A Peridynamic-enhanced finite element method for Thermo–Hydro–Mechanical coupled problems in saturated porous media involving cracks

Ni, Tao; Fan, Xuanmei; Zhang, Jin; Zaccariotto, Mirco; Galvanetto, Ugo; Schrefler, Bernhard A.

doi:10.1016/j.cma.2023.116376

Cited by 22 publications

References 78 publications

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Matrix‐based implementation and GPU acceleration of hybrid FEM and peridynamic model for hydro‐mechanical coupled problems

Ni,

Zhang,

Zaccariotto

et al. 2024

Numerical Meth Engineering

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The hybrid finite element‐peridynamic (FEM‐PD) models have been evidenced for their exceptional ability to address hydro‐mechanical coupled problems involving cracks. Nevertheless, the non‐local characteristics of the PD equations and the required inversion operations when solving fluid equations result in prohibitively high computational costs. In this paper, a fast explicit solution scheme for FEM‐PD models based on matrix operation is introduced, where the graphics processing units (GPUs) are used to accelerate the computation. An in‐house software is developed in MATLAB in both CPU and GPU versions. We first solve a problem related to pore pressure distribution in a single crack, demonstrating the accuracy of the proposed method by a comparison of FEM‐PD solutions with those of PD‐only models and analytical solutions. Subsequently, several examples are solved, including a one‐dimensional dynamic consolidation problem and the fluid‐driven hydraulic fracture propagation problems in both 2D and 3D cases, to comprehensively validate the effectiveness of the proposed methods in simulating deformation and fracture in saturated porous media under the influence of hydro‐mechanical coupling. In the presented numerical results, some typical strong dynamic phenomena, such as stepwise crack advancement, crack branching, and pressure oscillations, are observed. In addition, we compare the wall times of all the cases executed on both the GPU and CPU, highlighting the substantial acceleration performance of the GPU, particularly when tackling problems with a significant computational workload.

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Matrix‐based implementation and GPU acceleration of hybrid FEM and peridynamic model for hydro‐mechanical coupled problems

Ni,

Zhang,

Zaccariotto

et al. 2024

Numerical Meth Engineering

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Performance Study of Variational Quantum Linear Solver for Linear Elastic Problems

Rao,

2024

Mechanisms and Machine Science

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Nonlocal Nernst-Planck-Poisson System for Modeling Electrochemical Corrosion in Biodegradable Magnesium Implants

Hermann,

Shojaei,

Höche

et al. 2024

J Peridyn Nonlocal Model

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This paper provides a comprehensive derivation and application of the nonlocal Nernst-Planck-Poisson (NNPP) system for accurate modeling of electrochemical corrosion with a focus on the biodegradation of magnesium-based implant materials under physiological conditions. The NNPP system extends and generalizes the peridynamic bi-material corrosion model by considering the transport of multiple ionic species due to electromigration. As in the peridynamic corrosion model, the NNPP system naturally accounts for moving boundaries due to the electrochemical dissolution of solid metallic materials in a liquid electrolyte as part of the dissolution process. In addition, we use the concept of a diffusive corrosion layer, which serves as an interface for constitutive corrosion modeling and provides an accurate representation of the kinetics with respect to the corrosion system under consideration. Through the NNPP model, we propose a corrosion modeling approach that incorporates diffusion, electromigration and reaction conditions in a single nonlocal framework. The validity of the NNPP-based corrosion model is illustrated by numerical simulations, including a one-dimensional example of pencil electrode corrosion and a three-dimensional simulation of a Mg-10Gd alloy bone implant screw decomposing in simulated body fluid. The numerical simulations correctly reproduce the corrosion patterns in agreement with macroscopic experimental corrosion data. Using numerical models of corrosion based on the NNPP system, a nonlocal approach to corrosion analysis is proposed, which reduces the gap between experimental observations and computational predictions, particularly in the development of biodegradable implant materials.

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A Peridynamic-enhanced finite element method for Thermo–Hydro–Mechanical coupled problems in saturated porous media involving cracks

Cited by 22 publications

References 78 publications

Matrix‐based implementation and GPU acceleration of hybrid FEM and peridynamic model for hydro‐mechanical coupled problems

Matrix‐based implementation and GPU acceleration of hybrid FEM and peridynamic model for hydro‐mechanical coupled problems

Performance Study of Variational Quantum Linear Solver for Linear Elastic Problems

Nonlocal Nernst-Planck-Poisson System for Modeling Electrochemical Corrosion in Biodegradable Magnesium Implants

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