Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48(1), 175–209 (2000). https://doi.org/10.1016/S0022-5096(99)00029-0. ISSN 0022-5096
Article
MathSciNet
MATH
Google Scholar
Javili, A., Morasata, R., Oterkus, E., Oterkus, S.: Peridynamics review. Math. Mech. Solids 24(11), 3714–3739 (2019)
Article
MathSciNet
MATH
Google Scholar
Coclite, G.M., Dipierro, S., Fanizza, G., Maddalena, F., Romano, M., Valdinoci, E.: Qualitative aspects in nonlocal dynamics. J. Peridyn. Nonlocal Model. (2021). https://doi.org/10.1007/s42102-021-00064-z
Article
Google Scholar
Seleson, P., Parks, M.L., Gunzburger, M., Lehoucq, R.B.: Peridynamics as an upscaling of molecular dynamics. Multiscale Model. Simul. 8(1), 204–227 (2009)
Article
MathSciNet
MATH
Google Scholar
Butt, S.N., Timothy, J.J., Meschke, G.: Wave dispersion and propagation in state-based peridynamics. Comput. Mech. 60(5), 725–738 (2017)
Article
MathSciNet
MATH
Google Scholar
Bažant, Z.P., Luo, W., Chau, V.T., Bessa, M.A.: Wave dispersion and basic concepts of peridynamics compared to classical nonlocal damage models. J. Appl. Mech. 83(11), 111004 (2016)
Article
Google Scholar
Ha, Y.D., Bobaru, F.: Studies of dynamic crack propagation and crack branching with peridynamics. Int. J. Fract. 162(1), 229–244 (2010)
Article
MATH
Google Scholar
Agwai, A., Guven, I., Madenci, E.: Predicting crack propagation with peridynamics: a comparative study. Int. J. Fract. 171(1), 65–78 (2011)
Article
MATH
Google Scholar
Ni, T., Zaccariotto, M., Zhu, Q.-Z., Galvanetto, U.: Static solution of crack propagation problems in peridynamics. Comput. Methods Appl. Mech. Eng. 346, 126–151 (2019)
Article
MathSciNet
MATH
Google Scholar
Lipton, R.: Dynamic brittle fracture as a small horizon limit of peridynamics. J. Elast. 117(1), 21–50 (2014)
Article
MathSciNet
MATH
Google Scholar
Silling, S.A., Weckner, O., Askari, E., Bobaru, F.: Crack nucleation in a peridynamic solid. Int. J. Fract. 162(1), 219–227 (2010)
Article
MATH
Google Scholar
Behzadinasab, M., Vogler, T.J., Peterson, A.M., Rahman, R., Foster, J.T.: Peridynamics modeling of a shock wave perturbation decay experiment in granular materials with intra-granular fracture. J. Dyn. Behav. Mater. 4(4), 529–542 (2018)
Article
Google Scholar
Askari, E., Bobaru, F., Lehoucq, R.B., Parks, M.L., Silling, S.A., Weckner, O.: Peridynamics for multiscale materials modeling. J. Phys. Conf. Ser., 125, 012078 (2008)
Article
Google Scholar
Madenci, E., Oterkus, E.: Peridynamic theory. In: Peridynamic Theory and Its Applications, Springer, Berlin, pp. 19–43 (2014)
Chapter
MATH
Google Scholar
Macek, R.W., Silling, S.A.: Peridynamics via finite element analysis. Finite Elem. Anal. Des. 43(15), 1169–1178 (2007)
Article
MathSciNet
Google Scholar
Sarego, G., Le, Q.V., Bobaru, F., Zaccariotto, M., Galvanetto, U.: Linearized state-based peridynamics for 2-d problems. Int. J. Numer. Methods Eng. 108(10), 1174–1197 (2016)
Article
MathSciNet
Google Scholar
Zaccariotto, M., Luongo, F., Galvanetto, U., et al.: Examples of applications of the peridynamic theory to the solution of static equilibrium problems. Aeronaut. J. 119(1216), 677–700 (2015)
Article
Google Scholar
Silling, S.A., Epton, M., Weckner, O., Xu, J., Askari, E.: Peridynamic states and constitutive modeling. J. Elast. 88(2), 151–184 (2007)
Article
MathSciNet
MATH
Google Scholar
Silling, S.A., Parks, M.L., Kamm, J.R., Weckner, O., Rassaian, M.: Modeling shockwaves and impact phenomena with Eulerian peridynamics. Int. J. Impact Eng. 107, 47–57 (2017)
Article
Google Scholar
Behzadinasab, M., Foster, J.T.: A semi-Lagrangian constitutive correspondence framework for peridynamics. J. Mech. Phys. Solids 137, 103862 (2020)
Article
MathSciNet
MATH
Google Scholar
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. Comput. Methods Appl. Mech. Eng. 366, 113101 (2020)
Article
MathSciNet
MATH
Google Scholar
Zhou, X.-P., Wang, Y.-T., Shou, Y.-D.: Hydromechanical bond-based peridynamic model for pressurized and fluid-driven fracturing processes in fissured porous rocks. Int. J. Rock Mech. Min. Sci. 132, 104383 (2020)
Article
Google Scholar
Song, X., Khalili, N.: A peridynamics model for strain localization analysis of geomaterials. Int. J. Numer. Anal. Methods Geomech. 43(1), 77–96 (2019)
Article
Google Scholar
Panchadhara, R., Gordon, P.A., Parks, M.L.: Modeling propellant-based stimulation of a borehole with peridynamics. Int. J. Rock Mech. Min. Sci. 93, 330–343 (2017)
Article
Google Scholar
Zhou, X.-P., Wang, Y.-T.: State-of-the-art review on the progressive failure characteristics of geomaterials in peridynamic theory. J. Eng. Mech. 147(1), 03120001 (2021)
Google Scholar
Lejeune, E., Linder, C.: Modeling tumor growth with peridynamics. Biomech. Model. Mechanobiol. 16(4), 1141–1157 (2017)
Article
Google Scholar
Taylor, M., Gözen, I., Patel, S., Jesorka, A., Bertoldi, K.: Peridynamic modeling of ruptures in biomembranes. PLoS ONE 11(11), e0165947 (2016)
Article
Google Scholar
Bobaru, F., Duangpanya, M.: The peridynamic formulation for transient heat conduction. Int. J. Heat Mass Transf. 53(19–20), 4047–4059 (2010)
Article
MATH
Google Scholar
Bobaru, F., Duangpanya, M.: A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities. J. Comput. Phys. 231(7), 2764–2785 (2012)
Article
MathSciNet
MATH
Google Scholar
Oterkus, S., Madenci, E., Agwai, A.: Peridynamic thermal diffusion. J. Comput. Phys. 265, 71–96 (2014)
Article
MathSciNet
MATH
Google Scholar
Foster, J.T.: Nonlocal and fractional order methods for near-wall turbulence, large-eddy simulation, and fluid-structure interaction. Technical report, University of Texas at Austin Austin United States (2019)
Zhao, J., Chen, Z., Mehrmashhadi, J., Bobaru, F.: Construction of a peridynamic model for transient advection-diffusion problems. Int. J. Heat Mass Transf. 126, 1253–1266 (2018)
Article
Google Scholar
Buryachenko, V.A.: Generalized effective fields method in peridynamic micromechanics of random structure composites. Int. J. Solids Struct. 202, 765–786 (2020)
Article
Google Scholar
Hu, Y.L., Madenci, E.: Peridynamics for fatigue life and residual strength prediction of composite laminates. Compos. Struct. 160, 169–184 (2017)
Article
Google Scholar
Oterkus, E., Madenci, E.: Peridynamic analysis of fiber-reinforced composite materials. J. Mech. Mater. Struct. 7(1), 45–84 (2012)
Article
Google Scholar
Zhao, J., Jafarzadeh, S., Rahmani, M., Chen, Z., Kim, Y.-R., Bobaru, F.: A peridynamic model for galvanic corrosion and fracture. Electrochim. Acta 391, 138968 (2021)
Article
Google Scholar
Wildman, R., Gazonas, G.: A dynamic electro-thermo-mechanical model of dielectric breakdown in solids using peridynamics. J. Mech. Mater. Struct. 10(5), 613–630 (2015)
Article
MathSciNet
Google Scholar
Randles, P.W., Libersky, L.D.: Smoothed particle hydrodynamics: some recent improvements and applications. Comput. Methods Appl. Mech. Eng. 139(1–4), 375–408 (1996)
Article
MathSciNet
MATH
Google Scholar
Ren, X.-H., Yu, S.-Y., Wang, H.-J., Zhang, J.-X., Sun, Z.-H.: An improved form of SPH method and its numerical simulation study on the rock crack propagation containing fissures and holes. Arab. J. Sci. Eng. 46(11), 11303–11317 (2021)
Article
Google Scholar
Moës, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46(1), 131–150 (1999)
Article
MathSciNet
MATH
Google Scholar
Rocha, A.V.M., Akhavan-Safar, A., Carbas, R., Marques, E.A.S., Goyal, R., El-zein, M., Da Silva, L.F.M.: Numerical analysis of mixed-mode fatigue crack growth of adhesive joints using CZM. Theor. Appl. Fract. Mech. 106, 102493 (2020)
Article
Google Scholar
Shojaei, A., Hermann, A., Cyron, C.J., Seleson, P., Silling, S.A.: A hybrid meshfree discretization to improve the numerical performance of peridynamic models. Comput. Methods Appl. Mech. Eng. 391, 114544 (2022)
Article
MathSciNet
MATH
Google Scholar
Lopez, L., Pellegrino, S.F.: A space-time discretization of a nonlinear peridynamic model on a 2D lamina. Comput. Math. Appl. 116, 161–175 (2022)
Article
MathSciNet
MATH
Google Scholar
Coclite, G.M., Fanizzi, A., Lopez, L., Maddalena, F., Pellegrino, S.F.: Numerical methods for the nonlocal wave equation of the peridynamics. Appl. Numer. Math. 155, 119–139 (2020). https://doi.org/10.1016/j.apnum.2018.11.007. ISSN 0168-9274
Article
MathSciNet
MATH
Google Scholar
Jafarzadeh, S., Larios, A., Bobaru, F.: Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methods. J. Peridyn. Nonlocal Model. 2(1), 85–110 (2020)
Article
MathSciNet
Google Scholar
Lopez, L., Pellegrino, S.F.: A spectral method with volume penalization for a nonlinear peridynamic model. Int. J. Numer. Methods Eng. 122(3), 707–725 (2021). https://doi.org/10.1002/nme.6555
Article
MathSciNet
Google Scholar
Lopez, L., Pellegrino, S.F.: A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models. Int. J. Numer. Methods Eng. 123(20), 4859–4876 (2022)
Article
Google Scholar
Liang, X., Wang, L., Xu, J., Wang, J.: The boundary element method of peridynamics. Int. J. Numer. Methods Eng. 122(20), 5558–5593 (2021)
Article
MathSciNet
Google Scholar
Silling, S.A., Askari, E.: A meshfree method based on the peridynamic model of solid mechanics. Comput. Struct. 83(17–18), 1526–1535 (2005)
Article
Google Scholar
Emmrich, E., Weckner, O.: Analysis and numerical approximation of an integro-differential equation modeling non-local effects in linear elasticity. Math. Mech. Solids 12(4), 363–384 (2007)
Article
MathSciNet
MATH
Google Scholar
Seleson, P., Littlewood, D.J.: Convergence studies in meshfree peridynamic simulations. Comput. Math. Appl. 71(11), 2432–2448 (2016)
Article
MathSciNet
MATH
Google Scholar
Bessa, M.A., Foster, J.T., Belytschko, T., Liu, W.K.: A meshfree unification: reproducing kernel peridynamics. Comput. Mech. 53(6), 1251–1264 (2014)
Article
MathSciNet
MATH
Google Scholar
Bobaru, F., Yang, M., Alves, L.F., Silling, S.A., Askari, E., Xu, J.: Convergence, adaptive refinement, and scaling in 1D peridynamics. Int. J. Numer. Methods Eng. 77(6), 852–877 (2009)
Article
MATH
Google Scholar
Le, Q.V., Bobaru, F.: Surface corrections for peridynamic models in elasticity and fracture. Comput. Mech. 61(4), 499–518 (2018)
Article
MathSciNet
MATH
Google Scholar
Bobaru, F., Ha, Y.D.: Adaptive refinement and multiscale modeling in 2D peridynamics. Int. J. Multiscale Comput. Eng. 9(6), 635–659 (2011)
Article
Google Scholar
Dipasquale, D., Zaccariotto, M., Galvanetto, U.: Crack propagation with adaptive grid refinement in 2D peridynamics. Int. J. Fract. 190(1), 1–22 (2014)
Article
Google Scholar
Ren, H., Zhuang, X., Cai, Y., Rabczuk, T.: Dual-horizon peridynamics. Int. J. Numer. Methods Eng. 108(12), 1451–1476 (2016)
Article
MathSciNet
Google Scholar
Gu, X., Zhang, Q., Xia, X.: Voronoi-based peridynamics and cracking analysis with adaptive refinement. Int. J. Numer. Methods Eng. 112(13), 2087–2109 (2017)
Article
MathSciNet
Google Scholar
Shojaei, A., Mossaiby, F., Zaccariotto, M., Galvanetto, U.: An adaptive multi-grid peridynamic method for dynamic fracture analysis. Int. J. Mech. Sci. 144, 600–617 (2018)
Article
Google Scholar
Henke, S.F., Shanbhag, S.: Mesh sensitivity in peridynamic simulations. Comput. Phys. Commun. 185(1), 181–193 (2014)
Article
MathSciNet
MATH
Google Scholar
Kilic, B., Madenci, E.: Coupling of peridynamic theory and the finite element method. J. Mech. Mater. Struct. 5(5), 707–733 (2010)
Article
Google Scholar
Chen, X., Gunzburger, M.: Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Comput. Methods Appl. Mech. Eng. 200(9–12), 1237–1250 (2011)
Article
MathSciNet
MATH
Google Scholar
Liu, Z., Cheng, A., Wang, H.: An hp-Galerkin method with fast solution for linear peridynamic models in one dimension. Comput. Math. Appl. 73(7), 1546–1565 (2017)
Article
MathSciNet
MATH
Google Scholar
Wang, H., Tian, H.: A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model. J. Comput. Phys. 231(23), 7730–7738 (2012)
Article
MathSciNet
MATH
Google Scholar
Huang, X., Bie, Z., Wang, L., Jin, Y., Liu, X., Su, G., He, X.: Finite element method of bond-based peridynamics and its ABAQUS implementation. Eng. Fract. Mech. 206, 408–426 (2019)
Article
Google Scholar
Zaccariotto, M., Tomasi, D., Galvanetto, U.: An enhanced coupling of PD grids to FE meshes. Mech. Res. Commun. 84, 125–135 (2017)
Article
Google Scholar
Zaccariotto, M., Mudric, T., Tomasi, D., Shojaei, A., Galvanetto, U.: Coupling of FEM meshes with peridynamic grids. Comput. Methods Appl. Mech. Eng. 330, 471–497 (2018)
Article
MathSciNet
MATH
Google Scholar
Galvanetto, U., Mudric, T., Shojaei, A., Zaccariotto, M.: An effective way to couple FEM meshes and peridynamics grids for the solution of static equilibrium problems. Mech. Res. Commun. 76, 41–47 (2016)
Article
Google Scholar
Zhang, Y., Madenci, E.: A coupled peridynamic and finite element approach in ANSYS framework for fatigue life prediction based on the kinetic theory of fracture. J. Peridyn. Nonlocal Model. 4(1), 51–87 (2022)
Article
MathSciNet
Google Scholar
Zheng, G., Shen, G., Xia, Y., Hu, P.: A bond-based peridynamic model considering effects of particle rotation and shear influence coefficient. Int. J. Numer. Methods Eng. 121(1), 93–109 (2020)
Article
MathSciNet
Google Scholar
Han, D., Zhang, Y., Wang, Q., Lu, W., Jia, B.: The review of the bond-based peridynamics modeling. J. Micromech. Mol. Phys. 4(1), 1830001 (2019)
Article
Google Scholar
Silling, S.A., Bobaru, F.: Peridynamic modeling of membranes and fibers. Int. J. Non-Linear Mech. 40(2–3), 395–409 (2005)
Article
MATH
Google Scholar
Chen, Z., Ju, J.W., Su, G., Huang, X., Li, S., Zhai, L.: Influence of micro-modulus functions on peridynamics simulation of crack propagation and branching in brittle materials. Eng. Fract. Mech. 216, 106498 (2019)
Article
Google Scholar
Kilic, B.: Peridynamic theory for progressive failure prediction in homogeneous and heterogeneous materials. The University of Arizona (2008)
Chen, Z., Bakenhus, D., Bobaru, F.: A constructive peridynamic kernel for elasticity. Comput. Methods Appl. Mech. Eng. 311, 356–373 (2016)
Article
MathSciNet
MATH
Google Scholar
Madenci, E., Barut, A., Futch, M.: Peridynamic differential operator and its applications. Comput. Methods Appl. Mech. Eng. 304, 408–451 (2016)
Article
MathSciNet
MATH
Google Scholar
Huang, D., Lu, G., Wang, C., Qiao, P.: An extended peridynamic approach for deformation and fracture analysis. Eng. Fract. Mech. 141, 196–211 (2015)
Article
Google Scholar
Coclite, G.M., Dipierro, S., Maddalena, F., Valdinoci, E.: Wellposedness of a nonlinear peridynamic model. Nonlinearity 32(1), 1–21 (2018). https://doi.org/10.1088/1361-6544/aae71b. ISSN 1361-6544
Article
MathSciNet
MATH
Google Scholar
Coclite, G.M., Dipierro, S., Fanizza, G., Maddalena, F., Valdinoci, E.: Dispersive effects in a peridynamic model. arXiv preprint, arXiv:2105.01558 (2021)
Gurtin, M.E., Fried, E., Anand, L.: The Mechanics and Thermodynamics of Continua. Cambridge University Press, Cambridge (2010)
Book
Google Scholar
Silling, S.A.: Solitary waves in a peridynamic elastic solid. J. Mech. Phys. Solids 96, 121–132 (2016)
Article
MathSciNet
MATH
Google Scholar
Pego, R.L., Van, T.-S.: Existence of solitary waves in one dimensional peridynamics. J. Elast. 136(2), 207–236 (2019)
Article
MathSciNet
MATH
Google Scholar
Emmrich, E., Puhst, D.: A short note on modeling damage in peridynamics. J. Elast. 123(2), 245–252 (2016)
Article
MathSciNet
MATH
Google Scholar
Du, Q., Tao, Y., Tian, X.: A peridynamic model of fracture mechanics with bond-breaking. J. Elast. 132(2), 197–218 (2018). https://doi.org/10.1007/s10659-017-9661-2. ISSN 0374-3535
Article
MathSciNet
MATH
Google Scholar
Boltzmann, L.: Zur Theorie der elastischen Nachwirkung. Ann. Phys. 241(11), 430–432 (1878)
Article
Google Scholar
Volterra, V.: Sur les équations intégro-différentielles et leurs applications. Acta Math. 35, 295 (1912)
Article
MathSciNet
MATH
Google Scholar
Coleman, B.D., Noll, W.: Foundations of linear viscoelasticity. Rev. Mod. Phys. 33(2), 239 (1961)
Article
MathSciNet
MATH
Google Scholar
Astarita, G., Marrucci, G., Joseph, D.D.: Principles of non-Newtonian fluid mechanics. J. Appl. Mech. 42(3), 750 (1975)
Article
Google Scholar