The norm of the difference between the response of the tested beam and that of the trial model (analyzed using PD), is minimized to find the position and depth of crack. Model calibration is discussed thoroughly. Five well-known metaheuristics as well as an upgraded charged system search algorithm are considered. Results reveal that the proposed procedure can effectively localize and detect the crack severity, even in noise contaminated cases.