Multiscale analysis-based peridynamic simulation of fracture in porous media

Abstract

The simulation of fracture in large-scale structures made of porous media remains a challenging task. Current techniques either assume a homogeneous model, disregarding the microstructure characteristics, or adopt a micro-mechanical model, which incurs an intractable computational cost due to its complex stochastic geometry and physical properties, as well as its nonlinear and multiscale features. In this study, we propose a multiscale analysis-based dual-variable-horizon peridynamics (PD) model to efficiently simulate macroscopic structural fracture. The influence of microstructures in porous media on macroscopic structural failure is represented by two PD parameters: the equivalent critical stretch and micro-modulus. The equivalent critical stretch is calculated using the microscale PD model, while the equivalent micro-modulus is obtained through the homogenization method and energy density equivalence between classical continuum mechanics and PD models. Numerical examples of porous media with various microstructures demonstrate the validity, accuracy, and efficiency of the proposed method.

Graphical abstract

Keywords

porous media / multiscale / variable-horizon peridynamic / equivalent critical stretch / equivalent micro-modulus

References

[1] AdlerP. Porous Media: Geometry and Transports. Stoneham, MA: Elsevier, 2013

[2] EhlersWBluhmJ. Porous Media: Theory, Experiments and Numerical Applications. Berlin: Springer Science & Business Media, 2002

[3] LiuP SChenG F. Porous Materials: Processing and Applications. Waltham, MA: Elsevier, 2014

[4] Kang Y J, Bolton J S. Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements. Journal of the Acoustical Society of America, 1995, 98(1): 635–643

[5] Han N, Guo R. Two new Voronoi cell finite element models for fracture simulation in porous material under inner pressure. Engineering Fracture Mechanics, 2019, 211: 478–494

[6] Zhang R, Guo R. Voronoi cell finite element model to simulate crack propagation in porous materials. Theoretical and Applied Fracture Mechanics, 2021, 115: 103045

[7] Nilsen H M, Larsen I, Raynaud X. Combining the modified discrete element method with the virtual element method for fracturing of porous media. Computational Geosciences, 2017, 21(5–6): 1059–1073

[8] De BorstR. Computational Methods for Fracture in Porous Media: Isogeometric and Extended Finite Element Methods. Cambridge, MA: Elsevier, 2017

[9] Mohtarami E, Baghbanan A, Hashemolhosseini H, Bordas S P. Fracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method. Theoretical and Applied Fracture Mechanics, 2019, 104: 102359

[10] Rezanezhad M, Lajevardi S A, Karimpouli S. An investigation on prevalent strategies for XFEM-based numerical modeling of crack growth in porous media. Frontiers of Structural and Civil Engineering, 2021, 15(4): 914–936

[11] He B. Hydromechanical model for hydraulic fractures using XFEM. Frontiers of Structural and Civil Engineering, 2019, 13(1): 240–249

[12] He B, Vo T, Newell P. Investigation of fracture in porous materials: A phase-field fracture study informed by ReaxFF. Engineering with Computers, 2022, 38(6): 5617–5633

[13] Lee S, Wheeler M F, Wick T. Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model. Computer Methods in Applied Mechanics and Engineering, 2016, 305: 111–132

[14] He B, Schuler L, Newell P. A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media. Computational Materials Science, 2020, 176: 109519

[15] Heider Y, Reiche S, Siebert P, Markert B. Modeling of hydraulic fracturing using a porous-media phase-field approach with reference to experimental data. Engineering Fracture Mechanics, 2018, 202: 116–134

[16] Zeng Q, Liu W, Yao J, Liu J. A phase field based discrete fracture model (PFDFM) for fluid flow in fractured porous media. Journal of Petroleum Science Engineering, 2020, 191: 107191

[17] Zhou S, Zhuang X, Rabczuk T. Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 169–198

[18] Heider Y, Markert B. A phase-field modeling approach of hydraulic fracture in saturated porous media. Mechanics Research Communications, 2017, 80: 38–46

[19] Cajuhi T, Sanavia L, de Lorenzis L. Phase-field modeling of fracture in variably saturated porous media. Computational Mechanics, 2018, 61(3): 299–318

[20] Zhou S, Zhuang X, Rabczuk T. Phase field method for quasi-static hydro-fracture in porous media under stress boundary condition considering the effect of initial stress field. Theoretical and Applied Fracture Mechanics, 2020, 107: 102523

[21] Dastjerdy F, Barani O, Kalantary F. Modeling of hydraulic fracture problem in partially saturated porous media using cohesive zone model. International Journal of Civil Engineering, 2015, 10: 86

[22] Komijani M, Gracie R, Yuan Y. Simulation of fracture propagation induced acoustic emission in porous media. Engineering Fracture Mechanics, 2020, 229: 106950

[23] Silling S A. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 175–209

[24] Sun W, Fish J. Coupling of non-ordinary state-based peridynamics and finite element method for fracture propagation in saturated porous media. International Journal for Numerical and Analytical Methods in Geomechanics, 2021, 45(9): 1260–1281

[25] Sun Y, Chen B, Edwards M G, Li C. Investigation of hydraulic fracture branching in porous media with a hybrid finite element and peridynamic approach. Theoretical and Applied Fracture Mechanics, 2021, 116: 103133

[26] Shen S, Yang Z, Han F, Cui J, Zhang J. Peridynamic modeling with energy-based surface correction for fracture simulation of random porous materials. Theoretical and Applied Fracture Mechanics, 2021, 114: 102987

[27] Ni T, Pesavento F, Zaccariotto M, Galvanetto U, Zhu Q Z, Schrefler B A. Hybrid FEM and peridynamic simulation of hydraulic fracture propagation in saturated porous media. Computer Methods in Applied Mechanics and Engineering, 2020, 366: 113101

[28] Ni T, Pesavento F, Zaccariotto M, Galvanetto U, Schrefler B A. Numerical simulation of forerunning fracture in saturated porous solids with hybrid FEM/Peridynamic model. Computers and Geotechnics, 2021, 133: 104024

[29] Mehrmashhadi J, Chen Z, Zhao J, Bobaru F. A stochastically homogenized peridynamic model for intraply fracture in fiber-reinforced composites. Composites Science and Technology, 2019, 182: 107770

[30] Wu L, Huang D, Wang H, Ma Q, Cai X, Guo J. A comparison study on numerical analysis for concrete dynamic failure using intermediately homogenized peridynamic model and meso-scale peridynamic model. International Journal of Impact Engineering, 2023, 179: 104657

[31] Wu P, Zhao J, Chen Z, Bobaru F. Validation of a stochastically homogenized peridynamic model for quasi-static fracture in concrete. Engineering Fracture Mechanics, 2020, 237: 107293

[32] Wu P, Yang F, Chen Z, Bobaru F. Stochastically homogenized peridynamic model for dynamic fracture analysis of concrete. Engineering Fracture Mechanics, 2021, 253: 107863

[33] Wu P, Chen Z. Peridynamic electromechanical modeling of damaging and cracking in conductive composites: A stochastically homogenized approach. Composite Structures, 2023, 305: 116528

[34] Chen Z, Niazi S, Bobaru F. A peridynamic model for brittle damage and fracture in porous materials. International Journal of Rock Mechanics and Mining Sciences, 2019, 122: 104059

[35] Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

[36] Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782

[37] Rabczuk T, Ren H, Zhuang X. A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem. Computers, Materials & Continua, 2019, 59(1): 31–55

[38] Ren H, Zhuang X, Rabczuk T. A nonlocal operator method for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering, 2020, 358: 112621

[39] Bie Y, Liu Z, Yang H, Cui X Y. Abaqus implementation of dual peridynamics for brittle fracture. Computer Methods in Applied Mechanics and Engineering, 2020, 372: 113398

[40] Zhang Y, Yang X, Wang X, Zhuang X. A micropolar peridynamic model with non-uniform horizon for static damage of solids considering different nonlocal enhancements. Theoretical and Applied Fracture Mechanics, 2021, 113: 102930

[41] Yang Z, Guan X, Cui J, Dong H, Wu Y, Zhang J. Stochastic multiscale heat transfer analysis of heterogeneous materials with multiple random configurations. Communications in Computational Physics, 2020, 27(2): 431–459

[42] ShenS KYangZ HCuiJ ZZhangJ Q. Dual-variable-horizon peridynamics and continuum mechanics coupling modeling and adaptive fracture simulation in porous materials. Engineering with Computers, 2022, 1–21

[43] Le Q V, Bobaru F. Surface corrections for peridynamic models in elasticity and fracture. Computational Mechanics, 2018, 61(4): 499–518

[44] Yang Z, Zhang Y, Dong H, Cui J, Guan X, Yang Z. High-order three-scale method for mechanical behavior analysis of composite structures with multiple periodic configurations. Composites Science and Technology, 2017, 152: 198–210

[45] Yang Z, Zheng S, Han F, Shen S, Guan X. An improved peridynamic model with energy-based micromodulus correction method for fracture in particle reinforced composites. Communications in Computational Physics, 2022, 32(2): 424–449

[46] Li Z, Han F. The peridynamics-based finite element method (PeriFEM) with adaptive continuous/discrete element implementation for fracture simulation. Engineering Analysis with Boundary Elements, 2023, 146: 56–65

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Higher Education Press