Fully coupled poroelastic peridynamic formulation for fluid-filled fractures

Modelling of stress-corrosion cracking by using peridynamics

Predicting fracture evolution during lithiation process using peridynamics

Finite element method (FEM) is commonly used with topology optimization algorithms to determine optimum topology of load-bearing structures. However, it may possess various difficulties and limitations for handling the problems with moving boundaries, large deformations, and cracks/damages. To remove limitations of the mesh-based topology optimization, this study presents a robust and accurate approach based on the innovative coupling of peridynamics (PD) (a meshless method) and topology optimization (TO), abbreviated as PD–TO. The minimization of compliance, i.e. strain energy, is chosen as the objective function subjected to the volume constraint. The design variable is the relative density defined at each particle employing bidirectional evolutionary optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. To present the capability, efficiency, and accuracy of the PD–TO approach, various challenging optimization problems with and without defects (cracks) are solved under different boundary conditions. The results are extensively compared and validated with those obtained by element-free Galerkin method and FEM. The main advantage of the PD–TO methodology is its ability to handle TO problems of cracked structures without requiring complex treatments for mesh connectivity. Hence, it can be an alternative and powerful tool in finding optimal topologies that can circumvent crack propagation and growth in two- and three-dimensional structures.

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Topology optimization of cracked structures using peridynamics

Finite element implementation of a peridynamic pitting corrosion damage model

A new peridynamic formulation is developed for cubic polycrystalline materials. The new approach can be a good alternative to traditional techniques such as finite element method and boundary element method. The formulation is validated by considering a polycrystal subjected to tension loading condition and comparing the displacement field obtained from both peridynamics and finite element method. Both static and dynamic loading conditions for initially damaged and undamaged structures are considered and the results of plane stress and plane strain configurations are compared. Finally, the effect of grain boundary strength, grain size, fracture toughness and grain orientation on time-to-failure, crack speed, fracture behaviour and fracture morphology are investig ated and the expected transgranular and intergranular failure modes are successfully captured. To the best of the authors’ knowledge, this is the first time that a peridynamic material model for cubic crystals is given in detail.

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Peridynamic Modeling of Granular Fracture in Polycrystalline Materials

An ordinary state-based peridynamic formulation is developed to analyse cubic polycrystalline materials for the first time in the literature. This new approach has the advantage that no constraint condition is imposed on material constants as opposed to bond-based peridynamic theory. The formulation is validated by first considering static analyses and comparing the displacement fields obtained from the finite element method and ordinary state-based peridynamics. Then, dynamic analysis is performed to investigate the effect of grain boundary strength, crystal size, and discretization size on fracture behaviour and fracture morphology.

Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics.

Fatigue analysis of polycrystalline materials using Peridynamic Theory with a novel crack tip detection algorithm

Peridynamic theory is a new continuum mechanics formulation that has several advantages over the traditional approaches, such as Classical Continuum Mechanics (CCM) and Molecular Dynamics (MD) Due to its length-scale parameter, horizon, it is capable of capturing phenomena occurring at different length scales, including the nano-scale Furthermore, van der Waals forces can be represented in a straightforward manner using a buffer-layer approach In this chapter, various demonstration problems are presented to show the capability of peridynamics at the nano-scale, including nano-indentation and failure analysis of graphene sheets

Ning Zhu

Papers

Modelling of stress-corrosion cracking by using peridynamics

Peridynamic Modeling of Granular Fracture in Polycrystalline Materials

Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics.

Fatigue analysis of polycrystalline materials using Peridynamic Theory with a novel crack tip detection algorithm

Utilization of peridynamic theory for modeling at the nano-scale