A mathematical model for elasticity using calculus on discrete manifolds

Dassios, Ioannis; O’Keeffe, G.J.; Jivkov, Andrey P.

doi:10.1002/mma.4892

Cited by 11 publications

(3 citation statements)

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“…In recent years, there has been a significant development in using matrix theory to study networks related to engineering problems [35][36][37][38] and the solutions of non-linear algebraic systems [39][40][41][42][43][44][45]. The idea is to provide new techniques and methods ready for software implementation in order to solve non-linear equations, similar to those for modelling gas pipelines.…”

Section: Literature Reviewmentioning

confidence: 99%

A Novel Approach to Model a Gas Network

et al. 2019

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The continuous uninterrupted supply of Natural Gas (NG) is crucial to today’s economy, with issues in key infrastructure, e.g., Baumgarten hub in Austria in 2017, highlighting the importance of the NG infrastructure for the supply of primary energy. The balancing of gas supply from a wide range of sources with various end users can be challenging due to the unique and different behaviours of the end users, which in some cases span across a continent. Further complicating the management of the NG network is its role in supporting the electrical network. The fast response times of NG power plants and the potential to store energy in the network play a key role in adding flexibility across other energy systems. Traditionally, modelling the NG network relies on nonlinear pipe flow equations that incorporate the demand (load), flow rate, and physical network parameters including topography and NG properties. It is crucial that the simulations produce accurate results quickly. This paper seeks to provide a novel method to solve gas flow equations through a network under steady-state conditions. Firstly, the model is reformulated into non-linear matrix equations, then the equations separated into their linear and nonlinear components, and thirdly, the non-linear system is solved approximately by providing a linear system with similar solutions to the non-linear one. The non-linear equations of the NG transport system include the main variables and characteristics of a gas network, focusing on pressure drop in the gas network. Two simplified models, both of the Irish gas network (1. A gas network with 13 nodes, 2. A gas network with 109 nodes) are used as a case study for comparison of the solutions. Results are generated by using the novel method, and they are compared to the outputs of two numerical methods, the Newton–Raphson solution using MATLAB and SAINT, a commercial software that is used for the simulation of the gas network and electrical grids.

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Section: Literature Reviewmentioning

confidence: 99%

A Novel Approach to Model a Gas Network

et al. 2019

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“…For example, calibration with experimental data for one specific stress state may not correctly predict the behaviour for other stress states. Some of the difficulties of FEM-based methods can be avoided by discrete methods, such as lattice methods (Zhang and Jivkov, 2016;Morrison et al, 2016;Dassios et al, 2018), lattice spring methods (Zhu et al, 2020) and discrete element methods (Amarasiri and Kodikara, 2013;Sima et al, 2014;Tran et al, 2020). Alternative approaches, including phase-field methods (Cajuhi et al, 2018) and smoothed-particle hydrodynamics (Tran et al, 2019), have also been adopted for soil desiccation problems.…”

Section: Introductionmentioning

confidence: 99%

Modelling soil desiccation cracking by peridynamics

2023

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Understanding of desiccation-induced cracking in soil has improved over the last 20–30 years through experimental studies, but progress in predictive modelling of desiccation cracking has been limited. The heterogeneous structure of soils and the multi-physics nature of the phenomenon, involving emergence and propagation of discontinuities, make the mathematical description and analysis a challenging task. The authors present a non-local hydro-mechanical model for soil desiccation cracking capable of predicting crack initiation and growth. The model is based on peridynamics (PD) theory. Attempts to model soil desiccation cracking by PD are limited to a purely mechanical description of the process that involves calibration of the parameters. In contrast, the model presented in this paper describes soil desiccation cracking as a hydro-mechanical problem, where moisture flow and deformation are coupled. This allows for investigating and explaining the mechanisms controlling the initiation and propagation of discontinuities. The model is applied and tested against two sets of experimental data to explain the typical features of drying-induced cracking of clays. The validations use experimental parameters (Young's modulus, water retention characteristics) and avoid calibrations to test the accuracy of the model. The correlations between the shrinkage of soil clay, changes in displacement fields and crack growth are demonstrated. Crack initiation, propagation and ultimate crack patterns simulated by the model are found to be in very good agreement with experimental observations. The results show that the model can capture realistically key hydraulic, mechanical and geometry effects on clay desiccation cracking.

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“…In Dassios et al [4,5] use networks to model plastic and elastic deformation. In general lattice models for deformation and fracture of solid materials were developed firstly for quasi-brittle materials, such as concretes and rocks [3,6], and extended recently for elastic-plastic materials, such as structural steels [5]. The benefit of modeling materials, treated as continua in classical mechanics, with discrete lattices is that the nucleation, growth and coalescence of discontinuities (cracks) become natural processes.…”

Section: Introductionmentioning

confidence: 99%

Ideas From Bounded Confidence Theory Applied to Dynamical Networks of Interacting Free-Bodies

O’Keeffe¹,

Dassios

2019

Front. Phys.

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An approximation method is introduced for simulating the motion of interacting free-bodies. Concepts from bounded confidence theory (in network science) and asymptotic analysis (in physics) are combined to create the method. This method can reduce the computational load required to simulate the dynamics of free-bodies. A case study is presented and a range of parameter values are explored to analyze the method's performance.

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A mathematical model for elasticity using calculus on discrete manifolds

Cited by 11 publications

References 11 publications

A Novel Approach to Model a Gas Network

A Novel Approach to Model a Gas Network

Modelling soil desiccation cracking by peridynamics

Ideas From Bounded Confidence Theory Applied to Dynamical Networks of Interacting Free-Bodies

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