Three-dimensional peridynamic modelling of quasi-brittle structural elements

The peridynamic theory provides a promising theoretical framework for developing robust numerical models capable of simulating the complex fracture processes in quasi-brittle materials. However, there is a lack of detailed validation studies in the literature, and significant work remains to quantify the predictive accuracy and generality of a peridynamic model. This thesis presents the development and validation of a three-dimensional bond-based peridynamic framework for modelling quasi-brittle structural elements. By following a rigorous validation process and carefully selecting validation problems that test a wide range of fundamental behaviours, a robust examination of the model is provided, and new insights into the capabilities of the bond-based model are gained. This thesis begins with an examination of existing constitutive laws and a new non-linear softening model is introduced. Predictions with the newly proposed non-linear model improve upon existing laws. In an attempt to explain the cause of discrepancies between experimental and numerical results, it was determined that the application of surface correction factors increases the energy required to produce a fracture surface. This is the first time that this effect has been described, and a correction scheme is proposed that is simple to implement and yields improved results. It is demonstrated that a bond-based peridynamic model can accurately capture the size effect in quasi-brittle materials. This is the first time that a peridynamic model has been used to examine the size effect and provides an important check on the validity of the numerical model. The thesis ends with an examination of the predictive accuracy and generality of the model against nine reinforced concrete beams that exhibit a wide range of failure modes. The shear-span-to-depth ratio is systematically varied from 1 to 8 to facilitate a study of different load-transfer mechanisms and failure modes. This is the first study to rigorously validate the predictive capability of a peridynamic model against a series of problems. The model is validated using published experimental data, and the predictive accuracy is equivalent to well-established numerical methods whilst offering several benefits that justify further research and development.UK Engineering and Physical Sciences Research Council (EPSRC), grant no. EP/L016095/1 - University of Cambridge Centre for Doctoral Training in Future Infrastructure and Built Environmen

Investigation of pulse fracturing via peridynamics modeling and simulation

Pulse fracturing is an alternative stimulation technology to enhance production from oil and gas wells, especially ones in fractured hydrocarbon reservoirs. This stimulation generates multiple radial fractures that initiate at the wellbore wall, via the application of pressure pulses at rates on the order of 10 MPa ms⁻¹ or more. These radial fractures act as conductive pathways for hydrocarbon flow into the bottom of the wellbore. Pulse fracturing has been tested via experiments and oil field implementations quite extensively in the 1970s and 1980s. The fracture mechanics of pulse stimulation, however, is not well understood. Computational efforts at modeling pulse fractures are relatively sparse in literature. Due to a recent renewal of interest in this form of stimulation, this computational study aims to develop a tool to simulate pulse fracturing. At the high loading rates experienced by rock during pulse stimulation, dynamic fracturing is expected to occur leading to the generation of a complex radial fracture network. A state-of-the-art continuum mechanics code called Peridigm is well equipped to handle dynamic fracture modeling. Peridigm's capabilities are explored to ascertain whether it can capture pulse fracture behavior accurately. Using concrete as the computational medium, the relevant modeling considerations are analyzed to determine the best approaches for modeling pulse fracturing in Peridigm. This tailored approach is then used for benchmarking Peridigm against published pulse fracturing experiments on sandstone core samples.Petroleum and Geosystems Engineerin

Simulating the Fracture of Notched Mortar Beams through Extended Finite Element Method (XFEM) and Peridynamics

This paper simulates fracture in notched mortar beams under three-point bending using extended finite element method (XFEM) and peridynamics. A three-phase microstructure (i.e., cement paste, aggregates, and paste-aggregate interface) is used for constitutive modeling of the mortar to obtain the elastic properties for simulation. In the XFEM approach, the simulated homogenized elastic modulus is used along with the total fracture energy of the cement mortar in a damage model to predict the fracture response of the mortar including crack propagation and its fracture parameters (Mode I stress intensity factor, KIC and critical crack tip opening displacement, CTODC). The damage model incorporates a maximum principal stress-based damage initiation criteria and a traction-separation law for damage evolution. In the peridynamics approach, a bond-based model involving a prototype microelastic brittle (PMB) material model is used. The elastic properties and fracture energy release rates are used as inputs in the PMB model, along with the choice of peridynamic horizon size. Comparison with experimental fracture properties (KIC, CTODC) as well as crack propagation paths from digital image correlation show that both the approaches yield satisfactory results, particularly for KIC and crack extension. Thus, both these methods can be adopted for fracture simulation of cement-based materials

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

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

Peridynamics modelling of weibull distributions for nuclear fuel fracture

Peridynamics is a non-local continuum mechanics modelling method, with fundamental equations built upon integrals as opposed to partial differentials, which gives benefits when modelling brittle fracture relative to other continuum mechanics modelling techniques. Notably absent from peridynamics literature is an investigation of the effect of fracture strength distributions (an important element of brittle fracture) in peridynamics. This thesis outlines a method for appropriately including fracture strength distributions in peridynamics, and presents a model of a UO2 fuel pellet fracturing in service using this method. It was shown that using a Weibull distribution in peridynamics without adjusting the distribution of strengths to account for the difference in size between bonds and the part to be modelled produces inaccurate results. Using Weibull scaling to account for this did not alone solve this problem, as there was still a disconnect between the stress at which the first bond fails (stage 1 failure) and the stress at which the overall part modelled fails (stage 2 failure). Bond strengths were localised by linking bond strength to the material points they are connected to. Combining this localisation with using the most extreme strengths, the shape of the Weibull curve was accurately recreated in 1D peridynamics. The method was applied in two dimensions, and it was shown that the method which had worked in one dimension is no longer adequate. It was found that edge length is the most appropriate size-scaling criteria, as opposed to total area of the two-dimensional model. The model was able to recreate Weibull distributions of fracture strain in a two dimensional tensile test using a Weibull modulus of 10, but was less accurate with lower Weibull moduli. The effect of Weibull distributions on radial crack numbers in in-service UO2 nuclear fuel pellets was investigated. It was found that using a Weibull distribution of fracture strains in a peridynamics model of fuel pellets allows the model to more accurately predict the number of cracks expected at a given power. The model was compared to low-burnup post irradiation examination data.Open Acces

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

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. © 2022, The Author(s)

Peridynamic modeling of mode-I delamination growth in double cantilever composite beam test: a two-dimensional modeling using revised energy-based failure criteria

This study presents a two-dimensional ordinary state-based peridynamic (OSB PD) modeling of mode-I delamination growth in a double cantilever composite beam (DCB) test using revised energy-based failure criteria. The two-dimensional OSB PD composite model for DCB modeling is obtained by reformulating the previous OSB PD lamina model in x–z direction. The revised energy-based failure criteria are derived following the approach of establishing the relationship between critical bond breakage work and energy release rate. Loading increment convergence analysis and grid spacing influence study are conducted to investigate the reliability of the present modeling. The peridynamic (PD) modeling load–displacement curve and delamination growth process are then quantitatively compared with experimental results obtained from standard tests of composite DCB samples, which show good agreement between the modeling results and experimental results. The PD modeling delamination growth process damage contours are also illustrated. Finally, the influence of the revised energy-based failure criteria is investigated. The results show that the revised energy-based failure criteria improve the accuracy of the PD delamination modeling of DCB test significantly

Nonlocal numerical simulation of low Reynolds number laminar fluid motion by using peridynamic differential operator

A considerable fluid load can cause local damages on the offshore structures, which may be a risk in the field of ocean engineering. Therefore, an accurate fluid motion prediction is a crucial issue in predicting the offshore structure motion. In this study, a non-local Lagrangian model is developed for Newtonian fluid low Reynold's number laminar flow. Based on the peridynamic theory, a peridynamic differential operator is recently proposed for directly converting the partial differential into its integral form. Therefore, the peridynamic differential operator is applied to convert the classical Navier-Stokes equations into their integral forms. The numerical algorithms are developed both in total and updated Lagrangian description. Finally, several benchmark fluid flow problems such as Couette flow, Poiseuille flow, Taylor Green vortex, shear-driven cavity problem and dam collapse problems are numerically solved. The simulation results are compared with the ones available in the published literature. The good agreements validate of the capability of the proposed non-local model for Newtonian fluid low Reynold's number laminar flow simulation