[1] Silling, S. A., “Reformulation of Elasticity Theory for Discontinuities and Long-range Forces,” Journal of the Mechanics and Physics of Solids, Vol. 48, 2000, pp. 175-209.

[2] Silling, S.A., Zimmermann, M. and Abeyaratne, R., “Deformation of a peridynamic bar,” J. Elasticity, Vol. 73, 2003,  pp. 173–190.

[3] Silling, S. A. and Bobaru, F., “Peridynamic modeling of membranes and fibers,” International Journal of Non-linear Mechanics, Vol. 40, 2005, pp. 395-409.

[4] Weckner, O. and Abeyaratne, R., “The Effect of Long-Range Forces on the Dynamics of a Bar,” Journal of the Mechanics and Physics of Solids, Vol. 53, No. 3, 2005,  pp. 705–728.

[5] Weckner, O. and Emmrich, E., “Numerical Simulation of the Dynamics of a Nonlocal, Inhomogeneous, Infinite Bar,” Journal of Computational and Applied Mechanics, Vol. 6, No. 2, 2005,  pp. 311–319.

[6] Silling, S.A. and Askari, A., “A Meshfree Method Based on the Peridynamic Model of Solid Mechanics,” Computers & Structures,  Vol. 83, No. 17–18, 2005,  pp. 1526–1535.

[7] Dayal, K. and Bhattacharya K.,  “Kinetics of phase transformations in the peridynamic formulation of continuum mechanics”. Journal of the Mechanics and Physics of Solids, Vol. 54, 2006, pp. 1811-1842.

[8] Emmrich, E. and Weckner, O., “Analysis and Numerical Approximation of an Integro-differential Equation Modeling Non-local Effects in Linear Elasticity,” Mathematics and Mechanics of Solids, Vol. 12, 2007, pp. 363-384.

[9] Silling, S.A,, Epton, M., Weckner, O. , Xu, J.  and Askari, A, “Peridynamics States and Constitutive Modeling,” Journal of Elasticity, Vol. 88, No. 2, 2007, pp. 151-184.

[10] Emmrich, E. and Weckner, O., “On the Well-posedness of the Linear Peridynamic Model and Its Convergence Towards the Navier Equation of Linear Elasticity,” Communications in Mathematical Sciences, Vol. 5, No. 4, 2007, pp. 851-864.  

[11] Weckner , O. and Emmrich, E., “The Peridynamic Equation and its Spatial Discretization,” Journal of Mathematical Modeling and Analysis, Vol. 12, No. 1, 2007, pp. 17-27.  

[12] Bobaru, F. “Influence of Van Der Waals Forces on Increasing the Strength and Toughness in Dynamic Fracture of Nanofiber Networks: A Peridynamic Approach”, Modeling and Simulation in Materials Science and Engineering , Vol. 15, 2007, pp. 397-417.

[13] Macek, R. W. and Silling, S. A., "Peridynamics via Finite Element Analysis," Finite Elements in Analysis and Design, Vol. 43, No. 15,  2007, pp. 1169-1178.

[14] Gerstle, W., Sau, N. and Silling, S.  "Peridynamic Modeling of Concrete Structures," Nuclear Engineering and Design, Vol. 237, No.  12-13,  2007, pp. 1250-1258.

[15] Demmie, P. N. and Silling, S. A.  "An Approach to Modeling Extreme Loading of Structures using Peridynamics," Journal of Mechanics of Materials and Structures, Vol. 2, No.  10,  2007, pp. 1921-1945.

[16] Xu, J., Askari, A., Weckner, O. and Silling, S. A., “Peridynamic Analysis of Impact Damage in Composite Laminates,” Journal of Aerospace Engineering,  Vol. 21, No. 3, 2008, pp. 187-194.

[17] Warren, T. L., Silling, S. A., Askari, A., Weckner, O., Epton, M. A. and Xu, J., “A Non-ordinary State-based Peridynamic Method to Model Solid Material Deformation and Fracture,” International Journal of Solids and Structures, Vol. 46, 2009, pp. 1186-1195.

[18] Bobaru, F., Yang, M., Alves, L. F., Silling, S. A., Askari, E. and Xu, J., “Convergence, Adaptive Refinement, and Scaling in 1D Peridynamics,” International Journal for Numerical Methods in Engineering, Vol. 77, 2009, pp. 852-877.

[19] Lehoucq, R. B. and Silling, S. A., “Force Flux and the Peridynamic Stress Tensor,” Journal of the Mechanics and Physics of Solids, Vol. 56, 2008, pp. 1566–1577.

[20] Silling, S. A. and Lehoucq, R. B., “Convergence of Peridynamics to Classical Elasticity Theory,” Journal of Elasticity, 2008

[21] Kilic, B., Agwai, A. and Madenci, E., “Peridynamic Theory for Progressive Damage Prediction in Centre-Cracked Composite Laminates” Composite structures, Vol. 90, 2009, pp. 141-151.

[22] Kilic, B., and Madenci, E., “Prediction of Crack Paths in a Quenched Glass Plate by Using Peridynamic Theory,” International Journal of Fracture, Vol. 156, 2009, pp. 165-177.

[23] Kilic, B., and Madenci, E., “Structural Stability and Failure Analysis Using Peridynamic Theory,” International Journal of Non-Linear Mechanics, Vol. 44, 2009, pp. 845-854.

[24] Weckner, O., Brunk, G., Epton, M. A., Silling, S. A. and Askari, E., “Green’s Functions in Non-local Three-dimensional Linear Elasticity,” Proceedings of the Royal Society A, Vol. 465, 2009, pp. 3463-3487.

[25] Seleson, P., Parks, M. L., Gunzburger, M. and Lehocq, R. B., “Peridynamics as an Upscaling of Molecular Dynamics,” Multiscale Modeling and Simulation, Vol. 8, No. 1, 2009, pp. 204-227.

[26] Kilic, B., and Madenci, E., “Peridynamic Theory for Thermomechanical Analysis,” IEEE Transactions on Advanced Packaging, Vol. 33, 2010, pp. 97-105.

[27] Kilic, B., and Madenci, E., “An Adaptive Dynamic Relaxation Method for Quasi-static Simulations using the peridynamic theory,” Theoretical and Applied Fracture Mechanics, Vol. 53, 2010, pp. 194-201..

[28] Kilic, B., and Madenci, E., “Coupling of Peridynamic Theory and Finite Element Method,” Journal of Mechanics of Materials and Structures, Vol. 5, 2010, pp. 707–733.

[29] Aksoy, H. G., and Senocak, E. S., “Discontinuous Galerkin Method Based on Peridynamic Theory,” IOP Conf. Series: Materials Science and Engineering, Vol. 10, 2010, 012227.

[30] Aksoylu, B., and Mengesha, T., “Results on Nonlocal Boundary Value Problems,” Numerical Functional Analysis and Optimization, Vol. 31, 2010, pp. 1301-1317.

[31] Bobaru, F., and Duangpanya, M., “The Peridynamic Formulation for Transient Heat Conduction,” International Journal of Heat and Mass Transfer, Vol. 53, 2010, pp. 4047-4059.

[32] Foster, J. T., Silling, S. A. and Chen, W. W., “Viscoplasticity Using Peridynamics,” International Journal for Numerical Methods in Engineering, Vol. 81, 2010, pp. 1242-1258.

[33] Ha, Y. D. and Bobaru, F., “Studies of Dynamic Crack Propagation and Crack Branching with Peridynamics,” International Journal of Fracture, Vol. 162, 2010, pp. 229-244.

[34] Silling, S. A., “Linearized Theory of Peridynamic States,” Journal of Elasticity, Vol. 99, 2010, pp. 85-111.

[35] Silling, S. A., Weckner, O., Askari, A. and Bobaru, F., “Crack Nucleation in a Peridynamic Solid,” International Journal of Fracture, Vol. 162, 2010, pp. 219-227.

[36] Silling, S. A. and Lehoucq, R. B., “Peridynamic Theory of Solid Mechanics,” Advances in Applied Mechanics, Vol. 44, 2010, pp. 73-168.

[37] Celik, E., Guven, I. and Madenci, E., “Simulations of nanowire bend tests for extracting mechanical properties,” Theoretical and Applied Fracture Mechanics, Vol. 55, 2011, pp. 185-191

[38] Agwai, A. Guven, I. and Madenci, E., “Predicting Crack Propagation with Peridynamics: A Comparative Study,” International Journal of Fracture, Vol. 171, 2011, pp. 65-78.

[39] Agwai, A. Guven, I. and Madenci, E., “Crack Propagation in Multilayer Thin-film Structures of Electronic Packages Using Peridynamic Theory,” Microelectronics Reliability, Vol. 51, 2011, pp. 2298-2305.

[40] Aksoy, H. G., and Senocak, E. S., “Discontinuous Galerkin Method Based on Peridynamic Theory for Linear Elasticity,” International Journal for Numerical Methods and Engineering, Vol. 88, 2011, pp. 673-692.

[41] Askari, A., Nelson, K., Weckner, O., Xu, J. and Silling, S., “Hail Impact Characteristics of a Hybrid Material by Advanced Analysis Techniques and Testing,” Journal of Aerospace Engineering, Vol. 24, 2011, pp. 210-217.

[42] Aksoylu, B., and Parks, M. L., “Variational Theory and Domain Decomposition for Nonlocal Problems,” Applied Mathematics and Computation, Vol. 217, 2011, pp. 6498-6515.

[43] Du, Q. and Zhou, K., “Mathematical Analysis for the Peridynamic Nonlocal Continuum Theory,” ESAIM: Mathematical Modeling and Numerical Analysis, Vol. 45, 2011, pp. 217-234.

[44] Gunzburger, M., and Chen, X., “Continuous and Discontinuous Finite Element Methods for a Peridynamics Model,” Computer Methods on Applied Mechanics and Engineering, Vol. 200, 2011, pp. 1237-1250.

[45] Ha, Y. D. and Bobaru, F., “Characteristics of Dynamic Brittle Fracture Captured with Peridynamics,” Engineering Fracture Mechanics, Vol. 78, 2011, pp. 1156-1168.

[46] Huang, D., Zhang, Q. and Qiao, P., “Damage and Progressive Failure of Concrete Structures Using Non-local Peridynamic Modeling,” Science China Technological Sciences, Vol. 54, 2011, pp. 591-596.

[47] Lehoucq, R. B.  and Sears, M. P., “Statistical Mechanical Foundation of the Peridynamic Nonlocal Continuum Theory: Energy and Momentum Conservation Laws,” Physical Review E, Vol. 84, 2011, 031112.

[48] Yu, K., Xin, X. J. and Lease, K. B., “A New Adaptive Integration Method for the Peridynamic Theory,” Modeling and Simulation in Materials Science and Engineering, Vol. 19, 2011, 045003.

[49] Silling, S. A., “A Coarsening Method for Linear Peridynamics,” International Journal for Multiscale Computational Engineering, Vol. 9, No. 6, 2011, pp. 609-622.

[50] Weckner, O. and Silling, S. A., “Determination of Nonlocal Constitutive Equations from Phonon Dispersion Relations,” International Journal for Multiscale Computational Engineering, Vol. 9, No. 6, 2011, pp. 623-634.

[51] Bobaru, F. and Ha, Y. D., “Adaptive Refinement and Multiscale Modeling in 2D Peridynamics,” International Journal for Multiscale Computational Engineering, Vol. 9, No. 6, 2011, pp. 635-660.

[52] Burch, N. and Lehocq, R. B., “Classical, Nonlocal, and Fractional Diffusion Equations on Bounded Domains,” International Journal for Multiscale Computational Engineering, Vol. 9, No. 6, 2011, pp. 661-674.

[53] Foster, J. T., Silling, S. A. and Chen, W., “An Energy Based Failure Criterion for Use with Peridynamic States,” International Journal for Multiscale Computational Engineering, Vol. 9, No. 6, 2011, pp. 675-688.

[54] Seleson, P. and Parks, M. L., “On the Role of Influence Function in the Peridynamic Theory,” International Journal for Multiscale Computational Engineering, Vol. 9, No. 6, 2011, pp. 689-706.

[55] Hu, W., Ha, Y. D. and Bobaru, F., “Modeling Dynamic Fracture and Damage in a Fiber-Reinforced Composite Lamina with Peridynamics,” International Journal for Multiscale Computational Engineering, Vol. 9, No. 6, 2011, pp. 707-726.

[56] Liu, W. and Hong, J., “Discretized Peridynamics for Brittle and Ductile Solids,” International Journal for Numerical Methods in Engineering, Vol. 89, No.8, 2012, pp. 1028-1046.

[57] Oterkus, E., Madenci, E., Weckner, O., Silling, S., Bogert, P. and Tessler, A., “Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot,” Composite Structures, Vol. 94, 2012, pp. 839-850.

[58] Oterkus, E. and Madenci, E., “Peridynamic Analysis of Fiber Reinforced Composite Materials,” Journal of Mechanics of Materials and Structures, Vol. 7, No. 1, 2012, pp. 45-84.

[59] Agwai, A. Guven, I. and Madenci, E., “Drop-Shock Failure Prediction in Electronic Packages by Using Peridynamic Theory,” IEEE Transactions on Advanced Packaging, Vol. 2, No.3, 2012, pp. 439-447.

[60] Alali, B., and Lipton, R., “Multiscale Dynamics of Heterogeneous Media in the Peridynamic Formulation,” Journal of Elasticity, Vol. 106, 2012, pp. 71-103.

[61] Oterkus, E. and Madenci, E., “Peridynamic Theory for Damage Initiation and Growth in Composite Laminate,” Key Engineering Materials, Vols. 488-489, 2012, pp. 355-358.

[62] Bobaru, F., and Duangpanya, M., “A Peridynamic Formulation for Transient Heat Conduction in Bodies with Evolving Discontinuities,” Journal of Computational Physics, Vol. 231(7), 2012, pp. 2764-2785.

[63] Lubineau, G., Azdoud, Y., Han, F., Rey, C. and Askari, A., “A Morphing Strategy to Couple Non-local to Local Continuum Mechanics,” Journal of the Mechanics and Physics of Solids, Vol. 60, 2012, pp. 1088-1102.

[64] Mikata, Y., “Analytical Solutions of Peristatic and Peridynamic Problems for a 1D Infinite Rod,” International Journal of Solids and Structures, Vol. 49, No. 21, 2012, pp. 2887-2897.

[65] Liu, W. and Hong, J. W., “Discretized Peridynamics for Linear Elastic Solids,” Computational Mechanics, Vol. 50, No. 5, 2012, pp. 579-590.

[66] Hu, W., Ha, Y. D. and Bobaru, F., “Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites,” Computer Methods in Applied Mechanics and Engineering, Vol. 217, 2012, pp. 247-261.

[67] Bobaru, F., and Hu, W., “The meaning, selection, and use of the peridynamic horizon and its relation to crack branching in brittle materials,” International Journal of Fracture, Vol. 176, No. 2, 2012, pp. 215-222.

[68] Wang, H. and Hao, T, “A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model,” Journal of Computational Physics, Vol. 231, No. 23, 2012, pp. 7730-7738.

[69] Hu, W., Ha, Y. D., Bobaru, F., and Silling, S. A., “The Formulation and Computation of the Nonlocal J-integral in Bond-based Peridynamics,” International Journal of Fracture, Vol. 176, No. 2, 2012, pp. 195-206.

[70] Oterkus, E., Guven, I. and Madenci, E., 2012, “Impact Damage Assessment by Using Peridynamic Theory,” Open Engineering, Vol. 2, No. 4, pp. 523-531.

[71] Liu, W. and Hong, J. W., “Discretized peridynamics for linear elastic solids,” Computational Mechanics, Vol. 50, No. 5, 2012, pp. 579-590.

[72] Hasan, H. M. A., Rahman, H. and Abed, R. H., “Wave Equation Applications in Peridynamic Model,” European Journal of Scientific Research, Vol. 88, No. 2, pp. 246-250.

[73] Bobaru, F., Ha, Y. and Hu, W., “Damage Progression from Impact in Layered Glass Modeled with Peridynamics,” Open Engineering, Vol. 2, .No. 4, 2012, 551-561.

[74] Ha, Y. D. and Cho, S., “Nonlocal Peridynamic Models for Dynamic Brittle Fracture in Fiber-Reinforced Composites: Study on Asymmetrically Loading State,” Journal of the Computational Structural Engineering Institute of Korea, Vol. 25, No. 4, 2012, pp. 279-285.

[75] Rahman, R. and Haque, A., “A Peridynamics Formulation Based Hierarchical Multiscale Modeling Approach Between Continuum Scale and Atomistic Scale,” International Journal of Computational Materials Science and Engineering, Vol. 1, No. 3, 2012, 1250029.

[76] Liu, W. and Hong, J. W., “A coupling approach of discretized peridynamics with finite element method,” Computer Methods in Applied Mechanics and Engineering, Vol. 245, 2012, pp. 163-175.

[77] Du, Q., Kamm, J. R., Lehoucq, R. B. and Parks, M. L., “A New Approach for A Nonlocal, Nonlinear Conservation Law,” SIAM Journal on Applied Mathematics, Vol. 72, No. 1, 2012, pp. 464-487.

[78] Vogler, T. J., Borg, J. P. and Grady, D. E., “On the Scaling of Steady Structured Waves in Heterogeneous Materials,” Journal of Applied Physics, Vol. 112, No. 12, 2014, 123507.

[79] Du, Q., Gunzburger, M., Lehoucq, R. B., and Zhou, K. “Analysis and approximation of nonlocal diffusion problems with volume constraints,” SIAM review, Vol. 54, No. 4, 2012, pp. 667-696.

[80] Erbay, H. A., Erkip, A. and Muslu, G. M., “The Cauchy Problem for a One-Dimensional Nonlinear Elastic Peridynamic Model,” Journal of Differential Equations, Vol. 252, No. 8, 2012, pp. 4392-4409.

[81] Mengesha, T., and Du, Q., “Analysis of a Scalar Peridynamic Model with a Sign Changing Kernel,” Discrete Contin,  Vol. 18, No. 5, 2013, pp. 1415.

[82] Tian, X., and Du, Q., “Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations,” SIAM Journal on Numerical Analysis, Vol. 51, No. 6, 2013, pp. 3458–3482.

[83] Du, Q., Tian, L., Zhao, X., “A convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models,” SIAM Journal on Numerical Analysis, Vol. 51, No. 2, 2013, pp. 1211–1234.

[84] Emmrich, E., and Puhst, D., “Well-posedness of the Peridynamic Model with Lipschitz Continuous Pairwise Force Function,” Communications in Mathematical Sciences,Vol. 11, No. 4, 2013, pp. 1039-1049.

[85] Du, Q., Gunzburger, M., Lehoucq, R.B., and Zhou, K., “Analysis of the Volume-constrained Peridynamic Navier Equation of Linear Elasticity,” Journal of Elasticity, Vol. 113, No. 2, 2013, pp. 193-217

[86] Du, Q., Ju, L., Tian, L., and Zhou, K., “A Posteriori Error Analysis of Finite Element Method for Linear Nonlocal Diffusion and Peridynamic Models,” Mathematics of Computation, Vol. 82, 2013,  pp. 1889-1922.

[87] Weckner, O., and Mohamed N., “Viscoelastic Material Models in Peridynamics,” Applied Mathematics and Computation, Vol. 219, No. 11, 2013, pp. 6039–6043

[88] Shen, F., Zhang, Q., and Huang, D., “Damage and Failure Process of Concrete Structure under Uniaxial Compression Based on Peridynamics Modeling,” Mathematical Problems in Engineering, (2013), 2013, No. 631074

[89] Hassan, H. M. A., “Dispersive Standing Waves in Peridynamic Model,” International Journal of Physics and Mathematical Sciences, Vol. 3, No. 4, 2013, pp.66-72.

[90] Tupek, M.R., Rimoli, J.J., and Radovitzky, R., “An Approach for Incorporating Classical Continuum Damage Models in State-based Peridynamics,” Computer Methods in Applied Mechanics and Engineering, Vol. 263, 2013, pp. 20-26.

[91] Wildman, R.A., and Gazonas, G.A., “A Perfectly Matched Layer for Peridynamics in Two Dimensions,” Journal of Mechanics of Materials and Structures, Vol.7, No. 8-9, 2012, pp. 765-781.

[92] Beckmann, R., Mella, R., and Wenman, M.R., “Mesh and Timestep Sensitivity of Fracture from Thermal Strains Using Peridynamics Implemented in Abaqus,” Computer Methods in Applied Mechanics and Engineering, Vol 263, 2013, pp. 71-80.

[93] Seleson, P., Beneddine, S., and Prudhomme, S., “A Force-based Coupling Scheme for Peridynamics and Classical Elasticity,” Computational Materials Science, Vol. 66, 2013, pp. 34-49.

[94] Seleson, P., Gunzburger, M. and Parks, M. L., “Interface Problems in Nonlocal Diffusion and Sharp Transitions between Local and Nonlocal Domains,” Computer Methods in Applied Mechanics and Engineering, Vol. 266, 2013, pp. 185-204.

[95] Aguiar, A. R. and Fosdick, R., “A Constitutive Model for a Linearly Elastic Peridynamic Body,” Mathematics and Mechanics of Solids, Vol. 19, 2014, pp. 502-523.

[96] Alimov, S. A., Cao, Y. and Ilhan, O. A., “On the Problems of Peridynamics with Special Convolution Kernels,” Journal of Integral Equations and Applications, Vol. 26, 2014, pp. 301-321.

[97] Bellido, J. C. and Mora-Corral, C., “Existence for Nonlocal Variational Problems in Peridynamics,” SIAM Journal on Mathematical Analysis, Vol. 46, 2014, pp. 890-916.

[98] Bessa, M. A., Foster, J. T., Belytschko, T. and Liu, W. K., “A Meshfree Unification: Reproducing Kernel Peridynamics,” Computational Mechanics, Vol. 53, 2014, pp. 1251-1264.

[99] Azdoud, Y., Han, F. and Lubineau, G., “The Morphing Method as a Flexible Tool for Adaptive Local/Non-local Simulation of Static Fracture,” Computational Mechanics, Vol. 54, No. 3, 2014, pp. 711-722.

[100] Ghajari, M., Iannucci, L. and Curtis, P., “A Peridynamic Material Model for the Analysis of Dynamic Crack Propagation in Orthotropic Media,” Computer Methods in Applied Mechanics and Engineering, Vol. 276, 2014, pp. 431-452.

[101] Seleson, P., “Improved One-Point Quadrature Algorithms for Two-Dimensional Peridynamic Models Based on Analytical Calculations,” Computer Methods in Applied Mechanics and Engineering, Vol. 282, 2014, pp. 184-217.

[102] Seleson, P., Parks, M. L. and Gunzburger, M., “Peridynamic State-Based Models and the Embedded-Atom Model,” Communications in Computational Physics, Vol. 15, No. 1, 2014, pp. 179-205.

[103] Taylor, M., and Steigmann, D.J., “A Two-dimensional Peridynamic Model for Thin Plates,” Mathematics and Mechanics of Solids, Vol. 20, No. 8, 2015, pp. 998-1010.

[104] Silling, S. A., Littlewood, D. J. and Seleson, P., “Variable Horizon in a Peridynamic Medium,” Journal of Mechanics of Materials and Structures, Vol. 10, No. 5, 2015, pp. 591-612.

[105] Chen, Z. and Bobaru, F., “Peridynamic Modeling of Pitting Corrosion Damage,” Journal of the Mechanics and Physics of Solids, Vol. 78, 2015, pp. 352-381.

[106] Chen, Z. and Bobaru, F., “Selecting the Kernel in a Peridynamic Formulation: A Study for Transient Heat Diffusion,” Computer Physics and Communication, Vol. 197, 2015, pp. 51-60.

[107] Huang, D., Lu, G., Wang, C. and Qiao, P., “An Extended Peridynamic Approach for Deformation and Fracture Analysis,” Engineering Fracture Mechanics, Vol. 141, 2015, pp. 196-211.

[108] Hu, Y. L., De Carvalho, N. V. and Madenci, E., “Peridynamic Modeling of Delamination Growth in Composite Laminates ,” Composite Structures, Vol. 132 , 2015, pp. 610-620.

[109] Huang, D., Lu, G. and Qiao, P., “An Improved Peridynamic Approach for Quasi-static Elastic Deformation and Brittle Fracture Analysis,” International Journal of Mechanical Sciences, Vols. 94-95, 2015, pp. 111-122.

[110] Chowdhury, S. R., Rahaman, M. M., Roy, D. and Sundaram, N., “A Micropolar Peridynamic Theory in Linear Elasticity,” International Journal of Solids and Structures, Vol. 59, 2015, pp. 171-182.

[111] Lai, X., Liu, L. S., Liu, Q. W., Cao, D. F., Wang and Z., Zhai, P. C., “Slope Stability Analysis by Peridynamic Theory,” Applied Mechanics and Materials, Vol. 744-746, 2015, pp. 584-588.

[112] Rahman, R. and Foster, J. T., “Peridynamic Theory of Solids from the Perspective of Classical Statistical Mechanics,” Physica A: Statistical Mechanics and its Application, Vol.437, 2015, pp. 162-183.

[113] Jabakhanji, R. and Mohtar, R. H., “A Peridynamic Model of Flow in Porous Media,” Advances in Water Resources, Vol. 78, 2015, pp. 22-35.

[114] Cheng, Z., Zhang, G., Wang, Y. and Bobaru F., “A Peridynamic Model for Dynamic Fracture in Functionally Graded Materials,” Composite Structures, Vol. 133, 2015, pp. 529-546.

[115] Bobaru, F. and Zhang, G., “Why do cracks branch? A Peridynamic Investigation of Dynamic Brittle Fracture,” International Journal of Fracture, Vol. 196, 2015, pp. 59-98.

[116] Mengesha, T. and Du, Q., “Multiscale Analysis of Linearized Peridynamics,” Communication in Mathematical Sciences, Vol. 13, No. 5, 2015, pp. 1193-1218.

[117] Ha, Y. D., “State-based Peridynamic Modeling for Dynamic Fracture of Plane Stress,” Journal of the Computational Structural Engineering Institute of Korea, Vol. 28, No. 3, 2015, pp. 301-307.

[118] Ha, Y. D., “Dynamic Fracture Analysis with State-based Peridynamic Model: Crack Patterns on Stress Waves for Plane Stress Elastic Solid,” Journal of the Computational Structural Engineering Institute of Korea, Vol. 28, No. 3, 2015, pp. 309-316.

[119] Diyaroglu, C., Oterkus, E., Oterkus, S. and Madenci, E., “Peridynamics for Bending of Beams and Plates with Transverse Shear Deformation,” International Journal of Solids and Structures, Vols. 69-70, 2015, pp. 152-168.

[120] Moon, M. Y., Kim, J. H., Ha, Y. D. and Cho, S., “Adjoint Design Sensitivity Analysis of Dynamic Crack Propagation using Peridynamic Theory,” Structural and Multidisciplinary Optimization, Vol. 51, No. 3, 2015, pp. 585-598.

[121] Jeon, B. S., Stewart, R. J. and Ahmed, I. Z., “Peridynamic Simulations of Brittle Structures with Thermal Residual Deformation: Strengthening and Structural Reactivity of Glasses under Impacts,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol.471, No. 2183, 2015, p.20150231.

[122] Emmrich, E. and Puhst, D., “Survey of Existence Results in Nonlinear Peridynamics in Comparison with Local Elastodynamics,” Comput. Methods Appl. Math., Vol. 15, 2015, pp. 483-496. 

[123] Emmrich, E. and Puhst, D., “Measure-valued and Weak Solutions to the Nonlinear Peridynamic Model in Nonlocal Elastodynamics,” Nonlinearity, Vol. 28, 2015, pp. 285-307. 

[124] Dell'Isola, F., Andreaus, U. and Placidi, L., “At the Origins and In the Vanguard of Peridynamics, Non-local and Higher-Gradient Continuum Mechanics: An Underestimated and Still Topical Contribution of Gabrio Piola,” Mathematics and Mechanics of Solids, Vol. 20, No. 8, 2015, pp. 887-928.

[125] Seleson, P., Ha, Y. D. and Beneddine, S., “Concurrent Coupling of Bond-Based Peridynamics and the Navier Equation of Classical Elasticity by Blending,” International Journal for Multiscale Computational Engineering, Vol. 13, No. 2, 2015, pp. 91-113.

[126] Ren, B., Fan, H., Bergel, G. L., Regueiro, R. A., Lai, X. and Li, S., “A Peridynamics-SPH Coupling Approach to Simulate Soil Fragmentation Induced by Shock Waves,” Computational Mechanics, Vol. 55, No. 2, 2015, pp. 287-302.

[127] Lai, X., Ren, B., Fan, H., Li, S., Wu, C. T., Regueiro, R. A. and Liu, L., “Peridynamics Simulations of Geomaterial Fragmentation by Impulse Loads,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 39, No. 12, 2015, pp. 1304-1330.

[128] Amani, J., Oterkus, E., Areias, P., Zi, G., Nguyen-Thoi, T. and Rabczuk, T., “A Non-ordinary State-based Periynamics Formulation for Thermoplastic Fracture,” International Journal of Impact Engineering, Vol. 87, 2016, pp. 83-94.

[129] Sarego, G., Le, Q. V., Bobaru, F., Zaccariotto, M. and Galvanetto, U., “Linearized State-based Peridynamics for 2-D problems,” International Journal for Numerical Methods in Engineering, Vol. 108(10), 2016, pp. 1174-1197.

[130] Han, F., Lubineau, G. and Azdoud, Y., “Adaptive Coupling Between Damage Mechanics and Peridynamics:_A Route for Objective Simulation of Material Degradation up to Complete Failure,” Journal of the Mechanics and Physics of Solids, Vol. 94, 2016, pp. 453-472.

[131] De Meo, D., Diyaroglu, C., Zhu, N., Oterkus, E. and Siddiq, M. A., “Modelling of Stress-Corrosion Cracking by Using Peridynamics,” International Journal of Hydrogen Energy, Vol. 41, No. 15, 2016, pp. 6593-6609.

[132] Han, F., Lubineau, G., Azdoud, Y. and Askari, A., “A Morphing Approach to Couple State-based Peridynamics with Classical Continuum Mechanics,” Computer Methods in Applied Mechanics and Engineering, Vol. 301, 2016, pp. 336-358.

[133] Mengesha, T. and Du, Q., “Characterization of Function Spaces of Vector Fields and an Application in Nonlinear Peridynamics,” Nonlinear Analysis: Theory, Methods and Applications, Vol. 140, 2016, pp. 82-111.

[134] Madenci, E., Colavito, K. and Phan, N., “Peridynamics for Unguided Crack Growth Prediction under Mixed-mode Loading,” Engineering Fracture Mechanics, 2016, in press.

[135] Wang, L., Xu, J. and Wang, J., “Static and Dynamic Green’s Functions in Peridynamics,” Journal of Elasticity, 2016, pp. 1-31

[136] Bergel, G. L. and Li, S., “The Total and Updated Lagrangian Formulations of State-based Peridynamics,” Computational Mechanics, 2016, pp. 1-20.

[137] Nishawala, V. V., Ostoja-Starzewski, M., Leamy, M. J. and Demmie, P. N., “Simulation of Elastic Wave Propagation Using Cellular Automata and Peridynamics, and Comparison with Experiments,” Wave Motion, Vol. 60, 2016, pp. 73-83.

[138] Prakash, N. and Seidel, G. D., “Electromechanical Peridynamics Modeling of Piezoresistive Response of Carbon Nanotube Nanocomposites,” Computational Materials Science, Vol. 113, 2016, pp. 154-170.

[139] Madenci, E. and Oterkus, S., “Ordinary State-based Peridynamics for Plastic Deformation According to von Mises Yield Criteria with Isotropic Hardening,” Journal of the Mechanics and Physics of Solids, Vol. 86, 2016, pp. 192-219.

[140] Fan, H., Bergel, G. L. and Li, S., “A Hybrid Peridynamics SPH Simulation of Soil Fragmentation by Blast Loads of Buried Explosive,” International Journal of Impact Engineering, Vol. 87, 2016, pp. 14-27.

[141] Diehl, P., Franzelin, F., Pfluger, D. and Ganzenmuller, G. C., “Bond-based Peridynamics: a Quantitative Study of Mode I Crack Opening,” International Journal of Fracture, 2016, pp. 1-14.

[142] Gu, X., Zhang, Q., Huang, D and Yv, Y., “Wave Dispersion Analysis and Simulation Method for Concrete SHPB Test in Peridynamics,” Engineering Fracture Mechanics, Vol. 160, 2016, pp. 124-137.

[143] Sadowski, T. and Pankowski, B., “Numerical Modelling of Two-phase Ceramic Composite Response Under Uniaxial Loading,” Composite Structures, Vol. 143, 2016, pp. 388-394.

[144] Nishawala, V. V. and Ostoja-Starzewski, “Peristatic Solutions for Finite One- and Two-dimensional System,” Mathematics and Mechanics of Solids, 2016.

[145] Jiang, H., He, L., Fan, L.. and Zhan, G., “Numerical Analysis Method of Cemented Carbide Turning Tool's Micro Breakage Based on Peridynamic Theory,” The International Journal of Advanced Manufacturing Technology, 2016, pp. 1-10.

[146] Silhavy, M., “Higher Gradient Expansion for Linear Isotropic Peridynamic Materials,” Mathematics and Mechanics of Solids, 2016.

[147] Sun, C. and Huang, Z., “Peridynamic Simulation to Impacting Damage in Composite Laminate,” Composite Structures, Vol. 138, 2016, pp. 335-341.

[148] Dipasquale, D., Sarego, G., Zaccariotto, M. and Galvanetto, U., “Dependence of Crack Paths on the Orientation of Regular 2D Peridynamic Grids,” Engineering Fracture Mechanics, Vol. 160, 2016, pp. 248-263.

[149] Lindsay, P., Parks, M. L. and Prakash, A., “Enabling Fast, Stable and Accurate Peridynamic Computation Using Multi-time-step Integration,” Computer Methods in Applied Mechanics and Engineering, Vol. 306, 2016, pp. 382-405.

[150] Hu, Y. L. and Madenci, E., “Bond-based Peridynamic Modeling of Composite Laminates with Arbitrary Fiber Orientation and Stacking Sequence,” Composite Structures, Vol. 153, 2016, pp. 139-175.

[151] Li, H., Zhang, H., Zheng, Y. and Zhang, L., “A Peridynamic Model for the Nonlinear Static Analysis of Truss and Tensegrity Structures,” Computational Mechanics, Vol. 57, No. 5, 2016, pp. 843-858.

[152] Xu, F., Gunzburger, M., Burkardt, J. and Du, Q., “A Multiscale Implementation Based on Adaptive Mesh Refinement for the Nonlocal Peridynamics Model in One Dimension,” Multiscale Modeling & Simulation, Vol. 14, No. 1, 2016, pp. 398-429.

[153] Emmrich, E. and Puhst, D., “A Short Note on Modeling Damage in Peridynamics,” J. Elasticity, Vol. 123, 2016, pp. 245-252. 

[154] Seleson, P. and Littlewood, D. J., “Convergence Studies in Meshfree Peridynamic Simulations,” Computers and Mathematics with Applications, Vol. 71, No. 11, 2016, pp. 2432-2448.

[155] Aguiar, A.R., “On the Determination of a Peridynamic Constant in a Linear Constitutive Model,” Journal of Elasticity, Vol. 122, No. 1, 2016, pp. 27-39.

[156] Fan, H. and Li, S., “Parallel Peridynamics-SPH Simulation of Explosion Induced Soil Fragmentation by Using OpenMP,” Computational Particle Mechanics, 2016, pp. 1-13.

[157] Tong, Q. and Li, S., “Multiscale Coupling of Molecular Dynamics and Peridynamics,” Journal of the Mechanics and Physics of Solids, Vol. 95, 2016, 169-187.

[158] Ren, H., Zhuang, X., Cai, Y. and Rabczuk, T., “Dual-Horizon Peridynamics,” International Journal for Numerical Methods in Engineering, 2016, accepted.

[159] Ren, H., Zhuang, X., and Rabczuk, T., “A New Peridynamic Formulation with Shear Deformation for Elastic Solid,” Journal of Micromechanics and Molecular Physics, 2016, accepted.

[160] Seleson, P., Du, Q., and Parks, M. L., “On The Consistency Between Nearest-Neighbor Peridynamic Discretizations and Discretized Classical Elasticity Models,”Computer Methods in Applied Mechanics and Engineering, Vol. 311, 2016, pp. 698-722.

[161] Tao, Y., Tian, X. and Du, Q., 2017. Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. Applied Mathematics and Computation305, pp.282-298.

[162] Oterkus, S., Madenci, E. and Oterkus, E., 2017. Fully coupled poroelastic peridynamic formulation for fluid-filled fractures. Engineering Geology.

[163] Liu, Z., Cheng, A. and Wang, H., 2017. An hp-Galerkin method with fast solution for linear peridynamic models in one dimension. Computers & Mathematics with Applications.

[164] Zeleke, M.A., Xin, L. and Liu, L.S., 2017. Bond Based Peridynamic Formulation for Thermoelectric Materials. In Materials Science Forum (Vol. 883, pp. 51-59). Trans Tech Publications.

[165] Oterkus, S. and Madenci, E., 2017. Peridynamic modeling of fuel pellet cracking. Engineering Fracture Mechanics176, pp.23-37.

[166] Liu, N., Liu, D. and Zhou, W., 2017. Peridynamic modelling of impact damage in three-point bending beam with offset notch. Applied Mathematics and Mechanics38(1), pp.99-110.

[167] Gu, X., Zhang, Q. and Yu, Y., 2017. An Effective Way to Control Numerical Instability of a Nonordinary State-Based Peridynamic Elastic Model. Mathematical Problems in Engineering2017.

[168] Diyaroglu, C., Oterkus, S., Oterkus, E., Madenci, E., Han, S. and Hwang, Y., 2017. Peridynamic wetness approach for moisture concentration analysis in electronic packages. Microelectronics Reliability70, pp.103-111.

[169] De Meo, D. and Oterkus, E., 2017. Finite element implementation of a peridynamic pitting corrosion damage model. Ocean Engineering135, pp.76-83.

[170] Yaghoobi, A. and Chorzepa, M.G., 2017. Fracture analysis of fiber reinforced concrete structures in the micropolar peridynamic analysis framework. Engineering Fracture Mechanics169, pp.238-250.

[171] Seitenfuss, A.B., Aguiar, A.R. and Pereira, M., 2017. NUMERICAL AND THEORETICAL STUDY OF THE PROPERTIES OF A LINEAR ELASTIC PERIDYNAMIC MATERIAL. Revista Interdisciplinar de Pesquisa em Engenharia-RIPE2(29), pp.104-114.

[172] Ahadi, A., Hansson, P. and Melin, S., 2017. Simulating Nanoindentation of Thin Cu Films Using Molecular Dynamics and Peridynamics. In Solid State Phenomena (Vol. 258, pp. 25-28). Trans Tech Publications.

[173] Vazic, B., Wang, H., Diyaroglu, C., Oterkus, S. and Oterkus, E., 2017. Dynamic propagation of a macrocrack interacting with parallel small cracks. AIMS Materials Science4(1), pp.118-136.

[174] Delorme, R., Tabiai, I., Lebel, L.L. and Lévesque, M., Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity. Mechanics of Time-Dependent Materials, pp.1-27.

[175] Lejeune, E. and Linder, C., 2017. Modeling tumor growth with peridynamics. Biomechanics and Modeling in Mechanobiology, pp.1-17.

[176] Ren, B., Wu, C.T. and Askari, E., 2017. A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis. International Journal of Impact Engineering99, pp.14-25.

[177] Panchadhara, R., Gordon, P.A. and Parks, M.L., 2017. Modeling propellant-based stimulation of a borehole with peridynamics. International Journal of Rock Mechanics and Mining Sciences93, pp.330-343.

[178] Hu, Y.L. and Madenci, E., 2017. Peridynamics for fatigue life and residual strength prediction of composite laminates. Composite Structures160, pp.169-184.

[179] Madenci, E. and Oterkus, S., 2017. Ordinary state-based peridynamics for thermoviscoelastic deformation. Engineering Fracture Mechanics.

[180] Yaghoobi, A., Chorzepa, M.G. and Kim, S.S., 2017. Mesoscale fracture analysis of multiphase cementitious composites using peridynamics. Materials10(2), p.162.

[181] Lejeune, E. and Linder, C., 2017. Quantifying the relationship between cell division angle and morphogenesis through computational modeling. Journal of Theoretical Biology418, pp.1-7.

[182] Du, Q. and Yang, J., 2017. Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications. Journal of Computational Physics332, pp.118-134.

[183] Wang, L., Xu, J. and Wang, J., 2017. Static and Dynamic Green’s Functions in Peridynamics. Journal of Elasticity126(1), pp.95-125.

[184] M. Bußler, P. Diehl, D. Pflüger, S. Frey, F. Sadlo, T. Ertl, and M. A. Schweitzer, Visualization of Fracture Progression in Peridynamics, Computer & Graphics, 67 (2017), pp. 45–57.

[185] P. Diehl, F. Franzelin, D. Pflüger, and G. C. Ganzenmüller, Bond-based peridynamics: a quantitative study of Mode I crack opening, International Journal of Fracture, 2 (2016), pp. 157–170.

[186] Diyaroglu, C., Oterkus, S., Oterkus, E. and Madenci, E., 2017. Peridynamic modeling of diffusion by using finite element analysis. IEEE Transactions on Components, Packaging and Manufacturing Technology.

[187] Diyaroglu, C., Oterkus, E. and Oterkus, S., 2017. An Euler-Bernoulli Beam Formulation in Ordinary State-Based Peridynamic Framework. Mathematics and Mechanics of Solids.

[188] Mossaiby, F., Shojaei, A., Zaccariotto, M. and Galvanetto, U., 2017. OpenCL implementation of a high performance 3D Peridynamic model on graphics accelerators. Computers & Mathematics with Applications.

[189] Zaccariotto, M., Tomasi, D. and Galvanetto, U., 2017. AN ENHANCED COUPLING OF PD GRIDS TO FE MESHES. Mechanics Research Communications.

[190] Butt, S.N., Timothy, J.J. and Meschke, G., 2017. Wave dispersion and propagation in state-based peridynamics. Computational Mechanics, pp.1-14.

[191] Yaghoobi, A. and Chorzepa, M.G., 2017. Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis. Mathematics and Mechanics of Solids, p.1081286517711495.

[192] Shojaei, A., Shojaei, A., Zaccariotto, M., Zaccariotto, M., Galvanetto, U. and Galvanetto, U., 2017. Coupling of 2D discretized Peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour. Engineering Computations34(5), pp.1334-1366.

[193] Jung, J. and Seok, J., 2017. Mixed-mode fatigue crack growth analysis using peridynamic approach. International Journal of Fatigue.

[194] Gu, X., Zhang, Q. and Xia, X., Voronoi‐based peridynamics and cracking analysis with adaptive refinement. International Journal for Numerical Methods in Engineering.

[195] Madenci, E., Dorduncu, M., Barut, A. and Futch, M., 2017. Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator. Numerical Methods for Partial Differential Equations.

[196] Van Le, Q. and Bobaru, F., 2017. Objectivity of State-Based Peridynamic Models for Elasticity. Journal of Elasticity, pp.1-17.

[197] Liu, Z. and Li, X., 2017. A Fast Finite Difference Method for a Continuous Static Linear Bond-Based Peridynamics Model of Mechanics. Journal of Scientific Computing, pp.1-15.

[198] Dayal, K., 2017. Leading-order nonlocal kinetic energy in peridynamics for consistent energetics and wave dispersion. Journal of the Mechanics and Physics of Solids105, pp.235-253.

[199] Silling, S.A., Parks, M.L., Kamm, J.R., Weckner, O. and Rassaian, M., 2017. Modeling shockwaves and impact phenomena with Eulerian peridynamics. International Journal of Impact Engineering107, pp.47-57.

[200] Naumenko, K., 2017. Florin Bobaru, John T. Foster, Philippe H. Geubelle, Stewart A. Silling, Handbook of Peridynamic Modeling. Cambridge Texts In Applied Mathematics, CRC Press, Hard Back£ 127.00, 2017, 548 p., ISBN 9781482230437. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik97(5), pp.616-616.

[201] Wang, Q., Wang, Y., Zan, Y., Lu, W., Bai, X. and Guo, J., 2017. Peridynamics simulation of the fragmentation of ice cover by blast loads of an underwater explosion. Journal of Marine Science and Technology, pp.1-15.

[202] Hafezi, M.H., Alebrahim, R. and Kundu, T., 2017. Peri-ultrasound for modeling linear and nonlinear ultrasonic response. Ultrasonics80, pp.47-57.

[203] Queiruga, A.F. and Moridis, G., 2017. Numerical experiments on the convergence properties of state-based peridynamic laws and influence functions in two-dimensional problems. Computer Methods in Applied Mechanics and Engineering322, pp.97-122.

[204] Yaghoobi, A. and Chorzepa, M.G., 2017. Higher-order approximation to suppress the zero-energy mode in non-ordinary state-based peridynamics. Computers & Structures188, pp.63-79.

[205] Silling, S.A., 2017. Stability of peridynamic correspondence material models and their particle discretizations. Computer Methods in Applied Mechanics and Engineering322, pp.42-57.

[206] Madenci, E., 2017. Peridynamic integrals for strain invariants of homogeneous deformation. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik.

[207] Zhou, W., Liu, D. and Liu, N., 2017. Analyzing dynamic fracture process in fiber-reinforced composite materials with a peridynamic model. Engineering Fracture Mechanics178, pp.60-76.

[208] Shojaei, A., Mudric, T., Zaccariotto, M. and Galvanetto, U., 2016. A coupled meshless finite point/Peridynamic method for 2D dynamic fracture analysis. International Journal of Mechanical Sciences119, pp.419-431.