Crack nucleation in brittle and quasi-brittle materials: A peridynamic analysis

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized.

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“…[162,[468][469][470][471]. As expected it is a very active area of interest both for PF [175,176,388,472] and PD [473][474][475]. 8.…”

Section: Common Challenges To Pd and Pfmentioning

confidence: 58%

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

et al. 2022

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“…At coarser discretizations and as a result of larger horizons, the likelihood increases that an irregular crack appears on the right-hand side of the hole. The irregular crack is caused by local stress peaks (a kind of numerical notch effect), which promotes an early failure [42]. This effect can be reduced by increasing the spatial resolution and / or using a conforming grid, meaning that all material points are positioned at the hole's circumference.…”

Section: Resultsmentioning

confidence: 99%

Peridynamic Simulation of a Mixed-Mode Fracture Experiment in PMMA Utilizing an Adaptive-Time Stepping for an Explicit Solver

Willberg

Hesse

Heinecke

2022

J Peridyn Nonlocal Model

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In this paper, a benchmark analysis of a peridynamic correspondence energy-based damage model is presented. The benchmark is an experimental setup of a Polymethyl methacrylate (PMMA) plate with a hole. The plate has a minotch and is subject to a compressive load. With increasing loads, a crack initiates at the tip of the notch and continuously grows. The benchmark is modeled utilizing the peridynamic correspondence formulation as a two-dimensional problem. To reduce numerical issues due to bond failure, an adaptive time-stepping method for a Verlet time integration schema is proposed. The method limits the maximum number of broken bonds per material point by adapting the time-step size. This allows the correspondence formulation to be significantly more stable. The benchmark involves a sensitivity analysis based on the Morris method, which is performed in this context. As a result, uncertainties and the impact of geometrical, numerical and material parameters are evaluated and discussed.

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“…This makes PD attractive in analysis of discontinuities such as cracks. Many numerical studies of complex fracture processes illustrate the ability of PD to capture crack initiation [2–4], crack branching [5], crack kinking [6] and crack interaction with initial heterogeneities, such as holes and pores [7, 8].…”

Section: Introductionmentioning

confidence: 99%

Some analytical solutions to peridynamic beam equations

et al. 2022

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Peridynamics (PD) has been introduced to account for long range internal force/moment interactions and to extend the classical continuum mechanics (CCM). PD equations of motion are derived in the form of integro-differential equations and only few analytical solutions to these equations are presented in the literature. The aim of this paper is to present analytical solutions to PD beam equations for both static and dynamic loading conditions. Applying trigonometric series, general solutions for the deflection function are derived. For several examples in the static case including simply supported beam and cantilever beam, the coefficients in the series are presented in a closed analytical form. For the dynamic case, the solution is derived for a simply supported beam applying the variable separation with respect to the time and the axial coordinate. Several numerical cases are presented to illustrate the derived solutions. Furthermore, PD results are compared against results obtained from the classical beam theory (CBT). A very good agreement between these two different approaches is observed for the case of the small horizon sizes (HSs), which shows the capability of the current approach. INTRODUCTIONPeridynamics (PD) is a non-local theory, which operates with long-range force/moment interactions [1]. Unlike the classical continuum mechanics (CCM), the deformation gradient, its higher gradients or gradients of internal state variables are not introduced. PD equations of motion are integro-differential equations, in contrast to CCM where partial differential equations are introduced. This makes PD attractive in analysis of discontinuities such as cracks. Many numerical studies of complex fracture processes illustrate the ability of PD to capture crack initiation [2-4], crack branching [5], crack kinking [6] and crack interaction with initial heterogeneities, such as holes and pores [7,8]. PD theories for components including rods and beams [9-13], plates [14][15][16][17][18][19] and shells [20][21][22] are developed. Within the CCM, these theories provide an efficient and robust approach for the analysis of structures. Indeed many analytical solutions for beams, plates and shells are available providing a direct insight into the deformation and stress states. On the other hand, they are useful to validate the numerical methods and computer codes, such as the finite element method. However, unlike the CCM, only few analytical solutions to PD equations are available.

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Crack nucleation in brittle and quasi-brittle materials: A peridynamic analysis

Cited by 56 publications

References 71 publications

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Peridynamic Simulation of a Mixed-Mode Fracture Experiment in PMMA Utilizing an Adaptive-Time Stepping for an Explicit Solver

Some analytical solutions to peridynamic beam equations

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